Base units in the context of Multiple (mathematics)

SI derived units are units of measurement derived from theseven SI base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionless, as when the units cancel out in ratios of like quantities.SI coherent derived units involve only a trivial proportionality factor, not requiring conversion factors.

The SI has special names for 22 of these coherent derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m), the SI derived unit of area; and the kilogram per cubic metre (kg/m or kg⋅m), the SI derived unit of density.

The specific weight, also known as the unit weight (symbol γ, the Greek letter gamma), is a volume-specific quantity defined as the weight W divided by the volume V of a material:$${\displaystyle \gamma ={\frac {W}{V}}\ .}$$Equivalently, it may also be formulated as the product of density, ρ, and gravity acceleration, g: $${\displaystyle \gamma =\rho \,g.}$$Its unit of measurement in the International System of Units (SI) is the newton per cubic metre (N/m), expressed in terms of base units as kg⋅m⋅s.A commonly used value is the specific weight of water on Earth at 4 °C (39 °F), which is 9.807 kilonewtons per cubic metre or 62.43 pounds-force per cubic foot.