Unit of measurement (sv: Måttenhet)

Units are the references we use to measure real world phenomena. They are either defined in relation to real world measurement, or in relation to other units.

A diagram of SI units and their relation to each other
Image by NIST.
License: Public domain.

Quantity

Units themselves do not carry quantities, nor do quantities carry units. That said, both must be notated for concrete measurements. Twelve is a an abstract quantity, and egg is an abstraction of a physical item. A dozen eggs, on the other hand, is something you can buy at the grocery store.

Quantities are often rounded to an extent. Three decimal points or three digits of precision is usually a good rule of thumb where precision is not required. Excessive precision makes you look like a know-it-all, or a conspiracy theorist.

Examples of notation for the frequency 20,327 Hz:

Notation Written
Plain 20,327 Hz
Prefixed 20 kHz
Scientific 2.0327×104 Hz
Engineering 20.033E3 Hz

Prefixes

Quantities are often specified by common prefixes.

From Wikipedia.

Prefix Symbol Factor Power
tera T 1000000000000 1012
giga G 1000000000 109
mega M 1000000 106
kilo k 1000 103
hecto h 100 102
deca da 10 101
(none) (none) 1 100
deci d 0.1 10-1
centi c 0.01 10-2
milli m 0.001 10-3
micro μ 0.000001 10-6
nano n 0.000000001 10-9
pico p 0.000000000001 10-12

Scientific notation

Scientific notation specifies quantity in the format of a × 10n for 1 ≤ a < 10 and any integer n.

The *10^n can be replaced by En, e.g. 48,000 = 4.8*10^4 = 4.8E4

Engineering notation.

Engineering notation is the same as scientific notation, but with exponents only divisible by 3. This makes them align with prefixes and makes verbal communication easier. Re-using the above example, 48,000 would be written as 48*10^3 or 48E3.

SI base units

Most base units have a historical definition grounded in simpler measurements. In modern times, they are put in relation to very specific physical constants in order to increase precision and to account for modern scientific theories.

For more, see Wikipedia: International System of Units.

Time

Time has the common symbol t.

Unit Symbol Defined by
second s Historically, a division of the day

Length

Length has the common symbol l.

Unit Symbol Defined by
meter m Historically, 10,000 km was the distance from the equator to the north pole
inch in or “ 2.54 cm
foot foot or ‘ 12 in
yard yd 3 feet
mile mi 1,760 yd
Swedish mile   10km

Mass

Mass has the common symbol m. It is commonly referred to as weight, but weight is rather force caused by gravity.

Unit Symbol Defined by
gram g Historically, 1 kg is the mass of one liter of water.
pound lb circa 0.454 kg
ounce oz 1/16 pound
stone st 14 pounds

Temperature

Temperature has the common symbol T.

Unit Symbol Defined by
Kelvin K The same scale as celsius, but 0K, absolute zero, equals -273.15°C
Celsius °C Linear scale where 0°C is the freezing temperature of water and 100°C is the boiling temperature of water
Farenheit °F Exact origins vague, but temperature defined in relation to Celsius as 5/9(x − 32) °C
Rankine °Ra As Kelvin is to Celsius, T°Ra = 5/9 × TK

Current

Current uses the symbol I.

Unit Symbol Defined by
Ampere A Historically, coloumb per second

The SI definition of ampere was formerly charge over time, with ampere being defined as coloumb per second. Later revisions has reversed the relation, and an ampere is technically defined directly as 6.241509074×1018 electrons per second.

Unnamed SI derived units

A few units relatively fundamental to the human experience don’t have SI names and are just referred to by their relation to the base units. However, historical named units may exist.

Velocity

meter per second knop

Acceleration

meter per second per second

Area

square meter hectare american football fields

Volume

cubic meter liter ounces

Named SI derived units

Force

Energy

Pressure

Rotation

Frequency

Electrical

Charge

Voltage

Voltage (sv: spänning, literally “tension”) measures electrical potential of charge.

Resistance

Impedance

Effect

Non-SI units


Further reading