Describe a quantity as a numerical value with a unit, and distinguish its physical kind from its dimension. Build length, area, volume and rate units, check meaningful combinations, and separate exact unit relations from measurement uncertainty.
Key knowledge
A physical quantity assigns a magnitude to a property of a phenomenon, body or substance; its value is expressed using a number and a reference, commonly a unit.
Conditions and scope
This is the metrological meaning of quantity; a nominal label alone is not a quantity value.
Sources · 11
References
Sources retain their recorded scope. A source link alone does not establish verification of every statement.
Bureau International des Poids et Mesures (BIPM)2 sources
2026-10-10 · Definition and number/reference distinction only; no claim that every property is quantitatively measurable.
Foundational review
2026-10-10 · Fresh primary-source inspection of the complete compact record, including every statement, equation, quantity and material condition, followed by independent AI editorial review. This check does not certify all linked lessons or every passage of every cited publication.
Sources from other places
Scope or convention differs
Measurement expresses a property using a numerical value and unit.
This practical guide supplements the fuller metrological definition; it does not classify every nominal property.
Average mass density is m/V. Fluid pressure parameterizes isotropic normal stress, with positive p denoting compression: uniform signed pressure p on a plane area A produces normal force magnitude |p|A. With nonuniform pressure, force must be integrated over the surface. Pressure and density describe different quantities and neither is a total force.
This relation concerns the stated density and fluid pressure claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.
Linear expansion coefficient is α_L=(1/L)(∂L/∂T) under the stated mechanical conditions. For small temperature changes and nearly constant α_L, ΔL≈α_LL₀ΔT. A freely expanding isotropic material has volume coefficient α_V≈3α_L in the small-strain limit. Coefficients can vary with temperature and need not always be positive.
This relation concerns the stated thermal expansion coefficients claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.
A quantity kind groups mutually comparable quantities. A quantity dimension expresses dependence on base quantities as a product of powers; quantities of the same kind have the same dimension, but equal dimensions need not imply the same kind. Energy and torque both have dimension ML²T⁻² yet have different meanings. Dimension-one quantities can also represent different kinds, so an omitted unit does not remove physical meaning.
This relation concerns the stated quantity kind and physical dimension claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.
A quantity value combines a number and a reference. For an ordinary unit-based scalar quantity, Q={Q}[Q], where {Q} is its numerical value in unit [Q]. Thus 5.34m and534cm express the same length with different numbers. Not every reference is a unit: specified procedures or reference materials can also define how a value is expressed.
This relation concerns the stated quantity value, numerical value and unit claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.
An ordinal quantity can be ranked by magnitude under a stated procedure but has no meaningful algebraic operations on that scale. A nominal property assigns categories without quantity magnitude. Numeric category codes are therefore labels, not automatically quantities, while a numerical ordinal scale supports ordering without automatically supporting differences, ratios or averages.
This relation concerns the stated ordinal quantities and nominal properties claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.
Learning guidance · 6 / 6
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