Density Converter — kg/m³, g/cm³ and lb/ft³

Background.

A European datasheet gives structural steel as 7,850 kg/m³. An American design table rounds it to 490 lb/ft³, and a machinist's handbook lists it as 0.284 lb/in³. All three describe the same metal; only the units differ, and converting between them means changing a mass unit and a volume unit at the same time. The volume half is where hand conversions go wrong. A foot is 12 inches, but a cubic foot is 12 × 12 × 12 = 1,728 cubic inches, so a density in pounds per cubic inch is 1,728 times its value in pounds per cubic foot, not 12 times.

The metric units are kinder, because their prefixes line up. A gram per cubic centimetre, a kilogram per litre and a gram per millilitre are the same quantity, and water sits close to 1 in all of them, which is why chemists and food scientists favour them. Engineers working in SI use kilograms per cubic metre, where water is close to 1,000, and gases are usually quoted in grams per litre, which turns out to be numerically identical to kg/m³. On the customary side, pounds per cubic foot is the everyday unit for building materials, soils and liquids in bulk, while pounds or ounces per cubic inch suit small, dense parts.

Enter one value and all seven units are shown together, so a slipped factor of a thousand stands out at a glance. What no conversion can do is change what the number describes: the density of water at 25 °C, the loose bulk density of gravel, or a plastic at its moulding temperature stays tied to those conditions in every unit.

What is density converter?

Density is mass divided by volume, and its SI unit is the kilogram per cubic metre. Every other unit here is that same ratio with a different mass unit on top and a different length, cubed, underneath. The metric relationships are exact by definition: a cubic centimetre is a millionth of a cubic metre and a gram a thousandth of a kilogram, so 1 g/cm³ is 1,000 kg/m³, and since 1964 the litre has been exactly one cubic decimetre, making kg/L identical to g/cm³. The customary units rest on the international definitions agreed in 1959: the pound is exactly 0.45359237 kg and the inch exactly 2.54 cm, so a foot is 0.3048 m. The ounce here is the avoirdupois ounce, one sixteenth of a pound, the one used for ordinary goods. The reciprocal of density, specific volume, is the space one kilogram occupies: 0.001 m³/kg for water, the form steam tables and thermodynamics use. Some reference points help with the scale: air at sea level is about 1.2 kg/m³, ice about 917, water 1,000, concrete around 2,400, aluminium 2,700, steel 7,850, lead 11,340 and gold 19,320.

How to use this calculator.

1. 01Enter the density as a number. It can be zero or any positive value up to 10¹², but not negative.
2. 02Set From unit to the unit the figure is written in. g/mL is the same as g/cm³, so choose that; kg/dm³ is the same as kg/L, and the tonne per cubic metre used for ore and aggregates is the same again, so 2.65 t/m³ goes in as 2.65 g/cm³.
3. 03Set To unit to the unit you need. The answer appears first, and the full list of seven units below it.
4. 04Glance down the list for sense. Water-like liquids sit near 1 g/cm³ and 62.4 lb/ft³, common metals from aluminium at 2.7 to gold at 19.3 g/cm³, gases around a gram per litre, give or take; a result a thousand times away from that suggests the wrong From unit.
5. 05Results are shown to at most four decimal places, so pick a unit in which your number is not tiny. Air is 1.225 g/L but only about 0.0000443 lb/in³, which would display as 0.
6. 06Carry the original conditions with the converted number: the temperature, whether it is bulk or solid density, the moisture basis for soils and timber.

The formula.

Every conversion goes through kilograms per cubic metre. The value is multiplied by the number of kg/m³ in one source unit, then divided by the number of kg/m³ in one target unit: result = value × f(from) ÷ f(to).

The factors come straight from the definitions. One g/cm³ and one kg/L are each 1,000 kg/m³, and one g/L is 1 kg/m³. One lb/ft³ is 0.45359237 kg spread over 0.3048³ = 0.028316846592 m³, which is 16.01846 kg/m³. One lb/in³ is the same pound over 0.0254³ = 0.000016387064 m³, or 27,679.9047 kg/m³, exactly 1,728 times the lb/ft³ factor. One oz/in³ is a sixteenth of that, 1,729.9940 kg/m³, which makes 1 oz/in³ very nearly 1.73 g/cm³.

Because the length is cubed, any error in a length factor is tripled in the density. Rounding the inch to 2.5 cm, a common mental shortcut, makes a cubic inch 15.625 cm³ instead of 16.387, and every conversion into or out of the per-cubic-inch units is off by almost 5%.

For rough work the factors round to easy numbers. Dividing kg/m³ by 16 gives lb/ft³ about 0.12% too high, so 1,000 kg/m³ becomes 62.5 against the true 62.428. Multiplying g/cm³ by 62.4 gives lb/ft³ within 0.05%. Between the metric units nothing more than a decimal shift is ever needed: kg/m³ to g/cm³ is a division by 1,000, and kg/m³ and g/L are the same number.

Units that are not on the list convert the same way once you know their kg/m³ value. The slug per cubic foot, the coherent mass-density unit of US aerodynamics, is 32.174 lb/ft³ or about 515.38 kg/m³, which is why sea-level air, 1.225 kg/m³, appears in American aerodynamics texts as 0.002377 slug/ft³. Enter such a figure in lb/ft³ after multiplying by 32.174.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST SP 811 Appendix B supplies the exact mass, length, volume and customary conversion definitions.
2. [2]BIPM SI Brochure defines kilogram and metre and accepts the litre as one cubic decimetre.
3. [3]NIST SP 330 independently documents SI derived-unit construction and litre usage.
4. [4]NIST Handbook 44 Appendix C provides customary/SI relationships for legal metrology.
5. [5]BIPM Measurement Units provides the current SI definition framework.