🏃 Kinematics Calculator

SUVAT equations: Enter any 3 variables and find the other 2.

Leave exactly 2 fields empty to solve for them.

u — Initial velocity (m/s)

v — Final velocity (m/s)

a — Acceleration (m/s²)

t — Time (s)

s — Displacement (m)

How to Use This Calculator

This tool solves the five SUVAT equations simultaneously. You give it any three of the five kinematic variables, and it finds the other two. The variables are: u (initial velocity), v (final velocity), a (acceleration), t (time), and s (displacement). All motion must be under constant acceleration for the equations to apply.

Identify the three variables you already know from the problem. For example, a car starts at rest (u = 0), accelerates at 3 m/s², and you want to know speed after 5 seconds.

Enter those three values in their labelled fields. Leave the other two fields blank — those are the unknowns the calculator will solve for.

Click Calculate (or the result updates automatically as you type). Both missing values appear with their units.

Check the sign conventions: positive direction is whatever you define as forward. Upward throws need a = -9.81 m/s² if positive is upward.

The Five SUVAT Equations

v = u + at s = ut + ½at² v² = u² + 2as s = ½(u + v)t s = vt - ½at² u = initial velocity (m/s), v = final velocity (m/s) a = acceleration (m/s²), t = time (s), s = displacement (m)

Each equation connects four of the five variables, leaving one out. That is why knowing three variables is always enough to solve for the remaining two. Pick the equation that has your three knowns and one unknown, then rearrange.

Worked Examples

Ball thrown up at 20 m/s (max height)u=20, v=0, a=-9.81 → s = 20.39 m

Car at rest, a=3 m/s², t=5 s (final speed)u=0, a=3, t=5 → v = 15 m/s

Braking from 30 m/s to 0, over 45 mu=30, v=0, s=45 → a = -10 m/s²

Object falls from rest for 3 secondsu=0, a=9.81, t=3 → s = 44.15 m

Where This Comes Up in Real Life

Kinematics is the starting point for almost every mechanics problem you will meet. When a driver brakes hard to avoid a collision, you can work backward: if the car travels 40 m before stopping from 80 km/h (22.2 m/s), the deceleration is about 6.1 m/s². That number tells engineers how much grip the tyres need. Crash investigators use the same approach to reconstruct how fast a vehicle was moving before impact.

In sport, kinematics describes a sprinter leaving the blocks: a typical acceleration of 5 m/s² for the first 2 seconds brings the athlete to 10 m/s before they shift to a top-speed phase. Coaches use these numbers to compare reaction time and drive phase between athletes. Space missions use the same equations at a larger scale, calculating burn times and velocity changes for orbital manoeuvres.

Frequently Asked Questions

What are the SUVAT equations?

v=u+at, s=ut+½at², v²=u²+2as, s=½(u+v)t, s=vt-½at². These 5 equations describe motion under constant acceleration.

Do I need all 5 variables?

No — you only need 3 known values to find the other 2. Enter any 3 and this calculator finds the rest.

What are typical values for g?

On Earth g=9.81 m/s² (downward). Use a=-9.81 for upward throw problems (deceleration going up).

What does negative velocity mean?

Negative velocity means motion in the opposite direction to positive (your defined reference direction).

Example: Ball thrown up at 20 m/s — max height?

u=20, v=0, a=-9.81. v²=u²+2as → 0=400+2(-9.81)s → s=20.39 m.