Work Calculator · W = F·d·cosθ in J, kJ & ft-lbs

Work Calculator

Calculate the work done by a force from force, displacement and angle — in J, kJ, ft-lbs, cal and more

Quick preset

Inputs

Force (F)

Displacement (d)

Angle between force & motion (θ)

Time taken (optional, for power)

Work is energy transferred by a force: W = F × d × cos(θ). When the force points along the motion (θ = 0°) the full force does work. At 90° no work is done; beyond 90° the work is negative — the force removes energy.

Quick examples

Work Result

Work done

— J

— — — —

Kilojoules

— kJ

Foot-pounds

— ft-lbs

Calories

— cal

Power

— W

Work scale — what this compares to

Energy range	Scale	Examples

Reference — common work & energy amounts

Action / source	Work	Category	Notes

Embed this calculator

Embed code

Live preview — identical to the main calculator EXACT MATCH

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Creator & Maintainer

Faiq Ur Rahman is a web designer, digital product developer, and founder of Toolraxy, a growing platform of web-based calculators and utility tools. He specializes in building structured, user-friendly tools focused on health, finance, productivity, and everyday problem-solving.

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Work Calculator: Force, Displacement, and Angle

This work calculator takes force, displacement, and the angle between them, then returns the work done in joules, kilojoules, foot-pounds, and calories. It also computes power if you provide a time. Pick a preset like pushing a cart or lifting a box, or enter your own values. Results update as you type. No sign-up, and the math stays in your browser.

Work is energy transferred when a force moves an object. A crane lifting a beam, a person climbing stairs, a car engine pushing a piston: all of these do work. This calculator runs the standard physics formula W = F × d × cos(θ). It handles force in newtons, kilonewtons, pounds-force, kilograms-force, and dynes. Displacement can be meters, centimeters, millimeters, kilometers, feet, inches, or miles. The angle input lets you model pushes, pulls, and braking. An optional time field returns power in watts. Eight presets cover everyday examples from lifting an apple to a crane lift.

How to Use This Work Calculator

Pick a preset from the dropdown, or leave it on Custom / manual input.
Enter the force. Choose N, kN, lbf, kgf, or dyn.
Type the displacement. Units include m, cm, mm, km, ft, in, and mi.
Set the angle between force and motion in degrees. Use 0° for a push along the motion.
Add a time value if you want power output. Units are seconds, minutes, or hours.
Watch the hero number update as you type.
Read the four tiles for kilojoules, foot-pounds, calories, and power.
Compare your result against the work scale and reference table.

How the Work Calculator Formula Works

Work equals force times displacement times the cosine of the angle between them. That’s the full formula for a constant force acting on an object that moves in a straight line.

Formula: W = F × d × cos(θ)

Formula: P = W ÷ t

W is work in joules. F is force in newtons. d is displacement in meters. θ is the angle between the force vector and the displacement vector. P is power in watts, and t is time in seconds.

The cosine term is what makes the angle matter. At 0°, cos(0) = 1, so the full force does work. At 90°, cos(90) = 0, so no work is done. At 180°, cos(180) = −1, so the work is negative, meaning the force removes energy from the object.

The calculator converts every force unit to newtons and every distance unit to meters before multiplying. Time converts to seconds for the power tile. If force or distance is negative, the tool shows a warning. Zero is allowed and returns zero work. The angle can be any value from −360 to 360 degrees.

Worked Example

Load the sled preset. Force is 100 N. Displacement is 20 m. Angle is 30°.

Step 1: Convert the angle to radians. 30° × π ÷ 180 = 0.5236 rad.

Step 2: Find the cosine. cos(0.5236) = 0.8660.

Step 3: Multiply force by displacement. 100 × 20 = 2,000.

Step 4: Multiply by the cosine. 2,000 × 0.8660 = 1,732 J.

The calculator reports 1,732 J, which is 1.732 kJ or about 1,277 ft-lbs. Power with a 1-second time is 1,732 W. The class banner labels this “High” work. Pulling a sled at an angle wastes some effort. If the rope were horizontal (0°), the same force over the same distance would do 2,000 J. The 30° angle costs you about 13% of the work.

Frequently Asked Questions

What is work in physics?

Work is the energy transferred when a force moves an object. It equals force times displacement times the cosine of the angle between them. The unit is the joule.

How do you calculate work done by a force?

Multiply force in newtons by displacement in meters by the cosine of the angle. A 100 N force over 5 m at 0° gives 500 J. At 60°, it gives 250 J.

What is a joule of work?

A joule is the work done when one newton moves an object one meter. Lifting a small apple one meter does about one joule. A heartbeat does about one joule.

Why does the angle matter in the work formula?

Only the force component along the motion does work. The cosine term extracts that component. At 0°, full force counts. At 90°, none counts. At 180°, work is negative.

What is the difference between work and energy?

Work is the transfer of energy. Energy is the capacity to do work. Both are measured in joules. The work-energy theorem says net work equals the change in kinetic energy.

What does negative work mean?

Negative work happens when the force opposes the motion. Friction and braking do negative work. The object loses energy. Angles above 90° produce negative work in the calculator.

Can work be zero?

Yes. Work is zero if force is zero, displacement is zero, or the angle is 90°. Holding a heavy box stationary does no work in the physics sense.

How do I convert work to foot-pounds?

Divide the work in joules by 1.3558. A 1,000 J result equals about 738 ft-lbs. The calculator shows foot-pounds automatically.

What units does the work calculator support?

Force supports N, kN, lbf, kgf, and dyn. Distance supports m, cm, mm, km, ft, in, and mi. Time supports s, min, and h. Output is in J, kJ, ft-lbs, cal, and W.

What is the work done lifting a 10 kg box 1 m?

The force is 98.1 N, the distance is 1 m, and the angle is 0°. Work equals 98.1 J. That’s the calculator’s preset for this scenario.

What is the work-energy theorem?

The work-energy theorem states that the net work done on an object equals its change in kinetic energy. Positive work speeds it up. Negative work slows it down.

Common mistakes when calculating work?

Forgetting unit conversions, using the wrong angle, and assuming work is always positive. Also, don’t confuse work with power. Work is energy; power is energy per time.