Kinematics Calculator

Enter any three of displacement, initial velocity, final velocity, acceleration and time. The solver picks the right SUVAT equation and finds the other two.

m
m/s
m/s
m/s²
s
Use SI units. Convert with the unit converter.
s
Displacement
44.145m
v
Final velocity
29.43m/s

Equations used: v = u + at, s = ut + ½at²

Area under a velocity–time graph is displacement

Every SUVAT equation is a fact about this graph. The slope is acceleration; the shaded area is how far you went. Drag the sliders.

t (s)v (m/s)v = 16.0

Rectangle (dashed) = u·t = 24 m. Triangle = ½·t·(v − u) = ½·a·t² = 36 m. Total s = ut + ½at² = 60 m.

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Which equation leaves out which variable

EquationMissing
v = u + ats
s = ut + ½at²v
s = vt − ½at²u
v² = u² + 2ast
s = ½(u + v)ta

Worked example

A car travelling at 25 m/s brakes to a stop in 40 m. What is its deceleration and how long does it take? Knowns: u = 25, v = 0, s = 40. No t, so v² = u² + 2as: 0 = 625 + 80a, a = −7.8 m/s². Then t = (v − u) ÷ a = 3.2 s. Type those three values above to check.

Frequently asked questions

What are the four kinematic equations?
For constant acceleration: v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t. A fifth, s = vt − ½at², is sometimes listed. Each leaves out one of the five variables s, u, v, a, t.
How do I choose which kinematic equation to use?
List the three values you know and the one you want. Pick the equation that contains those four and leaves out the fifth. No time given and not asked for? Use v² = u² + 2as.
What does SUVAT stand for?
The five variables: s (displacement), u (initial velocity), v (final velocity), a (acceleration), t (time). The name is common in UK and Commonwealth courses; US textbooks write Δx, v₀, v, a, t.
Why does the calculator show two answers?
When the unknowns come from v² = u² + 2as, the square root has a + and − value. A ball thrown upward passes the same height twice, going up and coming down; both are real. Choose the one that fits the situation.
Do these equations work if acceleration changes?
No. They assume constant acceleration. For changing acceleration use calculus (v = ∫a dt) or break the motion into stages that each have constant acceleration.
How do I handle direction?
Choose one direction as positive and stick to it. For a ball thrown up with up positive, u is positive and a = −9.81 m/s². Displacement and velocity can then come out negative, meaning below or downward.