Velocity Calculator
Find velocity from displacement and time, or from initial velocity and constant acceleration over a time or a distance, in m/s, km/h, mph and ft/s.
Velocity is how fast something moves in a particular direction. This calculator finds it three ways: from a displacement and the time it took, from a starting velocity plus a constant acceleration over a time, or from a starting velocity and acceleration over a displacement. Every answer is shown in m/s, km/h, mph and ft/s, and the acceleration methods also give the distance covered or the time taken.
How to use this tool
- Choose how you want to work it out.
- For displacement and time, enter both and pick their units.
- For the acceleration methods, enter the initial velocity in m/s and the acceleration in m/s² (negative for braking), then the time or the displacement.
- Read the velocity and its conversions below it.
Formula
v = Δx ÷ t · v = u + a·t · v² = u² + 2·a·s
Δx (or s) is displacement, the straight-line change in position, which can be negative. t is time, u the initial velocity and a a constant acceleration. The last two equations of motion only hold while the acceleration stays constant. The acceleration methods are one-dimensional classical mechanics. Results ignore drag; they are not a relativistic model.
Example
A ball is dropped from rest (u = 0) and falls 20 m with a = 9.81 m/s². Then v² = 0 + 2 × 9.81 × 20 = 392.4, so v ≈ 19.81 m/s — about 71.31 km/h or 44.31 mph — reached after 19.81 ÷ 9.81 ≈ 2.02 s. Air resistance is ignored.
Frequently asked questions
What is the difference between velocity and speed?
Speed is only a size; velocity also has a direction. Running one full lap of a 400 m track in 80 s is an average speed of 5 m/s but an average velocity of zero, because you finish where you started.
Why does the displacement method say the object never gets there?
A negative squared speed means that position is unreachable under the stated constant acceleration. Even with a nonnegative squared speed, the arrival times may all lie before the start. The calculator selects the first nonnegative arrival; if the requested displacement is zero, that includes time zero.
What acceleration should I enter?
Use metres per second squared. Gravity near the Earth’s surface is about 9.81 m/s². A car going from 0 to 100 km/h in 8 s averages about 3.5 m/s².
Can velocity be negative?
Yes. A negative velocity simply means motion in the direction you defined as negative, such as a ball falling back down after being thrown upward.
Last updated: 2026-10-30