Force, Work and Power

Written byOleh Soloninupdated 5 October 2026

Force

Mass, kg

Acceleration, m/s²

9.80665 is gravitational acceleration.

Distance, m

Angle between force and motion, °

0° means the force acts along the motion; at 90° it does no work.

Time, s

Result

Force, N98.0665
Work, J196.133
Power, W39.2266
Power, kW0.03923
Horsepower0.05333
Weight on Earth, N98.0665
Working
F = m × a = 10 × 9.80665 = 98.0665 N W = F × d = 98.0665 × 2 = 196.133 J P = W ÷ t = 196.133 ÷ 5 = 39.2266 W

A chain of three formulas

Force from mass and acceleration or entered directly, work W = F · d · cos θ with the angle, and power P = W ÷ t, with the working in watts, kilowatts and horsepower.

Three formulas form a chain: force F = m · a, work W = F · d · cos θ, power P = W ÷ t. Lifting 10 kg through 2 m in 5 s against gravity takes a force of 98.07 N, does 196.13 J of work and needs 39.23 W.

Problems often give the force directly, "a 20 N force moves a box 5 m", so choose "Force is given". When the force acts at an angle to the motion, only its component along the path does work, hence the cosine.

How to use

Choose how to set the force: from mass and acceleration, or a value in newtons.
Enter the distance, the time and, if the force is not along the motion, the angle between them.
Read the force, work and power with step-by-step working.

Force, work and power formulas

Newton's second law: F = m · a, in newtons from kilograms and m/s². Work: W = F · d · cos θ, in joules; at θ = 0° the cosine is 1 and W = F · d, at 90° no work is done, beyond 90° the work is negative. Power: P = W ÷ t, in watts.

With an angle: 20 N at 60° over 5 m does 20 × 5 × cos 60° = 20 × 5 × 0.5 = 50 J; if that takes 10 s, the power is 5 W.

Worked out with this calculator.
Angle θ	cos θ	Work by 20 N over 5 m
0°	1	100 J
30°	0.866	86.6 J
45°	0.707	70.71 J
60°	0.5	50 J
90°	0	0 J
120°	−0.5	−50 J

What this calculator shows

Force in newtons, work in joules and power in watts
Power in kilowatts and metric horsepower
Step-by-step working with your numbers
Weight on Earth when the force comes from mass

What to keep in mind

The force is constant along the path and the angle between force and motion does not change.
Metric horsepower is 735.49875 W.

FAQs

How do I calculate work?

Multiply force by distance and by the cosine of the angle between them: W = F · d · cos θ. Along the motion it is just F · d: 20 N × 5 m = 100 J.

How do I calculate power?

Divide work by time: P = W ÷ t. 196 J in 5 s is 39.2 W.

What if the force is at an angle?

Multiply by the cosine of the angle: 20 N at 60° over 5 m does 20 × 5 × 0.5 = 50 J. Enter the angle in the calculator.

Why is no work done holding a weight still?

Because nothing moves: d = 0, so W = F · d = 0. The same goes for a force at right angles to the motion, since cos 90° = 0.

How is force different from weight?

Weight is one particular force: mass times gravitational acceleration, 9.80665 m/s². A 10 kg mass weighs 98.07 N on Earth.

What force acts on a 10 kg mass?

98.07 N under gravity, from 10 × 9.80665. Lifting it steadily through two metres, the lifting force does 196.13 J of work (gravity itself does −196.13 J), and doing so in five seconds takes 39.23 W.

Why is the work zero when I just hold something up?

Work is force times displacement, and holding still moves nothing. The muscles tire regardless, but no mechanical work is done on the load.

Worked example

Lifting a load

Input: 10 kg through 2 metres in 5 seconds

Output: Force 98.07 N, work 196.13 J, power 39.23 W

Note: F = 10 × 9.80665 = 98.0665 N; W = 98.0665 × 2 = 196.133 J; P = 196.133 ÷ 5 = 39.2266 W.

Useful links

All tools in Math & Statistics

Force, Work and Power

Result

Related tools

Watts to Amps and Amps to Watts

Power Converter: kW, hp, BTU/h, kcal/h

Density, Mass and Volume

Useful links