Science calculators

Physics, chemistry, biology and ecology: first-principles formulas for the lab, the field and the classroom.

Physics

Mechanics, electricity, energy and waves: first-principles formulas with every constant stated.

Ohm’s lawVoltage, current, resistance and power from any two.Resistors in series & parallelCombined resistance of up to four resistors.Voltage dividerOutput voltage across the lower resistor of a pair.Electricity running costWhat an appliance costs to run over time.Force, mass & accelerationNewton’s second law, with weight under gravity.Kinetic & potential energyEnergy of a moving or raised mass.Speed, distance & timeJourney arithmetic in metric and imperial.Acceleration & stopping distanceUniform acceleration, braking distance and reaction gap.Projectile motionRange, peak height and flight time of a launched object.Density, mass & volumeAny one of the three from the other two.Pressure from force or depthPressure under a load, and water pressure at depth.Wave speed, frequency & wavelengthRelates the three properties of any wave.Work, power & efficiencyEnergy transferred, the rate of transfer and what is lost.Momentum & impulseMomentum of a mass and the force needed to change it.Ideal gas lawPressure, volume, temperature and moles of a gas.Torque & rotational powerTurning force, and the power it delivers at a given speed.VelocityAverage velocity from displacement and time, or from initial speed, acceleration and time.Watts to ampsCurrent from power and voltage, or power from current and voltage, both ways.Heat Capacity of WaterHeat energy to warm or cool a mass of water, using water's fixed specific heat, plus heating time.Evaporation RateEstimated water evaporation rate and volume lost per day from a surface, using a standard simplified formula.G-ForceConverts acceleration to g-force, or a target g-force back to acceleration, using standard gravity.Polar Moment of InertiaPolar moment of inertia and section modulus for a solid or hollow circular cross-section.Power-to-weight ratioPower divided by weight, in watts per kilogram or horsepower per tonne, for vehicles, engines or athletes.kVA to AmpsConverts electrical load between kVA and amps for single or three-phase supply, both ways.Water DensityDensity of pure water at a given temperature, from 0°C to 100°C.Dew PointDew point temperature from air temperature and relative humidity, using the Magnus formula.Normal ForceNormal force a surface exerts on an object, on a flat surface or an incline.Air DensityDensity of air from temperature, pressure and relative humidity, using the ideal gas law.Centrifugal ForceThe apparent outward force felt in a rotating reference frame, from mass, speed and radius.Hydrostatic PressureFluid pressure at depth from fluid density and depth, gauge and absolute.Angle of IncidenceAngle of reflection and total ray deflection, from the angle of incidence.Specific Gravity CalculatorRatio of a substance's density to a reference fluid (water or air), the standard sink/float and concentration check.Water ViscosityDynamic and kinematic viscosity of pure water at a given temperature, from 0°C to 100°C.Flow RateVolumetric and mass flow rate from cross-sectional area, velocity and fluid density.Wet Bulb TemperatureWet-bulb temperature from dry-bulb air temperature and relative humidity.Net ForceThe resultant of several forces acting along one line, and the acceleration it produces.Mechanical StressStress on a material from an applied force and the cross-sectional area it acts over.Inverse square lawHow intensity of light, sound, radiation or gravity falls off with distance from a source.Conservation of massSolves for a missing mass in a closed system using total mass in equals total mass out.Refractive indexRefractive index of a medium from the speed of light in that medium.AzimuthThe compass bearing from an observer to a target point, from the latitude and longitude of both.Low Pass Filter CalculatorRC low-pass filter cutoff frequency from resistance and capacitance, or solve for the resistance or capacitance needed for a target cutoff.Capacitance CalculatorCapacitance from stored charge and voltage (C = Q/V), or solves for charge or voltage, with a pF/nF/uF/F conversion table.High Pass Filter CalculatorRC high-pass filter cutoff frequency from resistance and capacitance, or solve for the resistance or capacitance needed for a target cutoff.Section Modulus CalculatorElastic section modulus of a rectangular beam cross-section, or from a known second moment of area and distance to the extreme fibre.Reaction Time CalculatorDistance travelled during a driver’s reaction time before braking begins, from speed and reaction time.Tension CalculatorTension in a rope or cable for a hanging or vertically accelerating mass, or a single cable holding a mass at an angle.Water Vapour Pressure CalculatorSaturation vapour pressure of water at a given temperature, using the Arden Buck equation.Specific Gas Constant CalculatorSpecific gas constant of any gas from its molar mass, using the universal gas constant.Charles' Law CalculatorVolume or temperature of a gas at constant pressure, using Charles' Law.Centripetal force & circular motionForce, acceleration and period of an object moving in a circle at constant speed.Hooke's law & spring