Work is the quiet workhorse of mechanics: it links force and motion to energy, and it is the idea that lets us say precisely how much a push or a pull has actually achieved. In everyday speech we use the word loosely, but in physics work has a strict meaning. Work is done only when a force moves something along the direction of that force, and the amount of work is the force multiplied by the distance multiplied by the cosine of the angle between them. This calculator takes those three inputs, the force in newtons, the distance in metres, and the angle in degrees, and returns the work done in joules and kilojoules so you can read the result at whatever scale suits the problem. The angle is the part people most often overlook. When you push a box straight along the floor the force and the motion point the same way, the angle is zero, the cosine is one, and the work is simply force times distance. But pull a sled by a rope held at an angle and only the part of the force lined up with the motion counts, which is why the cosine appears. Two special cases are worth remembering. When the force is perpendicular to the motion the angle is ninety degrees, the cosine is zero, and no work is done at all. When the angle is greater than ninety degrees the cosine turns negative and the work is negative, meaning the force is removing energy, as friction and braking do. It is built for students, teachers, engineers and anyone checking how much energy a force has delivered.
Mechanical work is the force multiplied by the distance moved multiplied by the cosine of the angle between the force and the direction of motion. The result is in joules when force is in newtons and distance is in metres.
W = F × d × cosθ
1 kJ = 1,000 J
A force of 100 newtons pushes an object 5 metres in the same direction as the force, so the angle is 0 degrees and the cosine is 1. The work is 100 × 5 × 1 = 500 joules, which is 0.5 kilojoules. If the same force acted at 90 degrees to the motion the cosine would be 0 and the work would be 0 joules.
This calculator is for students, teachers, engineers and anyone who needs to find the mechanical work done by a force acting over a distance.
Work is force times distance times the cosine of the angle between them, W = F d cosθ, giving joules when force is in newtons and distance in metres. When the force lines up with the motion the angle is zero and the work is simply force times distance.
At 90 degrees the cosine is zero, so the work is zero. A force at right angles to the motion neither speeds the object up nor slows it down along its path, so it transfers no energy.
Yes. When the angle is greater than 90 degrees the cosine is negative, so the work is negative. This happens when a force opposes the motion, such as friction or braking, taking energy out of the object.
One kilojoule is one thousand joules. To convert joules to kilojoules, divide by 1,000.
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.
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 via 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 2026-06-07 and checked on a twice-monthly cycle against IRD, RBNZ and Stats NZ. How we keep data current.
© 2026 Calculate.co.nz. All rights reserved. Building free NZ calculators since 2011.