# Unit of Power

## Introduction

In Physics, work is done when a force acting on an object results in its displacement. Work done is not determined by the amount of time the force took to cause the displacement. Sometimes the work is done quickly, and other times it might be slow and take longer. If a bodybuilder and a sixth-grader carry a weight of 10 kgs up a flight of stairs, then the bodybuilder would most likely take less time than the sixth-grader to finish the same job. Here we can say that the bodybuilder has a higher power rating than the sixth-grader.

So we see it is the power that has to do with the rate at which work is done. We will look into a few concepts around power, work, and energy in this article and discuss the unit of power in si unit and provide you with units of power list in different measurement systems.

### Formulas For Work and Power

The word “work” has a different meaning in the world of Physics. In Physics, work done is given by force applied on an object to move a distance (d), and its formula is:

W = F * d.

Even after applying a lot of force, if an object does not move, then in the eyes of a physicist, no work is done.

The word “power” is also used differently by physicists. Power is the ratio of work and time, i.e. the time taken to complete a work gives the power of an entity. It is expressed mathematically as:

Power = Work/Time or P = W/t.

Power is the rate at which work is done, and it is also the rate at which energy (heat and electrical) is transferred. While studying electricity, you would find the power is defined as:

Power = V * I, where V is the voltage within the circuit, and I is the current through the circuit.

We could derive another formula for power from the formula for work. Since Work = force * distance and power = work/time, then power = (force * distance)/time. Now we know that velocity = distance/time hence:

Power = force * velocity = F * V

### What is the SI Unit of Power in Physics?

To define units of power let us look into how the SI system works. The SI or metric system has only 7 base units, and all the other units are derived from these base units. In the metric system, mass is measured in kilograms, length in meters, and time in seconds. Unit of force (which is mass times acceleration) is kg-m/s2. From this, we can get the unit of work as kg-m2/s2. But this unit gets cumbersome to write in every equation, so scientists have defined another unit Joule (J), which is named after the physicist James Prescott Joule. I Joule = 1 kg-m2/s2and it is the unit of energy in the SI system.

Power is work divided by time; hence the SI unit of power is joules/second. Scientists have given a name for this unit, and the unit of power in the SI unit is Watt (named after James Watt, the Scottish inventor of steam engines that helped launch the Industrial revolution.).

1 Watt = 1 Joule/second = 1 kg-m2/s3

### Submultiples and Multiples of Watt

The SI multiples and submultiples of Watt are listed in the table below:

 Submultiples of Watt Name Symbol Value deciwatt dW 10-1 W centiwatt cW 10-2 W milliwatt mW 10-3 W microwatt 𝜇W 10-6 W nanowatt nW 10-9 W picowatt pW 10-12 W femtowatt fW 10-15 W attowatt aW 10-18 W zeptowatt zW 10-21 W yoctowatt yW 10-24 W

 Multiples of Watt Name Symbol Value decawatt daW 101 W hectowatt hW 102 W kilowatt kW 103 W megawatt MW 106 W gigawatt GW 109 W terawatt TW 1012 W petawatt PW 1015 W exwatt EW 1018 W zettawatt ZW 1021 W yottawatt YW 1024 W

### Units of Power in Other Systems and their Equivalent in Watts

You can find below units of power list with formula on how to convert them into Watt

 Unit Equivalent in Watt Horsepower (HP) 746 W BTU (British Thermal Unit) 1 Watt = 9.47 * 10-4 BTU Foot pounds 1 Watt = 0.737 foot-pounds Calories per sec 1 Watt = 0.24 calories per second

### How Can Varying Power Be Measured?

In certain setups like houses, the power is used to varying degrees. For example, we use less electricity during the day than at night when all the lights are on. In these situations, power is expressed in three ways:

• Instantaneous Power - This is the power measured at any given instant of time.

• Average Power - When you measure power over long periods of time, you can get average power. This can be calculated by plotting a graph of power vs time and finding the area under the curve, which gives the total work done, and then dividing it by the total time.

• Peak Power - The maximum value of instantaneous power in a specific system over a long period of time is peak power. In systems like car engines and stereo systems, peak powers occur much higher than the average power. But peak power is maintained only for a very short duration to avoid damages.