energyRestoring force and stored energy of a stretched or compressed spring.Pendulum periodSwing period of a simple pendulum for small angles.Elastic & inelastic collisionFinal velocities of two colliding masses, in a straight line.Capacitor charge & energyStored charge and energy of a capacitor at a given voltage.Inductor stored energyMagnetic energy stored in an inductor carrying current.RC circuit charge & dischargeHow a capacitor charges or discharges through a resistor over time.Carnot efficiencyMaximum possible efficiency of a heat engine between two temperatures.Linear thermal expansionHow much a material lengthens or shortens with a temperature change.Heat energy & specific heatHeat needed to change the temperature of a mass of material.Snell's law of refractionAngle of refraction as light passes between two media.Thin lens equationImage distance and magnification for a lens of known focal length.Doppler effect (sound)Observed frequency of a sound source moving relative to a listener.Sound intensity level (decibels)Decibel level of a sound from its intensity, referenced to the hearing threshold.Escape velocityMinimum speed to escape a body’s gravity from a given distance, ignoring drag.Circular orbital velocitySpeed and period needed to hold a circular orbit around a mass.Kepler's third lawOrbital period of a body from its orbit size and the mass it orbits.Buoyancy (Archimedes’ principle)Upward force on an object from the fluid it displaces, and whether it floats.Terminal velocityMaximum falling speed once drag balances gravity.Angular momentum (point mass)Rotational momentum of a point mass moving on a circular path.Resistor Colour Code CalculatorDecodes the coloured bands on a resistor into its resistance value and tolerance, for 4-band or 5-band resistors.Wire Size (AWG) CalculatorRecommends a copper wire gauge from current, cable run length and an acceptable voltage drop.DiopterOptical power in diopters from focal length, or focal length from a diopter value.Free Fall CalculatorFall time, distance and impact speed for an object dropped from rest, from any one of the three.Shear StressAverage and maximum shear stress in a material from a force acting parallel to a cross-section.Kinematic Viscosity of AirDynamic and kinematic viscosity of air at a given temperature and pressure.Parallel ResistorTotal resistance of up to four resistors wired in parallel, from the reciprocal-sum formula.ElongationHow much a bar or rod stretches under an axial load, from force, length and area.Friction Loss (pipe)Head loss and pressure loss from friction as water flows through a pipe.Enthalpy of ReactionEnthalpy change of a reaction from the total enthalpy of its products and reactants.y+ (Y-Plus) wall distanceDimensionless wall distance for CFD mesh sizing, and the cell height needed for a target y+.Average velocity (out and back)Average velocity versus average speed for a there-and-back journey, from two legs of distance and speed.Earth Curvature CalculatorHow much the Earth's surface drops (curves away) over a chosen horizontal distance.Engine DisplacementTotal swept volume of an engine from bore, stroke and cylinder count, in cc, litres and cubic inches.Semitone frequency shiftFrequency after shifting a note up or down by any number of semitones.Bernoulli's equationPressure at one point in a steady, frictionless flow from conditions at another point.Reynolds numberRatio of inertial to viscous forces in a flow, and whether it is laminar or turbulent.Coulomb's lawElectrostatic force between two point charges.Electric field of a point chargeField strength and potential at a distance from a single point charge.Magnetic field of a straight wireField strength at a distance from a long straight wire, from Ampère's law.Newton's law of universal gravitationGravitational force and potential energy between two masses.Time dilationHow much slower a clock moving at speed v runs, compared to a stationary observer.Length contractionHow much shorter a fast-moving object appears along its direction of motion.Mass-energy equivalenceEnergy contained in a rest mass, from Einstein’s E = mc².Mass-spring oscillator periodPeriod, frequency and peak speed of a mass bouncing on an ideal spring.Moment of inertia of standard shapesRotational inertia of common rigid shapes, and the resulting rotational kinetic energy.RLC circuit resonant frequencyResonant frequency, Q factor and bandwidth of a series RLC circuit.Photon energyEnergy of a single photon from its wavelength or frequency.De Broglie wavelengthWavelength associated with the momentum of any moving particle.Relativistic kinetic energyKinetic energy of an object moving fast enough that Newtonian mechanics breaks down.Wien's displacement lawPeak emission wavelength of a blackbody at a given temperature.Stefan-Boltzmann lawTotal power radiated by a hot surface, from its temperature and emissivity.Mach numberSpeed of an object relative to the local speed of sound in air.Shear Strain CalculatorShear strain from a lateral displacement and original length, or from the angle of deformation.Drag Coefficient CalculatorSolves for the drag coefficient (Cd) from a measured drag force, speed, fluid density and reference area.Telescope Field of ViewTrue field of view seen through a telescope and eyepiece