Density Conversion Formula: Units, Factors and Examples

Density Conversion Formula: Units, Factors and Examples

Density is mass divided by volume, ρ = m/V, and converting it between units means converting the mass part and the volume part. In practice you rarely need to do both: multiply g/cm³ by 1000 to get kg/m³, multiply lb/ft³ by 16.01846 to get kg/m³, and multiply specific gravity by the density of water to get density. The rest of this guide gives the exact factors, a chart you can keep, and worked examples so you can check your own numbers.

TL;DR

• Density formula: ρ = m/V. Rearranged, m = ρ × V and V = m ÷ ρ.
• g/cm³ to kg/m³: multiply by 1000. kg/m³ to g/cm³: divide by 1000.
• lb/ft³ to kg/m³: multiply by 16.01846. The reverse is dividing by the same number.
• Specific gravity to density: multiply by the reference density, usually water at about 1000 kg/m³ (1 g/cm³).
• g/L, kg/m³ and g/mL, g/cm³ are numerically identical pairs, so no arithmetic is needed for those.

Table of Contents

• The density formula and what each symbol means
• Common density units
• How to convert g/cm³ to kg/m³
• Converting to and from US customary units
• Density conversion chart
• Specific gravity to density
• Using density to convert between mass and volume
• Our perspective: where density conversions go wrong
• Run your conversions with MetriqaHub
• Common mistakes to avoid
• FAQ
• Sources

The density formula and what each symbol means

Density is mass per unit of volume. OpenStax Chemistry 2e writes it as ρ = m/V, where ρ is density, m is mass and V is volume. The same page gives the SI unit as the kilogram per cubic meter (kg/m³).

The formula has three forms, and you pick the one that matches what you are missing:

Common density units

No single unit fits every job. OpenStax Chemistry 2e notes that g/cm³ is commonly used for solids and liquids, while g/L is commonly used for gases. Engineers and physicists default to kg/m³ because it belongs to the SI system. In the US you will also meet pounds per cubic foot (lb/ft³), pounds per cubic inch (lb/in³) and pounds per gallon (lb/gal), the last one especially for fuels, paints and liquids sold by the gallon.

Other metric units you will see are g/mL, kg/L and tonne/m³, listed as non-SI metric density units next to kg/m³ and g/cm³.

A few of these are the same quantity written differently:

• 1 g/mL = 1 g/cm³, because a milliliter is exactly one cubic centimeter.


• 1 g/L = 1 kg/m³, because a liter holds 0.001 m³ and a gram is 0.001 kg, so the factors cancel.


• 1 kg/L = 1 g/cm³ = 1 tonne/m³ = 1000 kg/m³.

How to convert g/cm³ to kg/m³

This is the conversion most readers need. The rule: multiply the value in g/cm³ by 1000. OpenStax University Physics states that 1 g/cm³ = 1000 kg/m³, and NIST's SI conversion table gives the same factor.

Why 1000? Break it into the two parts:

• Mass: 1 g = 0.001 kg, so the numerator shrinks by a factor of 1000.


• Volume: 1 cm³ = 0.000001 m³ (10⁻⁶ m³), so the denominator shrinks by a factor of 1,000,000.

2.70 × 1000 = 2700 kg/m³

Going the other way, a concrete mix listed at 2400 kg/m³ is 2400 ÷ 1000 = 2.4 g/cm³.

Converting to and from US customary units

Pound-based units need a real factor, not a power of ten. The NIST table gives these multipliers to reach kg/m³:

If you want a cross-check, the density reference page gives approximately 62.427961 lb/ft³ per g/cm³, which agrees with dividing 1000 by 16.01846.

Density conversion chart

Keep this table nearby for common conversions. All values are rounded, and the lb/ft³ column comes from dividing kg/m³ by 16.01846.

Specific gravity to density

Specific gravity (SG), also called relative density, compares a substance's density with a reference substance, almost always water. It has no unit because it is a ratio of two densities. If you want a refresher on how ratios work, see our guide to converting ratios to percentages.

The conversion is a single multiplication:

With water as the reference, the reference density is about 1 g/cm³, or 1000 kg/m³. So:

• SG 0.79 gives 0.79 g/cm³, or 790 kg/m³.


• SG 1.025 gives 1.025 g/cm³, or 1025 kg/m³.


• SG 7.85 gives 7850 kg/m³, or about 490 lb/ft³.

Using density to convert between mass and volume

Density also works as a conversion factor. Chemistry LibreTexts/2.4.01%3A_Density_as_a_conversion_factor) explains it with mercury: at 13.6 g/mL, 13.6 g of mercury equals 1 mL, so you can use either g/mL or mL/g as the conversion factor. Volume times density gives mass, and mass divided by density gives volume. Its example turns 2.0 mL of mercury into 27 g.

