Kinematics Calculator (SUVAT)

Formula

How this is calculated

The five SUVAT variables describe one-dimensional motion under constant acceleration: u (initial velocity, m/s), v (final velocity, m/s), a (acceleration, m/s²), t (time, s) and s (displacement, m). Provide any three known values and leave the two unknowns blank; the solver picks the SUVAT equation that omits one of your unknowns, computes that value first, then uses a second equation to find the last one.

Each equation drops exactly one variable: v = u + a·t omits s, s = u·t + ½·a·t² omits v, v² = u² + 2·a·s omits t, s = ½·(u + v)·t omits a, and s = v·t − ½·a·t² omits u. By matching the missing variable to your blanks, the unknowns are isolated and solved algebraically. The v–t plot shows velocity v(τ) = u + a·τ as a straight line, whose slope is the acceleration and whose area under the curve equals the displacement.

Assumptions: acceleration is constant, motion is along a single straight line, and a consistent sign convention is used (a negative value means motion or acceleration in the opposite direction). When a value is found from a square root or quadratic, the calculator returns the physically sensible (non-negative time, positive speed) root. Edge cases such as dividing by zero time or zero acceleration are guarded and will show a warning instead of an invalid result.