combination, from focal lengths and the eyepiece apparent field of view.Quarter Mile CalculatorEstimated elapsed time and trap speed over a quarter mile from a vehicle’s weight and power, using a standard drag-racing approximation.Capacitive ReactanceCapacitive reactance of a capacitor at a chosen AC frequency, the opposition a capacitor presents to alternating current.Darcy Friction Factor CalculatorDarcy friction factor for pipe flow, from pipe roughness, diameter and Reynolds number.Wh (Watt-Hours) CalculatorEnergy used in watt-hours and kilowatt-hours from power draw and running time.Wire Gauge (AWG) CalculatorConverts an American Wire Gauge size to conductor diameter and cross-sectional area.Pitch Diameter CalculatorPitch diameter of a gear from its tooth count and diametral pitch or module.Von Mises Stress CalculatorEquivalent (von Mises) stress for a 2D plane-stress state, used to predict yielding under combined loading.Newton's Law of Cooling CalculatorTemperature of an object at a given time as it cools or warms towards its surroundings.Back Vertex DistanceHow a lens power changes when the distance between the lens and the eye changes.Angular FrequencyConverts between ordinary frequency, period and angular frequency (radians per second).Voltage Drop Calculator (mm2)Voltage drop along a cable run from its cross-sectional area, length, current and conductor material.Bore and Stroke CalculatorSolves for bore or stroke from a target engine displacement, using the reverse of the displacement formula.Hydraulic Radius CalculatorHydraulic radius of a rectangular, trapezoidal or circular channel from its cross-section and flow depth.Impedance CalculatorCombined AC impedance of a resistor with a capacitor or inductor, from Z = √(R² + X²).Sun Angle CalculatorSun elevation angle above the horizon from latitude, date and local solar time.Change in VelocityDelta-v from an initial and final speed, or from acceleration and time, with direction shown.Gay-Lussac's Law CalculatorPressure or temperature of a fixed gas volume after a change, using Gay-Lussac's Law.Lift Coefficient CalculatorSolves for the lift coefficient (Cl) from a measured lift force, air density, speed and wing area, or the reverse.Resultant Force CalculatorCombines two forces given as magnitude and angle into a single resultant force, with its magnitude and direction.Impact Force CalculatorAverage impact force from mass, speed and stopping distance, using the work-energy theorem.Wing Loading CalculatorWing loading of an aircraft or model, from total weight and wing area, in both metric and imperial units.Centre of Mass CalculatorBalance point of a system of point masses from their positions and masses.Thermal Conductivity CalculatorThermal conductivity of a material from heat transferred, thickness, area, temperature difference and time.Rotational Kinetic EnergyRotational kinetic energy of a spinning object from its moment of inertia and angular velocity.kW per TonneHVAC chiller efficiency: electrical power input divided by cooling capacity in tonnes of refrigeration.LMTD CalculatorLog mean temperature difference for a heat exchanger from the temperature differences at each end.Absolute Humidity CalculatorMass of water vapour per cubic metre of air, from temperature and relative humidity.LPH CalculatorFlow rate in litres per hour, minute and second, from a volume transferred and the time it took.Dipole Antenna LengthTotal length and leg length of a half-wave dipole antenna, from the operating frequency.Shear Force CalculatorMaximum shear force for a simply supported beam under a single central point load or a uniformly distributed load.Electric Motor Torque CalculatorTorque delivered by a motor from its power rating and shaft speed in RPM.dBm to Watt CalculatorConverts RF power between dBm, milliwatts and watts, and back again.Pressure Unit ConverterConverts pressure or stress between pascals, kilopascals, megapascals, bar, atmospheres, PSI and more.Relative Humidity CalculatorRelative humidity from dry-bulb air temperature and dew point, using the Magnus approximation.Wavenumber to Wavelength CalculatorConverts between wavenumber and wavelength using the spectroscopic convention (wavenumber = 1/wavelength).Heat Capacity CalculatorHeat energy to change the temperature of any mass, from a chosen or custom specific heat capacity.Simple harmonic motionPosition, velocity and energy of a mass-spring oscillator at a given moment.Beat frequencyHow fast two close sound frequencies pulse in and out of phase.AC power & power factorReal, reactive and apparent power in an AC circuit from RMS values and phase angle.Lensmaker's equationFocal length of a lens from its surface curvatures, thickness and refractive index.Schwarzschild radiusEvent-horizon radius of a black hole of a given mass, from general relativity.Mean free path of a gasAverage distance a gas molecule travels between collisions with other molecules.Wheatstone bridgeUnknown resistance from three known resistors at the balance point.Electron drift velocityAverage speed of charge carriers moving through a current-carrying wire.Redshift & blueshiftDoppler shift of light and the recession or approach velocity it implies.Compton scatteringWavelength shift of a photon scattered off a free electron at a given