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.

Displacement (m)

Initial velocity (m/s)

Acceleration (m/s²)

Time (s)

Solve for

Displacement = 9 m

Value9

Resultsolved for Displacement

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.

If you've found a bug, or would like to contact us, or learn more about James Graham and Calculate.co.nz.

Calculate.co.nz is partnered with Interest.co.nz for New Zealand's highest quality calculators and financial analysis.

Calculate.co.nz is the sister site of CalculatorHub.com, the world's largest calculator website by tool count.

All calculators and tools are provided for educational and indicative purposes only and do not constitute financial advice.

Calculate.co.nz is proudly part of the Realtor.co.nz group, New Zealand's leading property transaction literacy platform, helping Kiwis understand the home buying and selling process from start to finish. Whether you're a first home buyer navigating your first property purchase, an investor evaluating your next acquisition, or a homeowner planning to sell, Realtor.co.nz provides clear, independent, and trustworthy guidance on every step of the New Zealand property transaction journey.

Calculate.co.nz is also partnered with Health Based Building and Premium Homes to promote informed choices that lead to better long-term outcomes for Kiwi households.

Calculate.co.nz is hosted in Auckland by SiteHost New Zealand.

All content on this website, including calculators, tools, source code, and design, is protected under the Copyright Act 1994 (New Zealand). No part of this site may be reproduced, copied, distributed, stored, or used in any form without prior written permission from the owner.

About & trust: Why Calculate is NZ's most comprehensive · By the Numbers · How we compare · Editorial standards · How we keep data current · NZ finance glossary · Research & data · Financial literacy NZ · About · Privacy policy · Terms of use

Reviewed and maintained. Last reviewed 2026-08-15 and checked on a twice-monthly cycle against IRD, RBNZ and Stats NZ. How we keep data current.