What this calculator does
The SUVAT equations describe motion under constant acceleration, and take their name from the five quantities involved: s (displacement), u (initial velocity), v (final velocity), a (acceleration) and t (time). Given any three of the five, the other two can always be found, without needing calculus.
This calculator covers all ten possible combinations of three known quantities. Pick the two you want to solve for, enter the other three, and it works out which of the standard SUVAT equations applies and runs it, showing the values you supplied alongside the ones it calculated.
The formula
There are four SUVAT equations: v = u + at, s = ut + ½at², v² = u² + 2as, and s = ((u+v)/2)t. Depending on which three quantities are known, a different pair of these equations (or a rearrangement of one) is needed to isolate the remaining two. The calculator picks the right combination automatically based on which two fields you chose to solve for.
| Term | Meaning |
|---|---|
| s | Displacement: the straight-line change in position, in metres. |
| u | Initial velocity, in metres per second. |
| v | Final velocity, in metres per second. |
| a | Acceleration, assumed constant, in metres per second squared. |
| t | Time elapsed, in seconds. |
The inputs explained
| Field | What to enter |
|---|---|
| First unknown to solve for | The first of the two quantities you want the calculator to work out. |
| Second unknown to solve for | The second quantity to solve for. It must be different from the first. |
| s, displacement (m) | Displacement, used only when it is one of the three known values. |
| u, initial velocity (m/s) | Initial velocity, used only when it is one of the three known values. |
| v, final velocity (m/s) | Final velocity, used only when it is one of the three known values. |
| a, acceleration (m/s²) | Acceleration, used only when it is one of the three known values. |
| t, time (s) | Time, used only when it is one of the three known values. |
When to use it
A-level or GCSE mechanics problems
SUVAT questions typically give three of the five quantities and ask for one or two others; this handles any of the ten combinations without needing to look up or rearrange the right equation by hand each time.
Checking a braking or launch calculation
Given a starting speed, a constant deceleration and the time to stop, or given a distance and the speed at each end, the same five variables and equations apply whether the context is a vehicle, a lift shaft or a dropped object.
Verifying working from a textbook example
Plugging the same three known values in and comparing the two results against a worked solution is a quick way to check whether an equation was rearranged correctly by hand.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Solving for acceleration and time, from displacement and both velocities
A fixed initial velocity and displacement, across a range of final velocities.
| Final velocity (v) | Acceleration (a) | Time (t) |
|---|---|---|
| 10 m/s | 0.5000 m/s² | 20.000 s |
| 15 m/s | 1.125 m/s² | 13.333 s |
| 20 m/s | 2.000 m/s² | 10.000 s |
| 25 m/s | 3.125 m/s² | 8.000 s |
| 30 m/s | 4.500 m/s² | 6.667 s |
| 40 m/s | 8.000 m/s² | 5.000 s |
Solving for displacement and time, from both velocities and acceleration
A fixed pair of velocities, across a range of accelerations.
| Acceleration (a) | Displacement (s) | Time (t) |
|---|---|---|
| 1 m/s² | 200.000 m | 20.000 s |
| 2 m/s² | 100.000 m | 10.000 s |
| 4 m/s² | 50.000 m | 5.000 s |
| 5 m/s² | 40.000 m | 4.000 s |
| 8 m/s² | 25.000 m | 2.500 s |
| 10 m/s² | 20.000 m | 2.000 s |
Questions
What are the SUVAT equations?
Four equations linking displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t) under constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as, and s = ((u+v)/2)t.
Why do I only need three known values?
The five SUVAT quantities are related by these equations, so fixing any three of them mathematically determines the other two, provided the three chosen actually describe a consistent motion.
Can every combination of three knowns be solved?
Almost always, but a few edge cases have no unique answer, such as knowing only u, v and a when a is zero and u does not equal v, which describes an impossible motion, or the same case with u equal to v, which leaves s and t undetermined.
Do the SUVAT equations only work for objects moving in a straight line?
Yes, they apply to one-dimensional motion under constant acceleration. Directions are handled through the sign of velocity and acceleration (positive one way, negative the other), rather than through separate equations.
For a simpler starting-and-ending-speed acceleration figure without the full five-variable solver, see the acceleration calculator. For everyday speed, distance and time problems, see the speed, distance and time calculator.