angle.RMS speed of gas moleculesRoot-mean-square speed of molecules in an ideal gas from temperature and molar mass.Malus's lawLight intensity transmitted through a polarizer at an angle to the polarization axis.Aerodynamic drag forceDrag force on an object moving through a fluid, from its shape and speed.Lever & mechanical advantageEffort force needed to balance a load on a simple lever, from the arm lengths.Center of mass (two bodies)Balance point of two masses along a line, and its distance from each.Heisenberg uncertainty principleMinimum combined uncertainty in the position and momentum of a quantum particle.Capacitors in series & parallelCombined capacitance of up to four capacitors, wired in series or in parallel.Incline with frictionForces and acceleration of an object sliding down a ramp with friction.Dry Bulb TemperatureOrdinary air (dry-bulb) temperature worked back from a wet-bulb reading and relative humidity.RPM ConverterConverts rotational speed between RPM, hertz and radians per second.Pounds-Force to Newtons ConverterConverts pound-force to newtons and back, the standard unit conversion for force, not mass.Gravitational Potential EnergyGravitational potential energy of an object from its mass, height and local gravity.Acceleration Due to Gravity CalculatorSurface gravity of any body from its mass and radius, using Newton’s law of gravitation.Magnitude of Acceleration CalculatorResultant acceleration from separate x, y and z component accelerations.Elastic Modulus CalculatorYoung’s modulus of a material from applied force, cross-sectional area and the resulting stretch.SCFM Airflow CalculatorConverts actual airflow (ACFM) at your working temperature and pressure to standard airflow (SCFM), the industry comparison figure.Wind Load CalculatorEstimates wind force on a flat surface from wind speed, air density, drag coefficient and area.Pneumatic Cylinder Force CalculatorExtend and retract force of a pneumatic cylinder from bore diameter, supply pressure and optional rod diameter.Heat Index CalculatorThe "feels like" temperature from air temperature and relative humidity, using the NOAA formula.Pulley Speed CalculatorDriven pulley speed and belt speed from driver and driven pulley diameters and driver RPM.Critical Damping CalculatorCritical damping coefficient of a mass-spring-damper system from its mass and spring constant.Lightning to Thunder Distance CalculatorEstimated distance to a lightning strike from the seconds between the flash and the thunder.Duty Cycle CalculatorDuty cycle percentage of a repeating signal from its on-time and total period.Wire Resistance CalculatorResistance of a length of wire from its length, diameter and material resistivity.Hydraulic Conductivity CalculatorHydraulic conductivity K from Darcy's Law, using flow rate, flow path length, cross-sectional area and head difference.Power Physics CalculatorMechanical power from work done and time, or from force and velocity, using the standard power formula physics.Free Space Path Loss CalculatorSignal loss in decibels over a given distance and frequency in ideal, obstruction-free conditions.Slenderness Ratio CalculatorA column’s slenderness ratio from its effective length and radius of gyration, used to gauge buckling risk.Angular Speed CalculatorAngular speed in radians, degrees and RPM, from an angle turned over time, a linear speed and radius, or a rotational speed in RPM.Orifice Flow CalculatorFlow rate through a sharp-edged orifice from its diameter, discharge coefficient and head.Thermal Equilibrium CalculatorFinal common temperature reached when two substances at different temperatures exchange heat until equilibrium.Power DissipatedElectrical power dissipated as heat in a resistor, from any two of current, voltage and resistance.Ground Speed CalculatorGround speed from true airspeed and a wind component, using vector addition.Piston Speed CalculatorMean piston speed from stroke length and engine RPM, used to compare engine designs.Muzzle Energy CalculatorKinetic energy of a bullet or projectile at the muzzle, from its weight and muzzle velocity, in joules and foot-pounds.WBGT CalculatorOutdoor Wet Bulb Globe Temperature, the heat-stress index used in sport and workplace safety, from wet-bulb, globe and dry-bulb readings.Young's ModulusA material's stiffness from an applied force, cross-section area, and resulting elongation.Poiseuille's LawVolumetric flow rate of a viscous fluid through a cylindrical pipe under laminar flow.Brewster's AngleAngle of incidence where reflected light becomes fully polarized, from two refractive indices.Solenoid Magnetic FieldMagnetic field strength inside a long, tightly-wound solenoid carrying a steady current.Force Between Parallel WiresMagnetic force per unit length between two long, straight, parallel current-carrying wires.Radiation PressurePressure an electromagnetic wave, like sunlight, exerts on an absorbing or reflecting surface.Angular VelocityRotational speed from the angle turned over time, plus linear speed at a given radius.RMS Voltage & CurrentRMS, average and peak-to-peak values of a sinusoidal AC voltage or current from its peak value.Recoil CalculatorEstimated recoil velocity and recoil energy of a firearm from bullet weight, bullet velocity and firearm weight.Pixel Density