# SUVAT Calculator

URL: https://speedycalculator.com/calculators/physics/suvat/
Last updated: 2026-10-30

> The SUVAT calculator solves the equations of uniformly accelerated motion: from any three of displacement s, initial velocity u, final velocity v, acceleration a and time t, it finds the other two.

## Inputs

- Known values
- Displacement s (m, cm, mm, km, in, ft, yd, mi)
- Initial velocity u (m/s, km/h, mph, ft/s, knots, km/s)
- Final velocity v (m/s, km/h, mph, ft/s, knots, km/s)
- Acceleration a (m/s², ft/s², g, cm/s²)
- Time t (s, ms, min, h, days)

## Results

- Displacement s
- Initial velocity u
- Final velocity v
- Acceleration a
- Time t

## Formula

```
v = u + at · s = ut + ½at² · s = (u + v)t/2 · v² = u² + 2as · s = vt − ½at²
```

## Explanation

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

FieldWhat to enterKnown valuesChoose one: u, a, t → s, v, u, v, t → s, a, u, v, a → s, t, u, s, t → v, a …Displacement sUnits: m, cm, mm, km, in, ft …Initial velocity uUnits: m/s, km/h, mph, ft/s, knots, km/sFinal velocity vUnits: m/s, km/h, mph, ft/s, knots, km/sAcceleration aUnits: m/s², ft/s², g, cm/s²Time tUnits: 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)252537.525502562.525752510025

## 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.

## FAQ

**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.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)