Displacement (Uniform Acceleration)
Also known as second kinematic equation · d = v₀t + ½at² · SUVAT s = ut + ½at²
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
Learning zone
When acceleration is constant, displacement has two parts: the distance you would cover at your initial velocity alone, plus the extra distance contributed by speeding up — and that extra grows with the square of time. A jet starting its takeoff roll from rest and holding 2 m/s² covers d = 0 + ½(2)(30²) = 900 m in 30 seconds, which is why runways are measured in kilometres.
The ½ appears because the acceleration term is built from the average of a speed that grows linearly from zero. Galileo uncovered the underlying pattern — distances in successive equal time intervals follow the odd numbers 1, 3, 5, 7 — by rolling bronze balls down inclined planes. Note that solving for t would mean solving a quadratic with potentially two positive roots, so this calculator rearranges only for d, v₀, and a, where the answer is always single-valued.
- = Displacement
- = Initial velocity
- = Acceleration
- = Time
- Displacement — Velocity-Displacement Relation (v² = v₀² + 2ad), Displacement from Average Velocity
- Initial velocity — Final Velocity (Uniform Acceleration), Velocity-Displacement Relation (v² = v₀² + 2ad)
- Acceleration — Newton's Second Law, Final Velocity (Uniform Acceleration)
- Time — Speed, Distance & Time, Final Velocity (Uniform Acceleration)