Separate quantity, unit and numerical value
A physical quantity stays unchanged during conversion; its unit and numerical value change together. 3 m and 300 cm describe the same length. Select a factor for the quantity: a length factor cannot be used unchanged for area, volume or a ratio.
Braces denote the numerical value in the respective unit.[1]
A ratio of equal quantities equals 1; multiplying by it preserves the physical quantity. Orient the ratio so that the old unit cancels. If the desired units do not remain, the factor or its direction was wrong.
Decimal prefixes and the kilogram exception
SI prefixes denote exact powers of ten. Letter case distinguishes values: m means milli, M mega and k kilo. The added list also includes the prefixes ronna, quetta, ronto and quecto adopted in 2022. Attach a prefix directly to the unit symbol without a space.[1][2]
Mass prefixes attach to gram although kilogram is the SI base unit.
Do not stack prefixes: write mg for 10−6 kg rather than adding another milli to kg. Unit symbols are not freely editable abbreviations. Separate number and unit with a space; symbols take neither a plural ending nor an abbreviation period.
Area and volume factors arise from powers
The exponent applies to the entire prefixed unit symbol.[1]
1 mm2 is 10−6 m2 and 1 mm3 is 10−9 m3. Multiply cm2 by 100 for mm2 and cm3 by 1000 for mm3. If unsure, draw a square or cube: ten subdivisions along each edge produce a hundred small squares or a thousand small cubes.
The litre is exactly 10−3 m3, so one millilitre equals 1 cm3. A cubic metre contains 1000 L and one million cm3. Litres specify volume rather than mass; conversion to kilograms additionally requires density at the appropriate conditions.[1]
Convert numerator and denominator separately
Volume conversion is in the denominator, reversing its effect on the numerical value.
The same litre conversion combines with different numerator prefixes.
A larger denominator unit can yield a larger numerical value for the same ratio: 1 g/cm3 equals 1000 kg/m3. Do not judge the conversion solely by whether each unit is larger or smaller. Speed converts both distance and time; 1 km/h = 5/18 m/s.
Shift temperature values; scale differences
Celsius and kelvin have equal increments but different zeros.[1]
20.0 °C converts arithmetically to 293.15 K. With input resolution 0.1 °C, 293.2 K is an appropriately rounded display. Heating from 20 to 30 °C is a difference of 10 K, not 283.15 K. An exact offset does not increase input measurement precision.
The ideal gas law and radiation laws using powers of thermodynamic temperature require T in kelvin. Heat-capacity calculations often use ΔT; a Celsius difference can then use the same numerical value in kelvin. Decide whether a formula requires a state or a change before converting.
Equal dimensions do not mean the same quantity
Energy in J and torque magnitude in N·m have the same dimension but are different physical quantities. Hz and s−1 likewise share dimensions, while angular speed gains a factor 2π from a full revolution. A dimensional check alone cannot distinguish these meanings.[1]
This factor converts rotation frequency, not a speed already expressed in rad/s.
Watt measures power; watt-hour measures energy. 1 Wh = 3600 J and 1 kWh = 3.6 MJ. Likewise Pa·s is dynamic viscosity and m2/s kinematic viscosity; relating them requires density. Similar-looking numerical values are not interchangeable quantities.
Two complete calculations with unit checks
Density of a small sample
- Given
- Mass 54 g; volume 20 cm3.
- Find
- Find density in g/cm3 and kg/m3.
Form the ratio in the original units.
Convert mass and volume separately to SI.
Calculate the SI ratio.
Result: Density is 2.7 g/cm3 = 2700 kg/m3.
Check: 2700·20·10−6 kg = 0.054 kg reproduces the mass. Applying only the gram factor would omit volume conversion and produce an error by a factor of one million.
Travel at 90 km/h for a quarter minute
- Given
- Constant speed 90 km/h; duration 0.25 min.
- Find
- Find SI speed and travelled distance.
Convert distance and time in the speed ratio.
Convert duration separately.
Calculate distance using matching SI quantities.
Result: 90 km/h = 25 m/s; distance in 15 s is 375 m.
Check: Independently in hours: 0.25/60 h = 1/240 h; 90/240 km = 0.375 km. Both routes agree. Constant speed is a motion assumption, not a conversion rule.
Three exercises with solutions and reverse checks
Convert 12 mm2 to m2 and cm2.
Show hint
Square the corresponding length factor.
Show solution and calculation
12 mm2 = 12·10−6 m2 = 0.000012 m2 and 0.12 cm2.
Reverse check: 0.12·100 = 12 mm2.
Temperature rises from −5 °C to 18 °C. Find both kelvin values and ΔT.
Show hint
Add the offset to endpoints, not the difference.
Show solution and calculation
Initial 268.15 K, final 291.15 K. ΔT = 291.15 − 268.15 = 23 K, equal to the Celsius difference of 23 °C.
A rotor turns at 720 rev/min. Find f in Hz and ω in rad/s.
Show hint
Divide by 60 first, then multiply by 2π.
Show solution and calculation
f = 12 Hz and ω = 24π rad/s ≈ 75.398 rad/s. ω/(2π) = 12 s−1 reproduces rotation frequency.
Exact factors and measured inputs
An exact scale conversion preserves relative uncertainty. For xnew = kxold with exact k, unew = |k|uold. Calculator digits do not add measurement information. An exact temperature offset leaves absolute uncertainty unchanged.
Older energy or power unit names can be ambiguous. The thermochemical calorie has factor 4.184 J and the International Table calorie 4.1868 J. State the specific definition. Likewise decimal SI prefixes must not silently be interpreted as binary powers for data quantities.[3]
For a final check, inspect unit cancellation, order of magnitude and reverse conversion. Then check the physical model conditions of the formula itself. Correct conversion does not, for example, turn varying speed into uniform motion.
Sources for this explanation
Quanta · Updated October 1, 2026
- BIPM: SI Brochure, 9th edition
- NIST: SI Prefix Progress, adoption of four prefixes in 2022
- NIST SP 811 Appendix B.8: conversion factors
Editorial responsibility: Quanta Study editorial team
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This explanation, 2 worked examples and 3 exercises are available in German and English. Structure, source references and mathematical notation undergo automated checks. Calculations, model assumptions and both language versions receive a separate AI review.
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Editorial responsibility, sources and methodsCite this reference page
Quanta. Common conversions to SI. Updated October 1, 2026. https://quanta-study.de/en/formula-sheet/tables/si-umrechnungen
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