Quick answer
This SUVAT calculator solves motion problems with constant acceleration. Enter any three of s (displacement), u (initial velocity), v (final velocity), a (acceleration) and t (time), and it finds the other two using the correct SUVAT equation, showing every step.
SUVAT equations solver
How to Use the SUVAT Calculator
- Read the question and write down which three SUVAT values you know.
- Type those three values into the boxes, using SI units (m, m/s, m/s², s).
- Leave the two unknown boxes empty.
- Use a negative value for any quantity pointing in the negative direction, such as braking acceleration.
- Press Calculate to see both answers and the step-by-step working.
The Five SUVAT Equations
The calculator picks the right equation for you, but it helps to know them. Each one leaves out one of the five variables.
| Equation | Leaves out |
|---|---|
| v = u + at | s |
| s = ut + ½at² | v |
| s = vt − ½at² | u |
| v² = u² + 2as | t |
| s = ½(u + v)t | a |
For a full explanation of where these come from and how to choose between them, read our guide to the SUVAT equations.
Worked Example
Worked example: a train slowing down
Question: A train travelling at 30 m/s brakes steadily and stops in 50 s. Find its acceleration and stopping distance.
- Known: u = 30 m/s, v = 0 m/s, t = 50 s. Unknown: a and s.
- a = (v − u) ÷ t = (0 − 30) ÷ 50 = −0.6 m/s².
- s = ½(u + v)t = ½ × (30 + 0) × 50 = 750 m.
Answer: The acceleration is −0.6 m/s² and the train stops after 750 m. Enter u = 30, v = 0 and t = 50 in the calculator to check.
When Can You Use SUVAT?
SUVAT only works when the acceleration stays the same for the whole motion. That covers many textbook problems: a car speeding up steadily, an object in free fall where air resistance is small, or a ball rolling down a smooth ramp.
Common mistake: If the acceleration changes during the journey, split the motion into stages and solve each stage separately, or use calculus instead.
Tip: For vertical motion, choose up or down as positive at the start and keep it. If up is positive, g becomes −9.81 m/s².
Practise: try these SUVAT equations MCQs with step-by-step solutions.
Frequently Asked Questions
What does SUVAT stand for?
SUVAT stands for the five quantities in constant-acceleration motion: s (displacement), u (initial velocity), v (final velocity), a (acceleration) and t (time).
Why do I need exactly three values?
Each SUVAT equation links four of the five quantities. With any three known, two equations are enough to find the remaining two unknowns.
Can the SUVAT calculator handle negative values?
Yes. Negative values mean the quantity points in the negative direction. Braking, for example, is entered as a negative acceleration.