Kinematic Equations Calculator
Rearrange common constant-acceleration equations to solve velocity, displacement, acceleration or elapsed time, with signed one-dimensional inputs.
Choose a constant-acceleration equation and solve for the quantity you do not know. The menu identifies the three inputs each calculation uses, helping separate a valid equation from unrelated values left in other fields. Both metric and feet-based motion units are available, with time consistently measured in seconds.
How to use this tool
- Choose the unknown and its listed input combination.
- Choose metres or feet for velocity, acceleration and displacement.
- Enter the required signed velocities and acceleration, plus elapsed time where requested.
- Read the unknown and the corresponding signed displacement when it is determined.
Formula
v = u + at; u = v − at; a = (v − u)/t; t = (v − u)/a; s = (u + v)t/2
u and v are initial and final velocity; a is constant acceleration, t is elapsed time and s is displacement. An input field for the unknown is ignored. The displacement equation uses the average of the two endpoint velocities, which is valid under constant acceleration.
Example
Starting at 5 m/s and accelerating at 2 m/s² for 5 s gives a final velocity of 15 m/s. The mean velocity is 10 m/s, so displacement is 50 m. Selecting acceleration with those two velocities and 5 s recovers 2 m/s².
Frequently asked questions
Why is zero acceleration rejected when solving time?
Two equal velocities with zero acceleration could describe any duration. Unequal velocities would be inconsistent. Neither case determines a unique elapsed time.
Can velocity or acceleration be negative?
Yes. Their signs refer to a chosen direction. Elapsed time must be nonnegative; an inferred negative duration means the selected inputs are inconsistent with forward time.
Are all visible fields used at once?
No. Only the inputs named in the equation menu are read. This prevents an old value in an unused field from overconstraining the calculation.
Can displacement be zero after moving?
Yes. Opposite-direction travel can cancel. Use the kinematics calculator with a complete motion interval when total distance is required.
Sources
Last updated: 2026-10-30