The five SUVAT equations describe any motion with constant acceleration – a car braking, a ball thrown up, a train leaving a station. Each equation leaves out one variable, so three known values always determine the other two.
How to use the SUVAT Calculator
- Known values
- Displacement s
- Initial velocity u
- Final velocity v
- Acceleration a
- Time t
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose which three values you know. When a square root is needed (finding t or v from s), the positive solution is given.
Inputs explained
| Field | What to enter |
|---|---|
| Known values | Choose one: u, a, t → s, v, u, v, t → s, a, u, v, a → s, t, u, s, t → v, a … |
| Displacement s | Units: m, cm, mm, km, in, ft … |
| Initial velocity u | Units: m/s, km/h, mph, ft/s, knots, km/s |
| Final velocity v | Units: m/s, km/h, mph, ft/s, knots, km/s |
| Acceleration a | Units: m/s², ft/s², g, cm/s² |
| Time t | Units: s, ms, min, h, days |
What each result means
- Initial velocity u = [u]
- Final velocity v = [u] + [a]×[t]
- Acceleration a = [a]
- Time t = [t]
Example values
How the main result changes when Displacement s changes and everything else stays at the example values above:
| Displacement s (m) | Displacement s (m) |
|---|---|
| 25 | 25 |
| 37.5 | 25 |
| 50 | 25 |
| 62.5 | 25 |
| 75 | 25 |
| 100 | 25 |
Formula
v = u + at · s = ut + ½at² · s = (u + v)t/2 · v² = u² + 2as · s = vt − ½at²
Worked example
Inputs — Known values: u, a, t → s, v; Initial velocity u: 0 m/s; Acceleration a: 2 m/s²; Time t: 5 s.
Results — Displacement s = 25 m; Initial velocity u = 0 m/s; Final velocity v = 10 m/s; Acceleration a = 2 m/s²; Time t = 5 s.
Key terms
- Uniform acceleration
- Acceleration that does not change with time.
Frequently asked questions
What does SUVAT stand for?
Displacement (s), initial velocity (u), final velocity (v), acceleration (a), time (t).
When can I use the SUVAT equations?
Only when acceleration is constant.
Why might there be two answers for t?
The quadratic s = ut + ½at² can have two roots (e.g. passing a height going up and coming down).
Which sign should g have?
Choose a positive direction; if up is positive, g = −9.81 m/s².