Reading a quantity value
Length is a quantity, metre its SI unit and 0.25 the numerical value in 0.25 m. Writing the same length as 25 cm changes the number, not the length. A number alone does not identify a measurement. Neither does a unit alone: an experimental value of 5 s needs context such as travel time, period or waiting time.[5]
The chosen unit determines the numerical value.
Units remain part of a quantity equation. Evaluate v = l/t in metres and seconds or consistently in kilometres and hours. Mixed units are possible but require explicit conversion. A distance of 2.4 km in 120 s gives 2 400 m/120 s = 20 m/s. The bare calculation 2.4/120 would not identify that result.
What the seven rows cover
Second, metre and kilogram correspond to time, length and mass. Ampere belongs to electric current, kelvin to thermodynamic temperature and mole to amount of substance. Candela describes luminous intensity in a given direction; it is neither a lamp’s total light output nor illuminance on a surface. The base-unit list is complete. Newton, joule, volt and lux are derived from it, not additional base units.[2]
The choice of base quantities belongs to the agreed quantity system. This does not require each base unit to be realised independently in a laboratory. The current kilogram definition, for example, involves metre and second. Base refers to a structural role in the unit system, not a ranking of physical importance.[1]
Exact constants and real measurement procedures
Since 20 May 2019, fixed numerical values of seven defining constants determine the SI. The additional table provides their complete values and units. Their combination matters: h has unit J·s = kg·m2/s. Once second and metre are established, fixing h determines the mass unit. A simplified one-constant-per-unit picture hides these relationships.[2]
The Planck constant’s unit links mass, length and time.
An exactly defined metre does not make a ruler measurement exact. Practical realisation transfers the definition to instruments and procedures; calibration, resolution and experimental conditions limit the result. A constant-based definition supplies a stable reference, not extra decimal places for an imprecise measurement. A measurement report should include the value and uncertainty.[1]
Distinguishing dimension and unit
Dimension describes a quantity’s kind without selecting a unit. Length has dimension L whether expressed in metres or centimetres. Velocity has dimension L·T−1. The dimension table uses capital T for time and Θ for temperature; the quantity symbol T for temperature is therefore not automatically a dimension symbol. Likewise, the luminous-intensity dimension symbol J is not the unit joule J. Context prevents these ambiguities.[1]
Dimension is on the left and the coherent SI unit on the right.
A dimension check can detect a missing time factor but proves neither a physical model nor its numerical coefficient. l/t and 2l/t have identical dimensions. Energy and torque also share a dimension despite being different quantities. Correct calculation requires a unit check and justification of the equation.
Using mass, temperature and amount correctly
Mass is expressed in kg and weight force in N. With a specified local gravitational acceleration, the model gives FG = mg; identical masses can have different weights at different locations. Prefixes for small masses attach to gram: 1 mg = 10−3 g = 10−6 kg. μkg is not an allowed SI prefix construction.[3][1]
Kelvin has no degree sign. For a temperature value, T/K = t/°C + 273.15, while temperature differences of 1 K and 1 °C have equal size. Ratios of absolute temperatures, as in the ideal gas law, require kelvin. For amounts of substance, specify the entity: one mole of atoms and one mole of molecules contain equal numbers of their stated entities but do not describe the same sample.[4][2]
Example: density of a sample
Base quantities in a density calculation
- Given
- m = 84.0 g; cuboid edges 30.0 mm, 20.0 mm and 10.0 mm. Homogeneous sample; dimensions are measured values.
- Find
- Volume and mean density in coherent SI units.
Convert inputs to kg and m.
Multiply three lengths; apply the factor to each edge.
Divide mass by volume.
Result: V = 6.00 × 10−6 m3; ρ = 1.40 × 104 kg/m3, to three significant figures.
Check: In centimetres V = 3·2·1 cm3 = 6 cm3; 84 g/6 cm3 = 14 g/cm3. Since 1 g/cm3 = 1 000 kg/m3, the result agrees. Actual uncertainty requires uncertainties for all four inputs.
Example: entity count and an exact definition
Molecules from a measured amount
- Given
- n = (2.50 ± 0.02) mmol of a specified molecular species; ± denotes the stated standard uncertainty u(n).
- Find
- Molecule count N and its standard uncertainty.
Convert amount and uncertainty using the same exact factor.
Insert the exact Avogadro value.
Standard uncertainty scales equally under a linear transformation.
Result: N = (1.506 ± 0.012) × 1021 molecules, rounded consistently with the uncertainty.
Check: u(N)/N = u(n)/n = 0.008 = 0.8%. NA contributes no defining uncertainty, but the measured amount remains uncertain. This large value estimates a count; it is not a list of individually counted molecules.
Notation and limits of unit checking
Unit symbols are upright, do not take a plural s, and are separated from the number by a space: 12 kg, 5 A, 300 K. Unit products can use a centred dot or a space. Parentheses prevent ambiguity in fractions: J/(mol·K) is not (J/mol)·K. Quantity symbols are usually italic, distinguishing m for mass typographically from m for metre.[5]
A unit conversion is exact when its factor is exact by definition. It improves neither sensor resolution nor a model’s validity. Record the measured quantity and conditions first, convert its unit, then check meaningful result precision. The SI table supplies a reference system; it does not supply material properties, local gravity or an experimental model.
Three exercises with explained solutions
A sample has mass 750 mg. Express it in kg.
Show hint
Convert mg to g, then g to kg.
Show solution and calculation
750 mg = 0.750 g = 0.000750 kg.
Check: multiplying by 106 mg/kg returns 750 mg.
Temperature rises from 18 °C to 32 °C. Find both kelvin values and the difference.
Show hint
Apply the offset to values, not again to their difference.
Show solution and calculation
291.15 K and 305.15 K; ΔT = 14 K.
Check: 32 − 18 is a 14 °C difference. Adding the offset to the difference to obtain 287.15 K is incorrect.
Which expression has acceleration dimension: l/t, l/t2 or l2/t?
Show hint
Acceleration changes velocity per time.
Show solution and calculation
Only l/t2 has L·T−2 and SI unit m/s2.
This check does not prove that a particular acceleration equals l/t2; its model coefficient still needs justification.
Sources for this explanation
Quanta · Updated October 1, 2026
- BIPM: SI Brochure, 9th edition, version 4.01, §§2–5
- NIST: SI Units — defining constants and base quantities
- NIST: SI Units — Mass, mass and weight FAQ
- NIST: SI Units — Temperature
- NIST: SI unit rules and style conventions checklist
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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. SI base units. Updated October 1, 2026. https://quanta-study.de/en/formula-sheet/tables/si-basiseinheiten
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