Displacement Calculator — Kinematic SUVAT Formula

Formula

How this is calculated

This calculator applies the SUVAT kinematic equations, which describe motion under constant (uniform) acceleration. The displacement s — the net change in position measured in a straight line — is found from s = ut + ½at², where u is the initial velocity, a is the constant acceleration, and t is the elapsed time. A positive displacement means movement in the direction of the initial velocity; a negative result means the object has moved backwards (for example, decelerated from a positive velocity to a negative one).

Final velocity is v = u + at. The average velocity over the interval is simply s ÷ t (equal to (u + v) / 2 for constant acceleration). Note the distinction between displacement and distance: if the object decelerates to zero and reverses direction during the interval, the total distance travelled (path length) is greater than the magnitude of displacement, since displacement only measures start-to-finish separation.

The model assumes constant acceleration throughout the time interval — the key SUVAT assumption. Real-world scenarios such as air resistance, variable engine thrust, or friction that changes with speed require numerical integration rather than these closed-form equations. Gravitational free fall (a = −9.81 m/s²) and objects on frictionless inclines are well-modelled by this approach.