CalculatorScreen pixel density (PPI) from horizontal and vertical resolution and diagonal screen size.RAM latency (CAS latency to nanoseconds)Converts a CAS Latency (CL) spec into a real first-word access time in nanoseconds.Bolt torque to clamping forceTightening torque needed for a target bolt clamp load, using the standard T = K·D·F formula.Stellar Luminosity CalculatorA star's total power output from its radius and surface temperature, using the Stefan-Boltzmann law.Spring Constant CalculatorSolves Hooke's Law for the spring constant k, given a measured force and displacement.Kpag to Kpa (Gauge to Absolute Pressure)Converts a gauge pressure reading in kPa to absolute pressure by adding atmospheric pressure.Open Channel Flow CalculatorFlow rate through an open channel from cross-sectional area, hydraulic radius, slope and Manning's roughness coefficient.Drone Flight Time CalculatorEstimated flight time for a drone from battery capacity, average current draw and a reserve margin.Principal Stress CalculatorMaximum and minimum principal stresses and maximum shear stress for a 2D stress state, using Mohr’s circle.Effective Nuclear Charge CalculatorEffective nuclear charge (Zeff) felt by an electron, using Slater's Rules from the atomic number and subshell.Torsional Stiffness CalculatorTorsional stiffness of a solid circular shaft from shear modulus, diameter and length.Lumens to Candela CalculatorConverts light output in lumens to luminous intensity in candela, or back, over a chosen beam angle.Camera Field of View CalculatorHorizontal and vertical field of view in degrees, from sensor dimensions and lens focal length.Thermal Resistance CalculatorFinds the thermal resistance (R-value) of a material layer from its thickness, area and thermal conductivity.Ideal Rocket EquationVelocity change a rocket can achieve from its exhaust velocity and the propellant mass burned.Bragg's LawDiffraction angle for X-rays reflecting off crystal lattice planes at a given spacing.Rydberg EquationWavelength of light from an electron jumping between energy levels in a hydrogen-like atom.Stokes' Law Terminal VelocityFalling speed of a small sphere through a viscous fluid once drag balances its weight.Cyclotron FrequencyOrbital frequency of a charged particle circling in a uniform magnetic field.Distance to the HorizonGeometric sight distance to the horizon from an observer height above a sphere.Angular AccelerationRate of change of angular velocity over a time interval, from spin-up or spin-down.G-Force from AccelerationHow many g's a change in velocity over time represents, relative to standard gravity.Magnetic Dipole MomentStrength of the magnetic moment produced by a current flowing around a coil loop.Thermal DiffusivityHow quickly a material equalises temperature, from conductivity, density and specific heat.Poisson's RatioHow much a material bulges sideways when stretched or squeezed lengthways.Shear ModulusStiffness of a material against sideways (shear) deformation from an applied force.Specific ImpulseHow efficiently a rocket or jet engine converts propellant into thrust.Froude NumberRatio of flow inertia to gravity in open-channel or ship-hull flow.Hall CoefficientCharge-carrier density and sign in a conductor from a measured Hall voltage.Hoop StressCircumferential and longitudinal stress in a thin-walled pressure vessel.Synodic PeriodTime between successive alignments of a body with Earth, or another chosen reference body.Skin DepthDepth below a conductor surface where AC current density falls to 1/e of its surface value.Boyle's LawPressure or volume of a fixed gas amount after an isothermal change, from the other values.Photoelectric EffectKinetic energy and stopping voltage of electrons ejected from a metal by light.Blackbody RadiationSpectral radiance a hot object emits at one wavelength, from Planck's law.Hubble's LawRecession speed of a distant galaxy from its distance and the Hubble constant.Black Hole TemperatureHawking temperature and evaporation timescale of a black hole from its mass.Drake EquationOrder-of-magnitude estimate of communicating civilisations in the galaxy from seven factors.Hydrogen-Like AtomElectron energy level and orbital radius in a one-electron atom or ion, from the Bohr model.Diffraction GratingAngle at which a given order of light diffracts off a grating of known line spacing.Friction ForceFriction force resisting motion on a flat or inclined surface, from mass and coefficient.Angle Of ReposeSteepest stable slope angle for a granular pile from its static friction coefficient.Coriolis EffectCoriolis acceleration and force on a moving mass from its speed and latitude on Earth.Gear RatioOutput speed and torque of a gear pair from the tooth counts and the input speed.Latent HeatHeat energy absorbed or released during a phase change from mass and the specific latent heat.Weight On Other PlanetsHow much a mass would weigh on the Moon or another planet, from each body’s surface gravity.Speed of light travel timeHow long light takes to cross a distance, or how far it travels in a given time.Speed of sound in airSpeed of sound in air from temperature, plus how far it travels in a given time.Acceleration from initial and final speedUniform acceleration from a starting speed, an ending speed and the time taken.

