Displacement Calculator (s = ut + \u00BDat\u00B2)

This displacement calculator uses the SUVAT equation s equals ut plus one half a t squared, which gives the displacement of an object moving with constant acceleration. Choose the quantity you need and enter the others; the calculator solves for displacement, initial velocity, acceleration or time. Solving for time uses the quadratic formula and returns the first positive time. Use SI units throughout: metres, metres per second, metres per second squared and seconds. This is a core equation of motion in mechanics. The formula, a worked example and the assumptions are below.

Displacement (m)

Initial velocity (m/s)

Acceleration (m/s\u00B2)

Time (s)

Solve for

Value

Result

The formula

The equation is s = ut + one half a t squared. Rearranged: u = (s minus half a t squared) / t, a = 2(s minus ut) / t squared, and t comes from the quadratic half a t squared + ut minus s = 0, taking the positive root.

Worked example

From rest (u = 0) with a = 2 m/s squared for t = 3 s, the displacement is s = 0 + half times 2 times 9 = 9 m. Solve for s with u = 0, a = 2, t = 3 to confirm.

Frequently asked questions

What does this equation give?

The displacement of an object under constant acceleration, from its initial velocity, the acceleration and the time.

How is time found?

By solving the quadratic in t. The calculator returns the first positive time that fits.

What if acceleration is zero?

Then s = ut, and time is simply s divided by u.

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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