# Work and Power Calculator

Created by Luciano Mino
Last updated: Jul 23, 2022

The work and power calculator can help you calculate the power produced by a machine or obtain the amount of work it will perform during a given period.

This tool contains both a power calculator and a work done calculator. Within a few paragraphs, we will talk about:

• Work and power definitions;
• The power formula;
• Work formula;
• How to calculate work from power and time.

## Work definition and formula

First, let's explain the definition of work.

Work is a concept referring to the energy transferred to an object by an external force along the direction of movement of the object.

Like energy, the unit of work is the joule (J) or kg·m²/s².

### Work formula

Mathematically, we define work as the dot-product between the force $\overrightarrow{F}$ and the displacement $\overrightarrow{s}$ produced on the body:

$W=\overrightarrow{F}\cdot \overrightarrow{s}$

Alternatively, we can skip the dot product using $\theta$, the angle between $\overrightarrow{F}$ and $\overrightarrow{s}$:

$W=||\overrightarrow{F}||\ ||\overrightarrow{s}||\cos{\theta}$

## Definition of power and power formula

Power is the rate of change of work. In other words, it is the ratio between the amount of work performed by a machine and the time it took to produce said work.

Its unit is the watt (W) which is equivalent to kg·m²/s³.

### Equation for power

The equation for power is straightforward:

$P = \frac{W}{t}$

where $W$ is the work produced by the machine during $t$, the time.

🙋 With this equation, you can also calculate the work produced by a machine by multiplying its power by the time during which the machine is running.

## How to use the work and power calculator

To use our tool, simply input any two parameters (work, time, or power), and the calculator will automatically complete the missing variable.

This calculator can also find the work done by a force! Just toggle the advanced mode, and you can obtain its value from the force and displacement.

Luciano Mino
Work
J
Time
sec
Power
W
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