SI Units

Core Concepts

Standard International (SI) Units are the basis for all physical measurements, and therefore have an incredible importance in science today. In this article, we describe the base units, the derived units, and some important non-SI units.

Topics Covered in Other Articles

What Are SI Units?

The International System of Units (SI), sometimes referred to as the metric system, is the international measuring standard. The SI Units serve as a consistent way of communicating measurements like temperature, mass, and distance. It allows people from all over the world to be able to speak the same language when discussing physical quantities.

The Seven Base Units

The SI Units system is based around seven base units:

seconds for measuring time
meter for measuring length
kilogram for measuring mass
ampere for measuring electric current
Kelvin for measuring temperature
mole for measuring amount of a substance
candela for measuring luminous intensity

The Derived Units

A derived unit is a unit of measurement derived from the seven SI base units. Derived units may not have dimensions or are a combination of base units. For example, the unit for area is a derived unit. To calculate area you multiply length by width, a distance by a distance, therefore the unit is a square meter (m²).

Named Derived Units

There are a total of 22 derived units with special names.

Quantity	Name	Symbol	Base Units
Pressure	pascal	Pa	kg m^-1 s^-2
Force	newton	N	kg m s^-2
Energy	joule	J	kg m² s^-2
Frequency	hertz	Hz	s^-1
Power	watt	W	kg m² s^-3
Voltage	volt	V	kg m² s^-3 A^-1
Charge	coulomb	C	A s
Angle	radian	rad	1
Solid Angle	steradian	sr	1
Electrical Capacitance	farad	F	kg^-1 m^-2 s⁴ A²
Electrical Resistance	ohm	Ω	kg m² s^-3 A^-2
Electrical Conductance	siemens	S	kg^-1 m^-2 s³ A²
Magnetic Flux	weber	Wb	kg m² s^-2 A^-1
Magnetic Flux Density	tesla	T	kg s^-2 A^-1
Electrical Inductance	henry	H	kg m² s^-2 A^-2
Temperature relative to Kelvin	degree Celsius	°C	K
Luminous Flux	lumen	lm	cd
Illuminance	lux	lx	cd m²
Radioactive decays per second	becquerel	Bq	s^-1
Absorbed dose of ionizing radiation	gray	Gy	m² s^-1
Equivalent dose of ionizing radiation	sievert	Sv	mol s^-1
Catalytic activity	katal	kat	mol s^-1

Unnamed Derived Units

Mathematical combinations of SI base units make up many more derived units that don’t have special names.

Quantity	Symbol	Base Units
Area	A	m²
Volume	V	m³
Density	ρ	kg/m³
Speed	v	m/s
Acceleration	a	m/s²
Specific Volume	v	m³/kg
Concentration	M	mol/dm³ (mol/L)
Angular Velocity	rad/s	rad/s
Current Density	A/m²	A/m²
Wave Number	m^-1	m^-1

The Accepted Non-SI Units

There are also a number of units in the metric system that are neither base units nor derived units. Because they are multiples or fractions of SI units or because they are practical, these units are included in the metric system. Accepted units are units that can be used with the SI Units. In other words, accepted units are accepted in most journals and research papers but are not base units of the SI system.

Quantity	Name	Symbol
TIme	minute	min
Time	hour	h
Time	day	d
Length	astronomical unit	au
Length	inch	in
Length	foot	ft
Length	mile	mi
Plane Angle	degree	°
Plane Angle	second	“
Plane Angle	minute	‘
Area	hectare	ha
Volume	liter, milliliter	l, ml
Volume	cubic centimeter	cc
Mass	tonne	t
Mass	dalton	Da
Density	gram per milliliter	g/ml
Energy	electron volt	eV
Sound	bel, decibel	B, dB

SI Units Practice Problems

Problem 1

An imprecise physicist might call a certain derived unit a “newton meter per second”. What derived unit would he or she therefore be talking about?

Problem 2

The Ideal Gas Law has the following equation:

$PV=nRT$

P is for pressure
V is for volume
n is for moles
T is for temperature
R is a constant

What base SI units are involved in the Ideal Gas Law? (i.e. not just the derived units)

SI Units Practice Problem Solution

The Watt
kg, m, s, mol, K