Unit of measurement

A unit of measurement is a chosen reference for comparing magnitudes of a physical quantity. A value written as a number times a measurement unit changes its numerical part when the measurement unit changes, while representing the same physical quantity.

A unit of force specifies the reference magnitude used to express a force. The SI derived unit is the newton, defined by $1\mathrm{N}=1\mathrm{kg}\mathrm{m}{\mathrm{s}}^{-2}$, consistent with Newton's second law.

A force of one newton gives a one-kilogram body an acceleration of one metre per second squared when it is the net applied force. A kilogram is a unit of mass, so it cannot replace the newton without also specifying an acceleration or a conventional gravitational reference.^[ref]

A unit of volume is a reference for expressing a three-dimensional volume. In the International System of Units its coherent form is the cubic metre, ${\mathrm{m}}^3$. A litre is $10^{-3}{\mathrm{m}}^3$ and a millilitre is $10^{-6}{\mathrm{m}}^3$.

Length conversions must be cubed: because $1\mathrm{cm}=10^{-2}\mathrm{m}$, one cubic centimetre equals $10^{-6}{\mathrm{m}}^3$, rather than $10^{-2}{\mathrm{m}}^3$. This accounting matters when a measured mass and volume determine a mass density, or when a number density is converted between laboratory and SI conventions.^[ref]

A unit of mass is a reference for expressing mass. The SI base unit is the kilogram; the gram is $10^{-3}\mathrm{kg}$. A unit of mass differs from a unit of force: a balance may infer mass from a gravitational force, but a newton measures force and is not another name for a kilogram.

In a weighing experiment the relation $F=mg$ connects the two, with local gravitational acceleration $g$. An instrument calibrated to display mass therefore incorporates a reference or an assumed local $g$. Moving a force-sensing instrument to a different gravitational environment can change that inference even though the specimen's mass is unchanged.^[ref]

The gram is the unit of mass equal to $10^{-3}$ kilogram. Its symbol is $\mathrm{g}$. Thus $250\mathrm{g}=0.250\mathrm{kg}$.

The kilogram is the SI base unit; prefixes for decimal multiples and submultiples of mass are attached to gram. This special convention gives milligram and microgram, rather than stacked prefixes on kilogram. Mass remains distinct from weight, a force.^[ref]

A milligram is $10^{-3}$ gram, equivalently $10^{-6}$ kilogram. Its symbol is $\mathrm{mg}$. For example, $25\mathrm{mg}=0.025\mathrm{g}$.

The prefix specifies a decimal scaling of mass; it gives no information about measurement precision. An instrument displaying milligrams can still have a larger measurement uncertainty because of calibration, drift or environmental effects.^[ref]

One thousandth of a litre, equal to one cubic centimetre.

A unit of volume equal to one cubic decimetre.

A microlitre, symbol $\mu \mathrm{L}$, is one millionth of a litre, a unit of volume. Since a litre is exactly one cubic decimetre,The prefix micro fixes the factor $10^{-6}$; it does not describe how accurately an instrument can deliver that volume.^[ref]

A $20\mu \mathrm{L}$ sample occupies $0.020\mathrm{mL}$, the same volume as twenty cubes each one millimetre on a side. Delivering $19\mu \mathrm{L}$ instead produces a 5% shortfall: a small absolute volume error can therefore matter greatly in a small-scale chemical reaction.

The microlitre is a volume unit, not a mass unit. To infer delivered volume from a balance measurement, use $V=m/\rho$ with the appropriate liquid density; careful calibration also accounts for effects such as air buoyancy and evaporation. Thus “one microlitre equals one milligram” is an approximation for water under particular conditions, not a unit identity. Gilson's calibration protocol illustrates repeated gravimetric measurements that separate systematic delivery error from scatter between deliveries.^[ref]

The British pharmaceutical volume of 60 minims; 8 make an Imperial fluid ounce.

A unit of volume; the Imperial and United States measures differ. An Imperial fluid ounce contains 8 fluid drachms.

One eighth of an Imperial gallon, containing 20 fluid ounces.

A unit of volume containing 8 Imperial pints.

One sixteenth of an avoirdupois pound, containing 437.5 grains.

A unit of mass containing 16 avoirdupois ounces or 7000 grains.

A unit of time equal to $86400$ seconds.

A unit of area used for scattering cross-sections.

The second, symbol $\mathrm{s}$, is the SI base unit of time. Its definition fixes the unperturbed frequency of the ground-state atomic transition between levels split by hyperfine structure in caesium with mass number $133$ to exactly $9192631770\mathrm{Hz}$. One second therefore corresponds to that many cycles of the specified electromagnetic radiation.^[ref]

A practical atomic clock realizes the reference by interrogating atoms and controlling a reference oscillation. Magnetic fields, motion and environmental effects require corrections: an exact unit definition does not make every physical realization free of measurement uncertainty.

An attosecond is one quintillionth of a second.