Velocity Squared Calculator (v\u00B2 = u\u00B2 + 2as)

This velocity squared calculator uses the time-free SUVAT equation, v squared equals u squared plus 2as, which links final and initial velocity to acceleration and displacement without needing the time. Choose the unknown and enter the rest; the calculator solves for any of the four. It is the equation to reach for when you know a distance and an acceleration but not how long the motion took. Velocities come out as positive magnitudes. Use SI units throughout. The formula, a worked example and the assumptions are below.

Final velocity (m/s)

Initial velocity (m/s)

Acceleration (m/s\u00B2)

Displacement (m)

Solve for

Value

Result

The formula

The equation is v squared = u squared + 2as. Rearranged: u = the square root of (v squared minus 2as), a = (v squared minus u squared) / (2s), and s = (v squared minus u squared) / (2a).

Worked example

From rest (u = 0) with a = 2 m/s squared over s = 9 m, v squared = 0 + 2 times 2 times 9 = 36, so v = 6 m/s. Solve for v with u = 0, a = 2, s = 9 to confirm.

Frequently asked questions

When should I use v squared = u squared + 2as?

When you know displacement and acceleration but not time, and want a velocity, or vice versa.

Why are velocities positive?

The square root gives a magnitude. Assign a direction based on the physical setup if needed.

Is this a SUVAT equation?

Yes, the third of the four equations of motion for constant acceleration.

Who this calculator is for

This calculator is for physics students, teachers and engineers.

What this calculator assumes

You enter SI units as labelled.
One variable is solved from the others.
Results are rounded for display.

Formula and sources

Related calculators

Kinetic Energy Calculator: energy of motion.
Momentum Calculator: mass times velocity.
Projectile Motion Calculator: range and height.

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