SUVAT Kinematics Solver
Constant-acceleration motion: enter any three of displacement, initial and final velocity, acceleration and time, and get the other two with the equations used.
The two missing SUVAT quantities, the pair of equations that solved them, the average velocity, and both roots when a square root gives two — with the sign convention stated.
Example: From rest at 9.80665 m/s² for 3 s: s = 44.13 m, v = 29.42 m/s. Thrown up at 20 m/s, when is it 20 m high? v = ±2.83 m/s at t = 1.75 s going up and 2.33 s coming down.
Five equations,
two unknowns at a time.
Which equation pair solves which case, the sign convention, and the two-root cases.
The equations
With constant acceleration a over time t, starting at velocity u and ending at v over displacement s: v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u + v)t and s = vt − ½at². Each links four of the five quantities, so any three determine the other two; the page picks the pair that avoids the unknowns and names it.
Signs and units
Everything is along one straight line: choose a positive direction and give velocities, acceleration and displacement their signs accordingly (a ball thrown up with gravity acting down has u positive and a negative, or the reverse). Units only need to be consistent; the selector labels them. Standard gravity is 9.80665 m/s² by definition, typed by you.
Two roots
When v or u comes from a square root, both signs are mathematically valid — a ball passes the same height going up and coming down. Both are shown with their times; the earlier non-negative time is the main answer. A time that comes out negative describes the motion before your start and is rejected. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- The five equations of uniformly accelerated motion: v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u + v)t, s = vt − ½at² (elementary mechanics)
Last reviewed 20 September 2026. How results are checked: How we verify.