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Work and Power Calculator

Solve W = F·d·cos θ and P = W ÷ t for work, force, distance, angle, power or time, with newton, foot, joule, kWh and horsepower units built in.

500 J
Work done

W = F · d · cos θ

  • W = 50 N × 10 m × cos 0° = 500 J
  • 500 J = 0.5 kJ = 119.5029 cal = 0.00013889 kWh = 368.7811 ft·lbf
  • The force is fully aligned with the motion, so cos θ = 1 and all of it does work.

These equations assume a constant force acting along a straight path. If the force varies you need the integral W = ∫F·ds instead, and P = F·v holds only while the speed is steady. One joule is one newton-metre; one watt is one joule per second.

What is the Work and Power Calculator?

Work is force multiplied by the distance moved along the force, W = F·d·cos θ, measured in joules. Power is how fast that work is done, P = W ÷ t, measured in watts: one watt is one joule per second.

  • Three linked equations: W = F·d·cos θ, P = W ÷ t and P = F·v
  • Solves for any variable, including the angle between force and motion
  • Unit dropdowns converted to SI before any arithmetic happens
  • Answers restated in J, kJ, cal, kWh and ft·lbf, or W, kW, hp and BTU/h
  • Step-by-step working with the rearranged formula, copyable in one click
  • 100% local — the numbers never leave your browser

How to use the Work and Power Calculator

  1. 1

    Pick the equation you need: work W = F·d·cos θ, power P = W ÷ t, or power at constant speed P = F·v.

  2. 2

    Choose the unknown in the Solve for dropdown — work, force, distance, angle, power, time or speed.

  3. 3

    Enter the remaining values and set each unit dropdown next to them.

  4. 4

    For the work equation, set the angle θ between the force and the direction of motion; 0° means the force is fully aligned.

  5. 5

    Read the answer and press Copy working to take the rearranged formula and every step with you.

About the Work and Power Calculator

The ByteTools Work and Power Calculator solves the three equations that tie force, distance, energy and time together: W = F·d·cos θ, P = W ÷ t, and the constant-speed case P = F·v. Choose which quantity is unknown, fill in the rest, and the tool rearranges the formula, converts every entry to SI units first, then prints the working line by line.

Unit dropdowns cover newtons, kilonewtons and pounds-force for force, metres, kilometres and feet for distance, and joules, kilojoules, calories, kilowatt-hours and foot-pounds for energy. Power comes back in watts, kilowatts, horsepower and BTU per hour at the same time, so a physics homework answer and an engineering estimate both come out of the same box.

Every calculation runs in JavaScript inside your browser. Nothing you type is uploaded, logged or sent to a server, so the answers appear as you type and the page keeps working offline once it has loaded. That makes it safe to use for coursework, site estimates or anything else you would rather not paste into a web form.

Frequently asked questions

What is the formula for work in physics?

Work equals force times distance times the cosine of the angle between them: W = F·d·cos θ. When you push straight along the direction of motion the angle is 0°, cos θ = 1, and the formula simplifies to W = F·d. The answer is in joules when force is in newtons and distance is in metres.

What is the difference between work and power?

Work is the total energy transferred, measured in joules, while power is the rate at which that transfer happens, measured in watts. Lifting a box onto a shelf takes the same work whether you do it in one second or one minute, but doing it in one second needs sixty times the power.

Why does a force at 90 degrees do no work?

Only the part of the force pointing along the motion transfers energy, and at 90° that component is zero because cos 90° = 0. That is why carrying a suitcase horizontally does no physical work on it, even though your arm gets tired holding it up.

How do I convert watts to horsepower?

Divide watts by 745.7 to get mechanical horsepower, so 1 kW is about 1.341 hp. This calculator shows the horsepower figure alongside watts and kilowatts automatically, using the exact factor 745.6998715822702 W per hp.

When can I use P = F·v instead of P = W ÷ t?

P = F·v gives the instantaneous power only while the force and the speed are both steady, such as an engine pushing against constant drag at cruising speed. If either changes during the interval, work out the total work first and divide by the time instead.

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