From Archimedes' principle to the petroleum API scale: how to convert density without the factor-of-1,000 error.
Density is the physical quantity that expresses the relationship between the mass of a substance and the volume it occupies. In the International System of Units (SI), the standard unit of density (more precisely, volumetric density or specific mass) is the kilogram per cubic metre (kg/m³). The concept is ancient: Archimedes, in the 3rd century BC, had already realized that equal volumes of different materials have different weights, and the legendary story of his "Eureka!" cry upon noticing that the water displaced by his body in the bath revealed his volume is linked precisely to the idea of relating mass and volume to identify materials.
The most common laboratory unit for density is the gram per cubic centimetre (g/cm³), equivalent to 1,000 kg/m³. This equivalence is a direct consequence of the metric system: 1 g = 0.001 kg and 1 cm³ = 0.000001 m³, therefore 1 g/cm³ = 0.001/0.000001 = 1,000 kg/m³. Thus, the density of pure water at 4 °C — the temperature at which it reaches its maximum density — is approximately 1,000 kg/m³ or 1 g/cm³, a reference value so useful that it serves as the basis for defining the unit of relative density (dimensionless density relative to water).
Other density units appear in specific contexts. The gram per millilitre (g/mL) is identical to g/cm³ and widely used in chemistry and pharmacy. The pound per cubic foot (lb/ft³), equivalent to approximately 16.0185 kg/m³, is common in American engineering and in U.S. construction material specifications. The pound per gallon (lb/gal) appears in American industrial fluid data. For gases, the kilogram per litre (kg/L) or the gram per litre (g/L) is often used, the latter being identical to kg/m³.
The conversion formulas derive directly from the relationships between mass and volume units. The main factors are: 1 g/cm³ = 1,000 kg/m³ = 1 g/mL = 1 kg/L; 1 lb/ft³ = 16.0185 kg/m³; 1 lb/gal (U.S.) ≈ 119.826 kg/m³. Since density involves two quantities (mass and volume), it is easy to confuse the direction of conversion — for example, forgetting that 1 g/cm³ equals 1,000 kg/m³ and not 1 kg/m³. This factor-of-1,000 error is one of the most common in density conversions and can completely invalidate an engineering calculation.
A practical example: the density of common steel is about 7.85 g/cm³. Converting to kg/m³: 7.85 × 1,000 = 7,850 kg/m³. This means a 1 m³ steel beam weighs approximately 7,850 kg, or 7.85 tonnes — essential information for structural and transport calculations. In the reverse direction, the density of air at sea level is about 1.225 kg/m³, or 0.001225 g/cm³, a value so small it illustrates why air feels "light," yet is sufficient to generate the 101,325 Pa atmospheric pressure we feel.
In the petroleum industry, density is measured in degrees API, an inverse scale created by the American Petroleum Institute: liquids less dense than water have higher degrees API. The formula is °API = (141.5 / relative density at 60 °F) − 131.5. Thus, water (relative density 1.000) has 10 °API, and a light crude oil of relative density 0.85 has approximately 34.3 °API. This scale is fundamental in oil trading, as lighter oils (higher °API) usually command a higher market value because they are easier to refine.
Care with precision is important because density varies with temperature — most materials expand when heated and become less dense. For this reason, technical specifications always indicate the reference temperature (for example, 20 °C or 15 °C). Converting densities measured at different temperatures without correcting for this variation introduces a systematic error. In the laboratory, use exact factors and round only the final result; in field applications, two to three decimal places in g/cm³ are usually sufficient.
Real applications are broad: materials engineers calculate the weight and strength of components from density, chemists identify unknown substances by measuring density, the mining and metallurgy industry uses density to classify ores, and civil construction considers density in sizing foundations and structures. The TudoConversor density converter calculates between kg/m³, g/cm³, g/mL, lb/ft³, and other units with official factors and double precision, ensuring reliable results in any direction.