Physics / Motion
SUVAT Calculator: Equations of Motion Solver
Solve constant-acceleration problems: enter any three of displacement, initial velocity, final velocity, acceleration, and time, and get the other two, both answers when there are two, and the equation used.
SUVAT Calculator: Equations of Motion Solver: The tool picks the equation that contains your three knowns and the unknowns: v = u + at, s = ut + ½at², s = vt − ½at², v² = u² + 2as, or s = (u + v)t ÷ 2. Dropping from rest with a = 9.81 m/s² for 2 s gives v = 19.62 m/s and s = 19.62 m. When the quadratic has two positive times, both are shown. Runs 100% locally in your browser with zero server file uploads.
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Used: v = u + at; s = ut + ½at²
The five SUVAT equations hold when acceleration is constant: v = u + at, s = ut + ½at², s = vt − ½at², v² = u² + 2as, and s = (u + v)t ÷ 2. Each leaves out one of the five quantities, so any three known values give the other two. Choose a positive direction and keep to it: an object thrown upwards with gravity acting down has a negative acceleration.
Example with two answers
A ball thrown up at 20 m/s with a = −9.8 m/s² is 15 m up at 0.99 s on the way up and again at 3.09 s on the way down; both satisfy s = ut + ½at².
Two dimensions
Throws and jumps combine a constant horizontal speed with constant vertical acceleration; the projectile motion calculator does both at once.
How to use it
- Fill in three of the five values and leave the other two empty.
- Use negative numbers for quantities in the opposite direction.
- Read the missing values and the equation used.
Privacy & limitations
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Frequently asked questions
What does SUVAT stand for?
The five quantities: s displacement, u initial velocity, v final velocity, a acceleration, and t time.
Why are there two answers?
A ball thrown up passes a given height twice, once going up and once coming down, so the time equation has two solutions.
When do the equations not apply?
When acceleration changes, such as a falling object reaching terminal velocity or a car with varying throttle.
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