Chemistry

Concentrations, pH, dilutions and reaction yields: the maths behind the lab bench.

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Electronegativity CalculatorPauling-scale electronegativity of an element, or the difference between two elements to judge bond polarity.Molarity from massConcentration of a solution made from a known mass of solute.Solution dilution (C₁V₁ = C₂V₂)Stock volume and diluent needed to hit a target concentration.pH from hydrogen ion concentrationConversion between [H⁺] and pH, with pOH and [OH⁻] at 25 °C.Henderson–Hasselbalch (buffer pH)Buffer pH from the acid dissociation constant and the base/acid ratio.Percent yieldHow much product a reaction actually gave versus the theoretical maximum.Mass percent concentrationSolute mass as a percentage of total solution mass, plus ppm.Radioactive decay & half-lifeAmount of a substance remaining after a given elapsed time.Beer–Lambert law (absorbance)Absorbance and transmittance of a solution from its concentration.Osmotic pressure (van’t Hoff)Pressure needed to stop osmosis across a semipermeable membrane.Solubility Rules CalculatorPredicts whether an ionic compound is soluble in water, using the standard solubility rules.Mole CalculatorConverts between mass and moles of a substance using its molar mass.Types of Chemical Reactions ClassifierIdentifies the standard reaction type from the number of reactants and products.Ionic CalculatorThe correct chemical formula of an ionic compound from a chosen cation and anion, by balancing charges.Mole Ratio CalculatorMole ratio between two substances in a balanced reaction, from their equation coefficients or from given mole amounts.Net Ionic Equation CalculatorBalances a double-displacement reaction between two soluble ionic compounds and removes the spectator ions.Theoretical Yield CalculatorMaximum mass of product obtainable from a limiting reagent, using molar masses and the balanced equation ratio.Entropy of ReactionEntropy change of a reaction from the total entropy of its products and reactants.Water Boiling Point (Altitude)How the boiling point of water falls as elevation rises, from the drop in atmospheric pressure.Electron Configuration CalculatorFull electron configuration for any element from atomic number 1 to 56, following the Aufbau principle.Molality of a solutionMoles of solute per kilogram of solvent, a concentration measure independent of temperature.Acid-base titration (equivalence point)Unknown acid or base concentration from the titrant volume at the equivalence point.Freezing point depressionHow much a solvent’s freezing point drops when a solute is dissolved in it (a colligative property).Boiling point elevationHow much a solvent’s boiling point rises when a solute is dissolved in it (a colligative property).Buffer capacity (Van Slyke equation)How resistant a buffer solution is to pH change, from its total concentration and pKa.Arrhenius equationReaction rate constant at a given temperature from activation energy and pre-exponential factor.Mole fraction of a mixtureFraction of the total moles in a mixture contributed by each component.Water hardness (as CaCO₃)Total water hardness as calcium carbonate equivalent, from calcium and magnesium ions.Serial dilution seriesFinal concentration after a series of equal-factor dilutions, and the concentration at each step.Raoult’s law (vapor pressure of a solution)Vapor pressure of an ideal solution containing a non-volatile solute.Mol/L to mg/L CalculatorConverts molar concentration (mol/L) to mass concentration (mg/L) and back, using the molar mass of the substance.Weak acid/base pH from Ka or KbpH of a weak acid or base solution from its dissociation constant and starting concentration.Activation energy from two rate constantsActivation energy from rate constants at two temperatures (two-point Arrhenius equation).Kp ↔ Kc equilibrium constant conversionConvert between pressure-based and concentration-based equilibrium constants for a reaction.Degree of unsaturation (DBE)Number of rings and pi bonds in a molecule from its molecular formula.Empirical formula from mass percentSimplest whole-number atom ratio of a compound from percent composition and atomic masses.Ionic strength of a solutionIonic strength from the concentration and charge of every ion present in a solution.Graham's law of effusion/diffusionRelative rate at which two gases effuse or diffuse, from their molar masses.Radioactive activity (Bq / Ci)Decay rate of a radioactive sample from its amount and half-life, in becquerels and curies.Rate constant from concentration vs. timeReaction rate constant k from concentration data, for zero, first or second order kinetics.Atom economyShare of reactant mass that ends