Velocity Squared Calculator (v² = u² + 2as)
This velocity squared calculator solves the SUVAT equation of motion, v squared equals u squared plus 2as, which links final velocity, initial velocity, acceleration and displacement without needing the time taken. It matters because plenty of real problems give you a displacement and an acceleration but never mention time, so the usual v equals u plus at approach cannot be used. Choose which variable to solve for from the dropdown, final velocity, initial velocity, acceleration or displacement, then enter the other three, working in SI units throughout: metres per second for velocity, metres per second squared for acceleration and metres for displacement. The calculator rearranges the equation for you and returns the solved value in the results card, labelled with its variable name and unit, alongside a note confirming which variable was solved. Because the equation involves a square root, velocity results show as a positive magnitude, so you need to assign direction yourself based on the physical setup. This makes the tool handy for physics students, teachers and anyone working through equations of motion who wants a quick answer without rearranging algebra by hand. The worked example below solves the equation from rest with an acceleration of 2 metres per second squared over a displacement of 9 metres. As with any physics calculation, the result is only as accurate as the figures you enter.
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
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