# SI derived units

SI is built on seven fundamental standards called base units. All other SI units are derived by multiplying, dividing or powering the base units in various combinations, For example:

mechanical work is force applied multiplied by distance moved and has the unit newton metre written as Nm

speed is distance divided by time and has the unit metre per second written as ms-1

area is length multiplied by width and has the unit m2.

## SI derived unit names and symbols

A significant number of SI derived units have been named in honour of individuals who did ground-breaking work in science.

### James Watt

James Watt (1736–1819) was a Scottish inventor and mechanical engineer who developed a more efficient steam engine. The unit of power, the watt, has been named in his honour.

Painting by Henry Howard.

**Rights:**Public domain

James Watt (1736–1819) was a Scottish inventor and mechanical engineer who developed a more efficient steam engine. The unit of power, the watt, has been named in his honour.

The watt is a commonly used unit. In the article renewable energy the section on solar power states: The amount of solar radiation that reaches the Earth is 340 watts per square metre of surface (340 W m-2).

### James Prescott Joule

James Prescott Joule (1818–1889) was an English physicist who studied the nature of heat and its relationship to mechanical work. The unit of energy, the joule, has been named in his honour.

**Rights:**Public domain

James Prescott Joule (1818–1889) was an English physicist who studied the nature of heat and its relationship to mechanical work. The unit of energy, the joule, has been named in his honour.

The article on the body’s energy requirements states: ...the boy’s total metabolic rate is about 11,000 kilojoules per day and the girl’s 9200 kilojoules per day.

If a unit has been named in honour of a famous scientist, the unit name is written with a lower case first letter and the symbol is most often the capitalised first letter. For example, the unit of energy is the joule, named in honour of James Prescott Joule, and has the symbol J. However, with the ohm, its symbol is the capitalised form of the Greek letter omega (Ω), not O. This is because the symbol ‘O’ can be confused with the number zero.

Physical quantity

Unit

Symbol

Scientist named after

Electric charge

coulomb

C

Charles-Augustin de Coulomb

Electric potential difference

volt

V

Alessandro Volta

Electric resistance

ohm

Georg Simon Ohm

Energy

joule

J

James Prescott Joule

Force

newton

N

Isaac Newton

Frequency

hertz

Hz

Heinrich Hertz

Power

watt

W

James Watt

Pressure

pascal

Pa

Blaise Pascal

Acceleration

metre per second squared

m s-2

Area

square metre

m2

Density

kilogram per cubic metre

kg m-3

Heat capacity

joule per kelvin

J K-1

Speed

metre per second

m s-1

## Relationships between units

The quantities connected by blue lines multiply and those connected by red lines divide. For example, watt (W) is joule divided by second (1 W = 1 Js-1) whereas newton (N) is kilogram multiplied by acceleration (1 N = 1 kg ms-2).

### Relationship between units

Table showing how five of the seven base units are combined to form a number of derived units with special names and symbols.

**Rights:**The University of Waikato Te Whare Wānanga o Waikato

## Physics relationships

A number of useful physics relationships can be derived. For example:

pressure = force/area

work = force x distance

resistance = voltage/current.

Here are three worked examples using these relationships.

The area of the heel of a women’s fashion shoe is 30 mm2. The effective body weight force when standing completely on one heel for an average sized woman is 600 N. Calculate the heel pressure.

Pressure

= force/area

= 600/30

= 20 N/mm2 → 20 x 106 N/m2 (there are 1 million mm2 in 1 m2)

= 20 million Pa

Calculate the work done when a 65 kg teenage boy climbs a flight of stairs that lifts him 20 m above ground level.

Work

= force x distance

= (65 x 10) x 20

= 13,000 joules or 13 kilojoules

A domestic light bulb operates at a voltage of 240 volts and takes a current of 0.1 amp. Calculate the resistance of the light bulb.

Resistance

= voltage/current

= 240/0.1

= 2,400 ohms

**Published:**17 August 2011