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SUVAT calculator

Enter any three of s, u, v, a and t and this SUVAT calculator finds the other two. It shows which equations it used, both answers when there are two, and the displacement, velocity and acceleration graphs.

Units: metres, seconds, m/s and m/s². Free to use, with no sign-up, no adverts and no personal tracking. A learning and checking tool: check the signs and your exam board’s value of g.

Start from an example

Fill in any three boxes and leave the other two empty. Pick a direction as positive and keep to it: a value in the opposite direction is negative.

Displacement s (m)Initial velocity u (m/s)Final velocity v (m/s)Acceleration a (m/s²)Time t (s)

Gravity g Significant figures

Result

66.0 mDisplacement s (found)5.00 m/sInitial velocity u (given)17.0 m/sFinal velocity v (found)2.00 m/s²Acceleration a (given)6.00 sTime t (given)

The gradient of the velocity graph is the acceleration, and the area under it is the displacement. The acceleration is constant, so the velocity graph is a straight line and the displacement graph is a parabola.

Working

Known values
Initial velocity u = 5 m/s
Acceleration a = 2 m/s²
Time t = 6 s
Unknown: s and v.
Find the final velocity
Use v = u + at.
v = u + at = 5 + 2 × 6 = 17.0 m/s
Find the displacement
Use s = ut + ½at².
s = ut + ½at² = 5 × 6 + ½ × 2 × 6² = 66.0 m

Practise SUVAT questions

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

How the suvat calculator works

SUVAT stands for the five quantities used for motion with constant acceleration: displacement s, initial velocity u, final velocity v, acceleration a and time t. To solve a problem:

Write down the three quantities you know, with signs.
Name the quantity you want.
Choose the equation that contains those four and leaves out the fifth.
Substitute, solve and check the sign and size of the answer.

Equation	Leaves out	Use it when
v = u + at	s	you have no displacement
s = ut + ½at²	v	you have no final velocity
v² = u² + 2as	t	you have no time
s = ½(u + v)t	a	you have no acceleration
s = vt − ½at²	u	you have no initial velocity

Sign convention

You choose the positive direction. For a ball thrown upward, take up as positive so that a = −9.81 m/s². For a dropped stone, take down as positive so that a = +9.81 m/s². A quantity in the opposite direction is negative.

Worked example

A car travelling at 25 m/s brakes with a constant deceleration of 5 m/s² until it stops. Take the direction of travel as positive. Find the braking time and the stopping distance.

Known values
Initial velocity u = 25 m/s
Final velocity v = 0 m/s
Acceleration a = −5 m/s²
Unknown: s and t.
Find the time
Use v = u + at.
t = (v − u) / a = (0 − 25) / (−5) = 5.00 s
Find the displacement
Use v² = u² + 2as.
s = (v² − u²) / 2a = (0² − 25²) / (2 × (−5)) = 62.5 m

The unknown quantities are s = 62.5 m and t = 5 s.

Stopping distances at a deceleration of 5 m/s²

These come from the calculator with u, v = 0 and a = −5 m/s². Doubling the speed multiplies the stopping distance by four, because s = u² / 2a.

Starting speed	Time to stop	Stopping distance
10 m/s (36 km/h)	2 s	10 m
15 m/s (54 km/h)	3 s	22.5 m
20 m/s (72 km/h)	4 s	40 m
25 m/s (90 km/h)	5 s	62.5 m
30 m/s (108 km/h)	6 s	90 m

Which formulas does this use?

Constant-acceleration displacement, Mean acceleration, Braking distance, Total stopping distance with reaction time, Gravitational field and orbit.

Related calculators

Equations of motion calculator, Free fall calculator, Projectile motion calculator, and the A-level physics equation calculator for the rest of the A-level equations.

Common questions

What does SUVAT stand for?

S is displacement, u is initial velocity, v is final velocity, a is acceleration and t is time. The SUVAT equations link these five quantities when the acceleration is constant. If you know three of them you can find the other two.

How do I choose which SUVAT equation to use?

List the five quantities, write down the three you know and the one you want. Pick the equation that contains those four and leaves out the fifth. For example, if time is not given and not wanted, use v² = u² + 2as.

Why does the calculator sometimes give two answers?

When you give s, u and a, the equation for time is a quadratic, so there can be two real times. A ball thrown upward passes a given height once on the way up and again on the way down. The calculator shows both and rejects any negative time.

What do the signs mean?

Choose a positive direction and keep to it. A velocity, displacement or acceleration in the opposite direction is negative. A car that brakes while moving forward has a negative acceleration, and a ball thrown upward with up positive has a = −9.81 m/s².

Is the calculator free, and does it keep my numbers?

It is free to use, with no sign-up, no adverts and no personal tracking. The numbers you type stay in your browser.

What do I assume about air resistance and g?

Air resistance is ignored, so these are the idealised answers used in GCSE, A-level and first-year university mechanics. Use g = 9.81 m/s² unless your exam board says 9.8 or 10. You can change g to compare other values or other worlds.