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.
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.
James Prescott Joule (1818–1889) was an English physicist who studied the nature of heat and its relationship to mechanical work.
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.
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 9,200 kilojoules per day.
| 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.
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.
Example 1
The area of the heel of a stiletto 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
Example 2
Calculate the work done when a 65 kg teenager climbs a flight of stairs that lifts them 20 m above ground level.
Work
= force x distance
= (65 x 10) x 20
= 13,000 joules or 13 kilojoules
Example 3
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
Related content
Find out more about the SI units used in scientific measurements – these can be derived from just seven fundamental standards called base units. A number of non-SI units are still commonly used, you might want to explore this further in Measurement systems.
Expressing quantities describes how unit symbols and names should be written and used and how the values of quantities should be expressed. Powers of 10 explains the prefix names and symbols for decimal multiples and submultiples of SI units.
Related activities
Measuring foot pressure provides practice using SI units, derived units and prefixes.
Precision and accuracy provides various datasets for students to judge precision and accuracy in scientific settings.
