Constant Acceleration (SUVAT) Calculator

Motion with constant acceleration

When velocity changes by the same amount every second, the motion has constant acceleration. A car pulling away, a train braking and a falling stone are all examples. Five quantities describe it: initial velocity (v₀), final velocity (v), acceleration (a), time (t) and displacement (x). Knowing three gives the other two.

The four kinematic equations

• v = v₀ + a × t
• x = v₀ × t + ½ × a × t²
• v² = v₀² + 2 × a × x
• x = (v₀ + v) / 2 × t

Each equation leaves out one of the five quantities. You pick the equation that omits the quantity you are neither given nor asked for. The calculator does this for you: fill in three fields and leave two empty. These are often called the SUVAT equations.

Example: braking distance

A vehicle travelling at 20 m/s (72 km/h) slows at 5 m/s² to a stop. Enter a final velocity of 0 and an acceleration of −5 m/s². From v² = v₀² + 2 × a × x, x = (0 − 400) / (2 × −5) = 40 m, and the time is t = (0 − 20) / −5 = 4 s.

Mind the signs

Velocity, acceleration and displacement have direction. Choose one direction as positive and enter every value accordingly. For an object slowing down, acceleration has the opposite sign to velocity. For an object thrown upward with up as positive, acceleration is −9.81 m/s².

When there are two solutions

An object thrown upward passes a given height twice: going up and coming down. If time is unknown the equation has two roots. The calculator shows the first pass as the main result and lists the second below it.

Limits

The equations hold only while acceleration is constant. They cannot be used where air resistance matters or acceleration changes with time.