# Unit of Power – SI Unit

Last Updated : 19 Mar, 2024

Unit of Power is Watt (J/s). It is named after the scientist James Watt in recognition of his contributions towards developing the steam engine. Power is defined as the rate at which work is done. Hence, the base unit of power is the unit of work divided by the unit of time. Several units used to measure the magnitude of power include Watt, Horsepower (HP), erg/s, BTU/hr etc.

In this article, we will learn the definition of Power, its unit in various systems, conversion between them, some practice problems and frequently asked questions related to the unit of power.

## Definition of Power

PowerÂ is a physical quantity that is a measure of energy transfer rate. Therefore, power is defined as follows,

Power is the rate of work done or the rate at which energy is transferred from one system to another.

In physics, Power is denoted by the symbol P.

### Power Formula

Power is calculated using the following formula:

P = W/t

where,

P = Power gain or loss.

W = Work done, and

t = Time taken

## What is Unit of Power?

Unit of Power is a measure of the rate of work done or the rate at which energy is transferred from one system to the another. It represents the unit work done in unit amount of time.

The formula for power is Work done divided by the time taken. Thus, unit of power would directly depend upon the unit of the work done and the unit of time.

The SI unit of Work is Joule (J) and that of time is second (s). Thus, SI unit of Power would be J/s. It is called as Watt (W) in recognition to the name of the scientist James Watt.

Hence, SI unit of Power is Watt. Other units of power are horse power, ergs/s, BTU/hr, etc.

### Dimensional Formula for Power

The dimensional formula for power is [M1L2 T-3]. It can be derived using the formula for power, i.e. Power = Work Done / Time Taken

Substituting the dimensions for work and time, we get,

Dimension of Power = [M1L2T-2] / [M0L0T1]

Dimension of Power = [M1L2T-3]

### What is 1 Watt?

1 Watt is basically the SI unit of Power, i.e 1 J/s. It represents the power in which 1 Joule of work is done in 1 second of time.

## SI Unit of Power

S.I. unit of power is joules per second abbreviated as J/s and also called as Watt (W). It can be derived as follows:

• SI unit of Work = Joule (J)
• SI unit of time = second (s)

We know that Power = Work / Time

Hence, SI unit of Power = SI unit of Work / SI unit of Time = Joule/second = J/s = Watt (W).

SI Unit of Power is Watt (W).

## Unit of Power in other Systems

Unit is a standard measurement of any physical quantity that is used to express the size or magnitude of any physical quantity. There are different units chosen for the measurement of same physical quantity for its convenient representation in terms of magnitude. The unit of power in different systems is mentioned below:

System

Unit

MKS system

Watt (J/s)

CGS system

erg/s

Imperial system

BTU/hr

Others

cal/s, Horsepower

Similar to other SI units, the value of Watt can be adjusted to different magnitudes as shown in the table below:

Unit of Power

Symbol

Equivalent in Watt (W)

Watt

W

1

Milliwatt

mW

10-3

Microwatt

Î¼W

10-6

Nanowatt

nW

10-9

Kilowatt

kW

103

Megawatt

MW

106

Gigawatt

GW

109

## Conversion Between Units of Power

Conversion factors for different units are given in form of a table as follows. These conversion factors can be used to convert any unit of power to its corresponding another unit.

From/To

Watt

Erg/s

Horsepower

Kilowatt

Megawatt

Gigawatt

BTU/hr

Cal/s

Watt

1

107

0.00134

10-3

10-6

10-9

3.412

0.239

Erg/s

10-7

1

1.34 x 10-10

10-10

10-13

10-16

3.412 x 10-7

2.39 x 10-8

Horsepower

746

7460000000

1

0.746

0.000746

0.000000746

2536.4

177.62

Kilowatt

103

1010

1.34

1

0.001

0.000001

3400

238.1

Megawatt

106

1013

1340

1000

1

0.001

3400000

238095

Gigawatt

109

1016

1340000

1000000

1000

1

3400000000

238095000

BTU/hr

0.293

2.931 x 106

0.000394

2.941 x 10-4

2.941 x 10-7

2.941 x 10-10

1

0.0700

Cal/s

4.2

42000000

0.0056

0.0042

0.0000042

0.00000042

14.28

1

## Sample Problem on Unit of Power

Problem 1: Convert 2500 Watts to Kilowatts.

Solution:

We know that, 1 kW = 1000 W

or, 1 W = 0.001 kW

Thus, 2500 W = 2500 x 0.001 kW

â‡’ 2500 W = 2.5 kW

Thus, we get 2500 W equal to 2.5 kW.

Problem 2: Convert 3.5 Kilowatts into SI unit of Power.

Solution:

We know that, SI unit of Power is Watt.

Also, 1 kW = 1000 W

â‡’ 3.5 kW = 3.5 x 1000 W

â‡’ 3.5 kW = 3500 W

Therefore, we get 3.5 kW equal to 3500 W.

## Practice Problems on Unit of Power

Problem 1: Convert 4200 Watts to Cal/s.

Problem 2: Convert 220 Kilowatts to Megawatts.

Problem 3: Convert 4 Horsepower to Watts.

Problem 4: Convert 2.5 Kilowatts to Horsepower.

Problem 5: Convert 8 Megawatts to BTU/hr.

## FAQs on Unit of Power

### What is the SI Unit of Power?

The unit of Power in the International System of Units (SI) is the Watt (W).

### What is meant by 1 Watt of Power?

One Watt of Power describes the rate of work done such that 1 Joule of work is done 1 second of time.

### What are some commonly used units of power?

Commonly used units of power are Watt, Kilowatts, Megawatts, Horsepower, etc.

### What is the formula of Power?

The formula of power is : Power = Work/Time

### What is SI unit of Work done?

The SI unit of work done is Joule.