Physics · kinematics

SUVAT Calculator

Any three of s, u, v, a and t give you the other two — with the working shown.
constant acceleration
enter three values

What you know

0 of 3
Signs matter: pick a positive direction and stay with it.
Reference

The five equations, and what each one leaves out

Each equation is missing exactly one of the five quantities. That is the whole trick: look at which one you were not given and do not need, and the equation that omits it is the one to use. The row highlighted above is the one this solve used.
The motion

Displacement, velocity and acceleration against time

Velocity is a straight line because the acceleration is constant — that is the single assumption behind all five equations. Displacement is the area under the velocity line, which is why it curves, and why a negative area subtracts: displacement is where you ended up, not how far you travelled.
Examples

Worked problems — press one to load it

Field notes

Where these equations stop working

How it works

Three knowns, five unknowns, one assumption

SUVAT is five equations relating five quantities: displacement s, initial velocity u, final velocity v, acceleration a and time t. Each equation leaves one of them out, so with any three known you can always reach the other two — usually by picking the equation that omits the quantity you neither have nor want. All of it rests on a single assumption: the acceleration does not change over the interval. Everything else follows from that.

Worked example

A car brakes from 30 m/s to a stop in 45 m. You know s, u and v and want a, so use the equation without t: v² = u² + 2as gives a = (0 − 30²) ⁄ (2 × 45) = −10 m/s², almost exactly 1 g. Double the entry speed to 60 m/s and the distance becomes 180 m — four times as far, because the speed is squared.

Why do I sometimes get two answers?

Because there genuinely are two. Throw a ball upward at 20 m/s and ask when it is 15 m high: it passes that height at 0.99 s on the way up and again at 3.09 s on the way down, moving at the same speed in opposite directions. Solving for time uses a quadratic, and solving for a velocity takes a square root — both have two roots, and both roots are real motions. A calculator that silently returns one of them has picked for you without saying so.

What does a negative displacement mean?

That you finished on the negative side of where you started. s is displacement, not distance travelled. A ball thrown up that lands back in your hand has s = 0 even though it has covered several metres — and if it lands in a well below you, s is negative.

Should acceleration be positive or negative?

Whatever your chosen positive direction says. Pick one — up, or forwards — and every quantity takes its sign from that choice. If up is positive then gravity is a = −9.81 m/s², a ball thrown up starts with positive u, and braking gives a negative a while the car still moves forwards. Mixing conventions halfway through is the single most common way these problems go wrong.

Why does my answer disagree with reality?

Almost always air resistance, which SUVAT does not contain. A dropped feather, a long fall, a cyclist coasting — all of them have a force that grows with speed, so the acceleration is not constant and no SUVAT equation applies. The rule of thumb is that it holds well for dense objects over short falls, and starts to mislead beyond a few seconds of free fall. For a fall with real drag, see the Galileo drop simulator.

Constant acceleration only. These five equations assume the acceleration never changes over the interval. That is a good description of free fall over short distances, steady braking and a launch roll — and a poor one for anything with meaningful air resistance, a changing thrust, or a spring. For those, the acceleration is a function of time or position and you need calculus, not SUVAT.
Version history · unchanged

No changes to this tool’s own behaviour since the earliest archived release (v1.98). The full history for the site is in the changelog.