Kinematics Calculator
Give any three of starting speed, final speed, acceleration, time and distance, and the other two come out.
Results
What this tool does
Constant acceleration is described by five quantities and four equations, and the whole skill of a first physics course is picking the equation that uses what you have. This page removes that step. Fill in any three boxes, leave the other two empty, and it works out which relationships apply and applies them in turn until nothing is left unknown. It also tells you when a square root forced a choice between two valid answers, because that is the one place where these equations quietly assume which way you are going.
Formula
v = u + a t · s = u t + ½ a t² · v² = u² + 2 a s · s = (u + v) t ÷ 2
Variables
| Symbol | Meaning | Unit |
|---|---|---|
u | Initial velocity | m/s |
v | Final velocity | m/s |
a | Acceleration | m/s² |
t | Time | s |
s | Distance travelled | m |
S | Distance travelled | m |
V | Final velocity | m/s |
U | Initial velocity | m/s |
A | Acceleration | m/s² |
T | Time | s |
AV | Average velocity | m/s |
DV | Change in velocity | m/s |
RT | Was a square root's sign chosen for you? | — |
KN | Values you gave | — |
Worked example
- Initial velocity0 m/s
- Final velocity m/s
- Acceleration2 m/s²
- Time5 s
- Distance travelled m
- Distance travelled25.000000 m
- Final velocity10.000000 m/s
- Initial velocity0.000000 m/s
- Acceleration2.000000 m/s²
- Time5.000000 s
- Average velocity5.000000 m/s
- Change in velocity10.000000 m/s
- Was a square root's sign chosen for you?No
- Values you gave3
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
Frequently asked questions
Which boxes do I fill in?
Any three of the five, and leave the other two empty. That is the whole idea: with three of {starting speed, final speed, acceleration, time, distance} the other two are determined, and there is an equation for every combination. Leave a box blank to say you do not know it — a zero is not the same thing, because zero is a perfectly good answer for a body that starts at rest.
What does "positive root taken" mean?
That one of the equations needed a square root, and a square root has two answers. When you give a distance and an acceleration but no time, v² = u² + 2as gives both +v and −v — the same speed in either direction. This page takes the positive one, which is the forward-moving answer and what almost every problem wants. If your body is travelling backwards, the magnitude is still right; put a minus sign on it yourself.
When do these equations stop working?
The moment the acceleration changes. All five rest on it being constant for the whole stretch — that is the only assumption, and everything else follows from it. A car braking harder as it slows, a rocket getting lighter as it burns fuel, anything falling far enough for air resistance to matter: none of those are constant-acceleration problems, and using these equations on them gives a confident wrong answer. Break the motion into stretches where the acceleration really is constant, and run each one separately.