Work Calculator
Find the work done by a force over a distance, solve for any variable in W = F d cos(theta), and handle friction, gravity and springs.
🏗️ What is Work in Physics?
Work is the energy transferred to or from an object when a force moves it through a displacement. For a constant force the work is the force times the distance moved along the force, which is W = F d cos(theta), where theta is the angle between the force and the direction of motion. The unit is the joule: one newton acting over one metre. This work calculator solves that equation for any one of the four variables, so you can find the work from a force and distance, the force needed to do a given amount of work, the distance, or the angle between the force and the motion.
The same page handles three special cases that textbooks keep returning to. Work against friction asks how much energy you spend dragging a load at constant speed, including the useful case of pulling a rope at an angle. Work by gravity shows why climbing a slope costs the same energy as lifting straight up to the same height, and it lets you compare Earth, the Moon, Mars and Jupiter. Work by a spring covers a variable force, where the force grows with stretch and the work is the area under the force-stretch line. Each mode draws its own chart so you can see how the work changes with angle or stretch.
Three ideas prevent most mistakes. First, only the component of the force along the displacement does work, which is why a force at 90 degrees does none, so carrying a box horizontally at constant speed involves zero work by the lifting force. Second, work has a sign: when the force opposes the motion the work is negative and the object loses energy, as with friction or braking. Third, work is not the same as effort or fatigue. Holding a heavy weight still tires your muscles but moves nothing, so the work on the weight is zero.
When time matters, move on to power, which is work per unit time, using the work and power calculator. The broader work, energy and power calculator links work to kinetic and potential energy, and the friction calculator goes deeper on friction coefficients.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Pushing a Cart at an Angle
A 50 N force acts 30 degrees from the direction of motion over 10 m
Example 2 — Finding the Angle
An 80 N force over 5 m does 300 J of work. At what angle does it act?
Example 3 — Force Needed for a Given Work
1200 J of work are done over 15 m with the force along the motion
Example 4 — Dragging a Crate
A 20 kg crate with friction coefficient 0.4 is pulled 5 m at constant speed along the floor
Example 5 — A Rover Climbing a Slope on Mars
A 180 kg rover drives 30 m up a 15 degree slope on Mars (g = 3.721 m/s²)
Example 6 — Stretching a Spring
A spring with k = 200 N/m is stretched from 0.1 m to 0.3 m
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for work in physics?
Work is W = F d cos(theta), where F is the force in newtons, d is the displacement in metres and theta is the angle between the force and the displacement. The result is in joules. When the force points along the motion, cos(theta) is 1 and W = F d.
When is work equal to zero?
Work is zero when the displacement is zero, when the force is zero, or when the force is perpendicular to the motion (theta = 90 degrees). Carrying a bag across level ground at constant speed is an example: the lifting force is vertical, the motion is horizontal.
Can work be negative?
Yes. When the angle between force and displacement is greater than 90 degrees, cos(theta) is negative and so is the work. Friction on a sliding box and gravity on a rising ball do negative work, because they take energy away from the object.
How do you calculate work done against friction?
Kinetic friction is f = mu m g on a level surface, and the work against it over a distance d is mu m g d. A 20 kg crate with mu 0.4 pulled 5 m needs 0.4 x 20 x 9.80665 x 5 = 392.27 J.
How do you find the work done by gravity?
Work by gravity is m g h with a sign. It is negative when the object rises by h and positive when it falls by h. Lifting a 10 kg load 2 m on Earth means gravity does -196.13 J and the lifter does +196.13 J.
What is the work done by a spring?
A spring with constant k stretched from x1 to x2 stores 1/2 k (x2 squared minus x1 squared) joules. You do that much work on the spring, and the spring does the negative of it on you. The spring force is not constant, so the area under the force-stretch graph is used.
What is the unit of work?
The SI unit of work is the joule (J). One joule is the work done by a force of one newton over a distance of one metre in the direction of the force, so 1 J = 1 N m = 1 kg m squared per second squared.
What is the difference between work and energy?
Work is the energy transferred by a force acting through a displacement. Energy is the stored capacity. By the work-energy theorem, the net work on an object equals its change in kinetic energy.
Why does pulling at an angle change the work?
Only F cos(theta) acts along the motion, so a tilted pull gives less work for the same force. But a tilted upward pull also lowers the normal force and so the friction, which can make the total work needed smaller.
Does the path matter for the work done by gravity?
No. Gravity is a conservative force, so only the change in height matters. A 30 m ramp at 15 degrees and a 7.76 m vertical lift reach the same height and need the same work against gravity.