up in the desired product versus all products formed.Average atomic mass from isotopesWeighted average atomic mass of an element from its isotope masses and natural abundances.Nernst equation (cell potential)Cell potential under non-standard conditions from the standard potential and reaction quotient.Molecular Weight CalculatorMolecular weight of a chemical formula, summing standard atomic weights for each element present.Nernst Equation CalculatorCell potential under non-standard conditions from standard potential, temperature, electrons transferred and the reaction quotient.Gibbs free energyReaction spontaneity from the change in enthalpy, entropy and temperature.Partial pressure (Dalton's law)Partial pressure of each gas in a mixture from its moles, volume and temperature.Bond order (MO theory)Bond order and bond stability of a molecule from its bonding and antibonding electron counts.Diffusion coefficient (Stokes-Einstein)Diffusion rate of a spherical particle in a fluid, from its size, viscosity and temperature.Young-Laplace pressure (capillary)Pressure difference across a curved liquid interface, from surface tension and curvature.Isoelectric point (pI)pH at which a molecule such as an amino acid carries no net electric charge.Grams to molesConverts a mass in grams to an amount in moles using the substance’s molar mass.Molar mass of a gasFinds a gas’s molar mass from its mass, pressure, volume and temperature (ideal gas law).Normality of a solutionConverts molarity to normality using the number of equivalents per mole.pKa from KaCalculates pKa from the acid dissociation constant Ka using pKa = -log10(Ka).Alligation mixing ratioFinds the ratio and volumes of two concentrations that mix to a target concentration.Crude protein from nitrogenEstimates crude protein percentage from measured nitrogen content and a conversion factor.PPM to molarityConverts a concentration in ppm (mg/L) to molarity using the solute molar mass.Reaction quotient (Q)Calculates the reaction quotient Q for aA + bB ⇌ cC + dD from current concentrations.Combustion analysisFinds the empirical formula of a CHO compound from the CO2 and H2O produced by combustion.Saponification valueDetermines a fat or oil’s saponification value from a KOH back-titration with HCl.Moles to atomsConverts an amount in moles to a number of atoms or particles using Avogadro’s number.Vapor pressure (Clausius–Clapeyron)Finds vapor pressure at a new temperature from a known point and enthalpy of vaporization.Avogadro's number (particles from moles)Number of particles and sample mass from an amount in moles.Atom composition (protons, neutrons, electrons)Subatomic particle counts from atomic number, mass number and charge.Percent ionic characterIonic character of a bond estimated from the electronegativity difference.Lattice energy (Kapustinskii equation)Ionic crystal lattice energy from ion charges, radii and formula-unit count.Cubic unit cell (packing efficiency)Edge length, atoms per cell and packing efficiency for SC, BCC and FCC lattices.Miller indices from axial interceptsMiller indices (hkl) of a crystal plane, plus interplanar spacing for a cubic lattice.Effective nuclear charge (Slater's rules)Net nuclear charge felt by an electron after shielding, using Slater's rules.Combustion reaction balancerBalanced coefficients for complete combustion of a CxHyOz compound in oxygen.Stoichiometric air-fuel ratioTheoretical air-to-fuel mass ratio for complete combustion of a CxHy hydrocarbon.STP conversionCorrects a measured gas volume to STP and finds the equivalent moles.Enzyme activity from absorbanceEnzyme activity in units (µmol substrate/min) from an absorbance-vs-time assay.Chemical oxygen demand (COD)COD of a water or wastewater sample from a ferrous ammonium sulfate (FAS) back-titration.Activity coefficient (Debye-Hückel)Ionic activity coefficient of a dissolved ion from its charge and the solution ionic strength.Gibbs' phase ruleDegrees of freedom of a chemical system from its number of components and coexisting phases.Bleach dilution to target strengthBleach and water needed to dilute a stock solution down to a target free-chlorine strength.Percent solution (% w/v)Weight-per-volume percent concentration of a solution from the mass of solute dissolved.Radiocarbon (carbon-14) datingEstimated age of an organic sample from the fraction of carbon-14 remaining.Rate constant from a rate lawReaction rate constant k from a single measured rate and reactant concentrations.Electrolysis mass deposited (Faraday's law)Mass of an element deposited or liberated during electrolysis, from current and time.Resuspension volume/concentrationBuffer volume to resuspend a dried sample to a target concentration, or vice versa.

