Displacement Calculator (s = ut + ½at²)
This calculator solves the SUVAT equation of motion, s = ut + half a t squared, for displacement, initial velocity, acceleration or time, for any object moving with constant acceleration. It is the equation to reach for whenever three of the four quantities are known and you need the fourth, whether checking a physics assignment, verifying a lab result or estimating how far something travels under steady acceleration. Choose which quantity to solve for from the dropdown, then enter the remaining three values in SI units: metres for displacement, metres per second for initial velocity, metres per second squared for acceleration, and seconds for time. The calculator instantly returns the solved value with its unit, plus a short summary confirming which quantity was found. Solving for time uses the quadratic formula and returns the first positive root, since a negative time has no physical meaning; if acceleration is zero, the equation collapses to s = ut, so time is simply displacement divided by velocity. A worked example below shows the sums for an object starting from rest under a steady acceleration of 2 metres per second squared. The tool suits physics students, teachers and engineers running a quick sanity check on motion. As with any equation of motion, it assumes acceleration stays perfectly constant, so treat the result as a straightforward physics calculation, not a substitute for full engineering analysis.
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
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