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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. 

FAQs (Frequently Asked Questions)

1. What is Joule?

Ans. Joule is the SI unit of work (or energy) which is equal to the work done by a force of 1 Newton to move the point of application 1 meter in the direction in which the force is acting (J = N * m) . 1 Joule is equivalent to 3600th of watt-hour, and it is approximately the amount of energy which is required to lift an apple against Earth’s gravity by a distance of 1 meter. One Joule is also the amount of energy required to move an electric charge of 1 coulomb through an electric potential difference of 1 volt (J = C * V). 

2. What is Horsepower?

Ans. A horsepower is a unit of power that originated in the 17th century and is still used. Horsepower is used to denote how much power a typical horse uses to turn a capstan. In an attempt to sell his steam engines, James Watt tried to quantify the amount of work it can do in a certain interval of time. A typical pony at that time could lift 220 pounds of coal to a height of 100 feet out of a mine in a minute which gave it the power of 22,000 ft-lb/min. Watt incorrectly assumed that a typical horse could perform 330 foot-pounds of work in a minute which is how the definition of horsepower came. In SI units 1 HP = 740 Watts. Horsepower is still used in some countries like the US, where the Imperial system of measurement continues to be used. A Horsepower unit is generally reserved for defining the capacity of air conditioners and engines.