Biology

Population genetics, enzyme kinetics, growth curves and lab concentration formulas.

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Hardy–Weinberg equilibriumExpected genotype frequencies in a non-evolving population from allele frequency.DNA/RNA concentration from A₂₆₀Nucleic acid concentration from a spectrophotometer absorbance reading.Log reduction (microbial kill)How many orders of magnitude a treatment reduces a microbial count.Michaelis–Menten kineticsEnzyme reaction rate at a given substrate concentration.Bacterial/cell growth (doubling time)Population size after exponential growth at a fixed doubling time.Q₁₀ temperature coefficientHow much a biological or chemical rate changes per 10 °C rise.Plant water potentialTotal water potential from solute and pressure potential in a plant cell.Can Cats Eat ChocolateTheobromine dose from chocolate eaten, checked against published toxicity thresholds for cats.Onion Toxicity in Dogs CalculatorEstimated onion dose per kg of body weight, checked against published toxicity thresholds.Adult dog weight predictorRough adult weight estimate for a medium or large breed puppy, from its weight at 14-16 weeks.Cattle per Acre CalculatorEstimated stocking density: cattle a given acreage can support, or acres needed per head, from your own assumption.Allele frequency from genotype countsDirect-count allele frequencies for a two-allele gene from observed genotype numbers in a sample.Multi-gene cross probabilityProbability of a given number of recessive traits among offspring of a multi-gene cross.DNA copy number from concentrationDNA or RNA molecules per microlitre from concentration and fragment length.PCR primer melting temperature (Tm)Estimated primer melting temperature from base composition (Wallace/Marmur-Doty).qPCR amplification efficiencyPCR amplification efficiency from the slope of a standard curve (log₁₀ starting quantity vs. Ct).Vapor pressure deficit (VPD)Gap between saturation and actual vapor pressure, the driving force for plant transpiration.Monohybrid Punnett Square CalculatorGenotype and phenotype ratios from a single-gene cross, the classic monohybrid Punnett square.Dog Body Condition CalculatorEstimate a dog's body condition score from rib, waist and abdomen checks, a standard vet screening guide.Daily light integral (DLI)Total photosynthetic light a plant receives per day, from light intensity and photoperiod.Mutation frequencyFraction of a tested population carrying a mutation, reported per cell or organism tested.Growing degree units (GDU)Accumulated heat units driving crop development, from daily high/low temperature and a base.Ligation molar ratio (insert:vector)Insert mass needed for a target insert-to-vector molar ratio in a DNA cloning ligation.Cricket chirp thermometerEstimate air temperature from a cricket’s chirp rate using Dolbear’s law.PCR annealing temperature (Ta)Optimal PCR annealing temperature from primer and product melting temperatures.Feed conversion ratio (FCR)Efficiency of converting feed into body weight gain for livestock or aquaculture.Corn yield estimatorEstimated corn yield in bushels per acre using the ear-count yield component method.Acres per hourField work rate from implement width and travel speed, accounting for overlap.Dry matter basis conversionConverts an as-fed nutrient percentage to a dry-matter basis using moisture content.DNA to mRNA transcriptionmRNA transcript from a DNA template strand using base-pairing rules.Tree height (clinometer method)Tree height from the angle to its top and your distance from it.Tree diameter at breast height (DBH)Trunk diameter and cross-sectional area from a measured circumference.Grain bin storage capacityBushel capacity of a cylindrical grain bin from its dimensions.Fertilizer application rateProduct needed to hit a target nutrient rate given the label percentage.Dihybrid cross ratiosGenotype and phenotype ratios from a cross of two heterozygous two-gene parents.Swine gestation (farrowing date)Expected farrowing date from the breeding date, using the average 114-day sow gestation.Water-soluble fertilizer dosingFertilizer weight needed to reach a target nutrient concentration in a given volume of water.

Ecology

Population and diversity formulas for the field: carrying capacity, species diversity and predator-prey dynamics.

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Logistic population growthPopulation size over time under a fixed carrying capacity (Verhulst model).Shannon diversity indexBiodiversity of a community from species counts.Lotka–Volterra predator–prey ratesInstantaneous population growth rates for a classic predator–prey pair.Kaya identity (CO₂ emissions)Global CO₂ emissions decomposed into population, wealth, energy and carbon factors.Tree basal areaCross-sectional trunk area at breast height (DBH), the standard forestry measure of stand density.Animal mortality ratePercentage of a population lost to death over a period, accounting for births during that period.Wind turbine power outputElectrical power generated by a wind turbine from rotor size, wind speed and efficiency.Hydroelectric power outputPower generated by a dam turbine from head, flow rate and efficiency.

Renewable Energy

Sizing maths for solar, battery storage and off-grid systems: panels, tilt angle and payback period.

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Solar System SizingSolar array size and panel count needed for a target daily usage, with optional battery sizing.Solar Payback PeriodYears to recoup a solar system's net cost from its annual electricity bill savings.Off-Grid Battery SizingBattery capacity needed to cover a daily energy load for a chosen number of autonomy days.Solar Panel Tilt AngleRule-of-thumb fixed tilt angle from latitude, for year-round, winter or summer weighting.Solar Energy YieldEstimated annual output from a solar array, from its size, sun hours and system efficiency.Battery RuntimeHow long a battery powers a continuous load, from capacity, depth of discharge and wattage.