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Calculators/Science/Physics

Physics calculators

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.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.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.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.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.

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