🚀SUVAT Calculator

About this tool

Fill in any three of s (displacement), u (initial velocity), v (final velocity), a (acceleration) and t (time), and leave the other two blank. The calculator finds the missing values, shows which equations it used and, when a problem has two physical answers, shows both. A button fills in a = 9.81 m/s² for free fall.

The SUVAT equations

For motion in a straight line with constant acceleration, five quantities are linked by five equations: v = u + at, s = ut + ½at², s = vt − ½at², s = ½(u + v)t and v² = u² + 2as. Each equation leaves out one quantity, so any three known values let you pick the equation that fits and solve for the rest. A stone dropped from rest, with u = 0 and a = 9.81 m/s², falls 44.1 m in 3 seconds and is then moving at 29.4 m/s. Some problems have two answers. A ball thrown upwards at 20 m/s passes 10 m above the start twice, at about 0.58 s on the way up and about 3.49 s on the way down, and both appear. Choose one direction as positive and keep the signs consistent. For a ball thrown up, take up as positive, so gravity is a = −9.81 m/s². Units must match too, such as metres, seconds, m/s and m/s². Honest limits: the equations assume constant acceleration and no air resistance, so long falls and fast objects in air travel less far than these ideal figures. The speed, distance and time calculator handles constant speed, the unit converter switches units and the scientific calculator helps with the algebra.

Frequently asked questions