Unit systems, prefixes and symbols

Choose the physical quantity first, then the unit convention. Identical dimensions do not always mean the same quantity: torque and energy, or gray and sievert, need distinct interpretations.

The SI system

The seven SI base quantities are length (meter, m), mass (kilogram, kg), time (second, s), electric current (ampere, A), thermodynamic temperature (kelvin, K), amount of substance (mole, mol), and luminous intensity (candela, cd). Derived units combine them: a newton is kg·m/s² and a joule is N·m.

International Bureau of Weights and Measures — SI definitions

US customary, Imperial and legacy measures

An international inch is exactly 25.4 millimeters, and an international foot is exactly 0.3048 meters. A US survey foot is a distinct legacy definition: 1200/3937 meters. Keep the recorded definition when interpreting old survey data.

Common definitions that must stay distinct
MeasureDefinition
US liquid gallon3.785411784 L
Imperial gallon4.54609 L
US dry gallonOne eighth of a Winchester bushel (2150.42 cubic inches)
Metric tonne1000 kg
US short ton2000 avoirdupois pounds
UK long ton2240 avoirdupois pounds

Cups and spoons also vary. The converter names a cup’s convention explicitly; a liquid-volume conversion cannot determine ingredient mass without density.

NIST conversion definitions · NIST survey-foot guidance · NIST household measures

SI prefixes

A prefix multiplies the unit by a power of ten. For squared or cubed units, raise the entire prefixed unit to that power: 1 cm² = 10⁻⁴ m² and 1 cm³ = 10⁻⁶ m³.

SI prefix names and case-sensitive symbols
PrefixSymbolMultiplier
quettaQ1030
ronnaR1027
yottaY1024
zettaZ1021
exaE1018
petaP1015
teraT1012
gigaG109
megaM106
kilok103
hectoh102
decada101
decid10-1
centic10-2
millim10-3
microµ10-6
nanon10-9
picop10-12
femtof10-15
attoa10-18
zeptoz10-21
yoctoy10-24
rontor10-27
quectoq10-30

BIPM — the complete SI prefix table · Convert prefix scales

Decimal and binary data

One byte is eight bits. Decimal prefixes use powers of 1000: 1 MB = 1,000,000 bytes. IEC binary prefixes use powers of 1024: 1 MiB = 1,048,576 bytes. The same distinction applies to transfer rates. 8 Mbit/s = 1 MB/s; protocol overhead is outside unit conversion.

NIST — IEC binary prefixes · Storage converter · Transfer-rate converter

Symbols, scales and quantity context

Symbols are case-sensitive: m is milli while M is mega; B means byte. Unit names may have regional spellings, but aliases must never merge distinct definitions.

Absolute temperature needs an offset. A temperature interval does not: an increase of 1 °C equals 1 K or 1.8 °F. Heat coefficients use intervals even when their unit labels contain °C or °F.

Typography uses the stated DTP/CSS convention of 72 points or 96 CSS reference pixels per inch. Actual display pixels and historical printer’s points need different context.

Temperature-interval converter · W3C — CSS unit conventions

Exact definitions and rounded results

An exact definition can produce an endlessly repeating decimal. The engine calculates separately from display rounding, using binary floating point for physical quantities and arbitrary-precision integers for number bases. Scientific notation prevents small nonzero values from being displayed as zero. More displayed digits do not establish more accurate measurements.

Reciprocal conversions need positive inputs; logarithmic levels can be negative. Invalid, overflowing or underflowing conversions show an error rather than a misleading number.

Sources, review policy and correction process · Browse all converters