Kinematics Calculator

How to use this calculator

Constant-acceleration motion is described by five quantities — initial velocity u, final velocity v, acceleration a, time t and displacement s — and any three of them fix the other two. Type the three you know; the calculator picks whichever SUVAT equation contains exactly one unknown and solves it, then repeats until everything is filled in.

Use a negative acceleration for braking. For a car stopping from 25 m/s in 40 m, enter u = 25 m/s, v = 0 and s = 40 m: the deceleration (−7.8 m/s²) and stopping time (3.2 s) appear. When time is solved from a quadratic, the calculator returns the first moment the displacement is reached.

The formula

v = u + at

s = ut + ½at²

s = ½(u + v)t

v² = u² + 2as

s = vt − ½at²

u: initial velocity
v: final velocity
a: acceleration
t: time
s: displacement

Worked example

A cyclist rolling at 3 m/s accelerates uniformly at 2 m/s² for 5 seconds. How fast are they going, and how far do they travel?

v = u + at = 3 + 2 × 5 = 13 m/s.
s = ut + ½at² = 3 × 5 + ½ × 2 × 5² = 15 + 25 = 40 m.
Check: s = (u + v)/2 × t = (3 + 13)/2 × 5 = 40 m.

After 5 s the cyclist is moving at 13 m/s (about 29 mph) and has covered 40 m.

Which equation is missing which variable?

Equation	Does not contain
v = u + at	s
s = ut + ½at²	v
s = ½(u + v)t	a
v² = u² + 2as	t
s = vt − ½at²	u

Solving by hand, pick the equation that leaves out the quantity you neither know nor need. The calculator does the same thing automatically.

Assumptions and limits

Acceleration is constant over the whole interval. For varying acceleration, split the motion into stages.
Motion is along a straight line in one direction, so speeds and displacement are entered as non-negative values. Use the projectile calculator for two-dimensional motion.

Frequently asked questions

What does SUVAT stand for?

The five symbols in the equations: s (displacement), u (initial velocity), v (final velocity), a (acceleration) and t (time).

How do I calculate stopping distance?

Enter the initial speed, a final velocity of 0 and the braking deceleration as a negative acceleration. The displacement is the braking distance; add reaction distance (speed × reaction time) for the total stopping distance.

Can I use this for free fall?

Yes — set a = 9.80665 m/s² (or 32.17 ft/s²) and u = 0 for an object dropped from rest. The dedicated free fall calculator does this with fewer fields.

Kinematics Calculator (SUVAT)