1Which of these is not an SI base quantity?
Electric charge is not a base quantity. It is built from base quantities: electric current × time, and its unit is the coulomb (C).
SI base quantities and units
Every physical quantity is built from seven base quantities, each with its own base unit. Every other unit, the newton and the joule included, is a product of powers of those seven.
SI base quantities and units, explained
The seven SI base units and the quantities they measure, how every other unit is built from them, and why the base unit of mass is the kilogram, not the gram.
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Seven quantities, seven units
- m Length metre, [L]
- kg Mass kilogram, [M]
- s Time second, [T]
- A Electric current ampere, [A]
- K Thermodynamic temperature kelvin, [K]
- mol Amount of substance mole, [mol]
- cd Luminous intensity candela, [cd]
Look up the dimensional formula of any quantity in the dimensional formula tool. When the mole is used, the entities must be named: atoms, molecules, ions, electrons or other particles.
The kilogram is the base unit of mass, not the gram
Base units of length, mass and time in three systems
- SI (MKS) metre, kilogram, second
- CGS centimetre, gram, second
- FPS foot, pound, second
The SI follows the MKS system. A gram is a thousandth of the base unit, which is why the newton is built from kilograms and the dyne from grams.
Every other unit is built from the seven
- N newton, the unit of force kg m s⁻²
- J joule, the unit of work kg m² s⁻²
- W watt, the unit of power kg m² s⁻³
- Pa pascal, the unit of pressure kg m⁻¹ s⁻²
- Hz hertz, the unit of frequency s⁻¹
- C coulomb, the unit of electric charge s A
- V volt, the unit of electric potential kg m² s⁻³ A⁻¹
- Ω ohm, the unit of electrical resistance kg m² s⁻³ A⁻²
- F farad, the unit of capacitance kg⁻¹ m⁻² s⁴ A²
- T tesla, the unit of magnetic field kg s⁻² A⁻¹
For example, force is mass times acceleration, so one newton is one kilogram times one metre per second squared.
Radian and steradian have no dimension
Angle: the radian (rad)
ds / r = m / m = 1
The angle is the ratio of arc length ds / radius r. Lengths cancel in the ratio, so the radian is a pure number.
Solid angle: the steradian (sr)
dA / r² = m² / m² = 1
The solid angle is the ratio of intercepted area dA / radius squared. Lengths cancel in the ratio, so the steradian is a pure number.
Besides the seven base units there are these two more. Both are dimensionless, which is why an angle can go inside sin and cos.
Three questions on SI units
2What is the SI base unit of amount of substance?
The mole (mol) is the base unit of amount of substance. One mole contains exactly 6.02214076 × 10²³ elementary entities, and the entities, such as atoms or molecules, must be named.
3Which of these is the newton written in SI base units?
Force is mass times acceleration, so one newton is kg m s⁻². With grams and centimetres the same force is g cm s⁻², which is the dyne.
SI units: quick answers
What are the seven SI base units?
The metre (m) for length, the kilogram (kg) for mass, the second (s) for time, the ampere (A) for electric current, the kelvin (K) for thermodynamic temperature, the mole (mol) for amount of substance and the candela (cd) for luminous intensity. In order: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).
Is the gram or the kilogram the SI base unit of mass?
The kilogram. The SI follows the MKS system, whose base units are the metre, the kilogram and the second. The gram is the base unit of mass in the CGS system.
What is the newton in SI base units?
One newton is kg m s⁻², because force is mass times acceleration, which is kg times m s⁻².
Are the radian and the steradian base units?
No. Besides the seven base units there are two more units, the radian (rad) for plane angle and the steradian (sr) for solid angle. Both are ratios of like quantities, so they are dimensionless.