Quick answer
The SUVAT equations for constant acceleration are v = u + at, s = ut + ½at², v² = u² + 2as and s = (u + v)t ÷ 2. Starting at u = 5 m/s with a = 2 m/s² for 10 s gives v = 25 m/s and s = 150 m.
Choose which quantities you know and enter them. The calculator returns the remaining ones.
Related tools: Acceleration Calculator: Average acceleration from change in velocity over time. Projectile Motion Calculator: Range, flight time and peak height of a projectile without air resistance. Free Fall Calculator: Fall time, height and impact speed in free fall from rest.
How to use the SUVAT Calculator
- Choose you know: Know u, a, t → v, s, Know u, v, t → a, s, Know u, v, a → t, s and Know u, a, s → v, t.
- Enter initial velocity u (m/s).
- Optionally, enter final velocity v (m/s).
- Optionally, enter acceleration a (m/s²).
- Optionally, enter displacement s (m).
- Optionally, enter time t (s).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| You know | Choose one: Know u, a, t → v, s; Know u, v, t → a, s; Know u, v, a → t, s; Know u, a, s → v, t | Starts at Know u, a, t → v, s |
| Initial velocity u | A number, in m/s | — |
| Final velocity v (optional) | A number, in m/s | — |
| Acceleration a (optional) | A number, in m/s² | — |
| Displacement s (optional) | A number, in m | — |
| Time t (optional) | A number, in s | — |
Formula and method
Formula
v = u + at; s = ut + ½at²; v² = u² + 2as; s = (u + v)t ÷ 2
IEEE-754 double precision; shown to the decimals indicated.
Straight-line motion with constant acceleration; the v² = u² + 2as case returns the positive root.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: You know = Know u, a, t → v, s; Initial velocity u = 5; Acceleration a = 2; Time t = 10.
| Result | Value |
|---|---|
| Final velocity v | 25 |
| Displacement s | 150 |
Example 2
Inputs: You know = Know u, v, t → a, s; Initial velocity u = 10; Final velocity v = 30; Time t = 4.
| Result | Value |
|---|---|
| Acceleration a | 5 |
| Displacement s | 80 |
Example 3
Inputs: You know = Know u, a, s → v, t; Initial velocity u = 10; Acceleration a = 2; Displacement s = 75.
| Result | Value |
|---|---|
| Final velocity v | 20 |
| Time t | 5 |
The first line is the headline result (final velocity v). Below it the sUVAT Calculator lists displacement s, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Worked example
v = 5 + 2 × 10 = 25. s = 5 × 10 + ½ × 2 × 100 = 150. Check with s = (u + v)t ÷ 2 = (5 + 25) × 10 ÷ 2 = 150 ✓.
Constant acceleration only
Pick the equation that omits the variable you don't know and don't need. They apply to constant acceleration in a straight line, like free fall (a = 9.81 m/s²) or braking. Three known quantities are needed.
How the result changes with initial velocity u
Holding every other input at the first worked example, this table changes only initial velocity u. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Initial velocity u | Final velocity v | Displacement s |
|---|---|---|
| 2.5 | 22.5 | 125 |
| 5 | 25 | 150 |
| 10 | 30 | 200 |
| 20 | 40 | 300 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Time t: left empty shows "Enter the time." beside that field and no result.
- Acceleration a: entering "0" shows "Acceleration cannot be zero here." beside that field and no result.
Choosing between the SUVAT Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Acceleration Calculator](/science/acceleration-calculator/) | initial velocity, final velocity and time | Acceleration |
| [Projectile Motion Calculator](/science/projectile-motion-calculator/) | launch speed and launch angle | Range |
| [Free Fall Calculator](/science/free-fall-calculator/) | i know the and height or time | Fall time |
| [Magnitude of Acceleration Calculator](/science/magnitude-of-acceleration-calculator/) | x component and y component | Magnitude |
| [Terminal Velocity Calculator](/science/terminal-velocity-calculator/) | mass, frontal area and drag coefficient | Terminal velocity |
Background: motion and mechanics
For constant acceleration the standard relations are v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t. Pick the equation that contains your three known quantities and the one you want. Use SI units (metres, seconds, kilograms, newtons, joules) throughout or the answer will be off by a factor.
These equations stop applying when acceleration changes during the motion, as with a rocket burning fuel; that needs calculus or numerical methods.
Assumptions and limitations
- Needs the three quantities of the chosen mode
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for time t and acceleration a to confirm this.
Frequently asked questions
What does SUVAT stand for?
Displacement, initial velocity, final velocity, acceleration and time.
Does it work for projectiles?
Separately in each direction.
When does it not apply?
When acceleration changes.
What does the SUVAT Calculator calculate?
Solve constant-acceleration motion for the missing quantities. It returns Final velocity v and Displacement s.
What formula does the SUVAT Calculator use?
v = u + at; s = ut + ½at²; v² = u² + 2as; s = (u + v)t ÷ 2. Straight-line motion with constant acceleration; the v² = u² + 2as case returns the positive root.
What do I need to enter in the sUVAT Calculator?
You enter You know and Initial velocity u (m/s). Optional: Final velocity v (m/s), Acceleration a (m/s²), Displacement s (m) and Time t (s).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Needs the three quantities of the chosen mode.
What does the “You know” option change?
It sets how the sUVAT is worked out. The choices are Know u, a, t → v, s, Know u, v, t → a, s, Know u, v, a → t, s and Know u, a, s → v, t.
What is an example of a sUVAT result?
With you know Know u, a, t → v, s, initial velocity u 5, acceleration a 2 and time t 10, the final velocity v is 25.
Related calculators
- Acceleration Calculator — Average acceleration from change in velocity over time.
- Projectile Motion Calculator — Range, flight time and peak height of a projectile without air resistance.
- Free Fall Calculator — Fall time, height and impact speed in free fall from rest.
- Magnitude of Acceleration Calculator — Magnitude of an acceleration vector from its components.
- Terminal Velocity Calculator — Terminal speed of a falling object from mass, area and drag coefficient.
- Dew Point Calculator — Dew point from temperature and relative humidity.
Sources
- OpenStax, University Physics Volume 1 (Rice University): mechanics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.