This answers the common question "how do I convert kilograms to cubic meters?" You cannot, without a density, because kilograms measure mass and cubic meters measure volume. With density you can:

• Density = 0.85 × 1000 = 850 kg/m³.
• V = m ÷ ρ = 500 ÷ 850 = 0.588 m³, or about 588 liters.

• 5 L = 0.005 m³.
• m = ρ × V = 850 × 0.005 = 4.25 kg.

• In g/cm³: 2000 g ÷ 250 cm³ = 8.0 g/cm³.
• In kg/m³: 8.0 × 1000 = 8000 kg/m³.

A shape example with a cylinder

When the volume comes from geometry, calculate it first. A solid aluminum rod has a radius of 5 cm and a length of 20 cm. Using the cylinder volume formula, V = πr²h = π × 25 × 20 ≈ 1570.8 cm³. With aluminum at 2.70 g/cm³, the mass is 1570.8 × 2.70 ≈ 4241 g, or 4.24 kg. Because the radius and length were in centimeters, the density in g/cm³ matched without conversion.

Our perspective: where density conversions go wrong

We build converters and calculators, and the errors we see are rarely about the formula. They come from three habits.

The first is converting the number but not the unit label. A value like 2.7 gets copied from a g/cm³ table into a kg/m³ field, and the result is off by a factor of 1000. Writing the unit beside every number, at every step, catches this faster than any calculator.

The second is trusting a rounded factor in a long chain. For classroom work, 16.02 for lb/ft³ is fine. For engineering, use the full published factor, 16.01846, and round only the final answer. Official factors from standards bodies such as NIST are the right place to take them from.

The third is forgetting that density changes with temperature and, for gases, pressure. A conversion tool can change units exactly, but it cannot tell you what temperature your sample was at. Where a result feeds billing, safety or a specification, check the governing standard, not just a converter.

Our approach is to give the exact factor, show the arithmetic, and keep results instant and free without registration, so you can verify a number in seconds and move on.

— Nkosi

Run your conversions with MetriqaHub

If you would rather not do the arithmetic by hand, MetriqaHub offers free unit conversion tools for length, mass, temperature and volume, with instant results and no sign-up. They pair well with the formulas above: convert your volume and mass first, then apply ρ = m/V with consistent units.

Browse the full set of free converters and calculators on the MetriqaHub home page.

Common mistakes to avoid

• Mixing units inside the formula. Convert mass and volume to a matched pair before dividing, or divide and then convert the result using the factors above.
• Confusing U.S. and imperial gallons. They differ by about 20%, which is why the NIST table lists separate factors, 119.8264 and 99.77637 kg/m³ per lb/gal.
• Confusing weight and mass. Density uses mass. Pounds in lb/ft³ are treated as a mass unit in these tables.
• Applying the 1000 rule to the wrong unit. It works for g/cm³ to kg/m³, and for g/mL or kg/L. It does not work for lb/ft³, where you need 16.01846.
• Forgetting the reference in specific gravity. SG against water is not SG against air.
• Over-rounding early. Keep at least four significant figures until the last step.

FAQ

What is the formula for converting density units?

There is no single formula, because each pair of units has its own factor. Multiply by 1000 for g/cm³ to kg/m³, and by 16.01846 for lb/ft³ to kg/m³. To go the opposite direction, divide by the same factor.

How many kg/m³ is 1 g/cm³?

One g/cm³ equals 1000 kg/m³, a value given in both OpenStax University Physics and the NIST table. A density of 2.5 g/cm³ is therefore 2500 kg/m³.

Is g/L the same as kg/m³?

Yes, numerically. One gram per liter is 0.001 kg per 0.001 m³, which is 1 kg/m³. That is why gas densities, usually quoted in g/L, can be read straight as kg/m³.

How do I get density from specific gravity?

Multiply the specific gravity by the density of the reference, which is normally water at about 1000 kg/m³ (1 g/cm³). A fluid with SG 0.85 has a density of 850 kg/m³. Check which reference temperature your source uses if you need high precision.

Can I convert kilograms to cubic meters?

Only if you know the substance's density. Divide the mass in kilograms by the density in kg/m³ to get cubic meters: 500 kg of a liquid at 850 kg/m³ fills about 0.588 m³.

Sources

• OpenStax Chemistry 2e, 1.4 Measurements
• OpenStax University Physics Volume 1, 14.1 Fluids, Density, and Pressure
• NIST Guide to the SI, Appendix B.9
• Chemistry LibreTexts, Density as a conversion factor/2.4.01%3A_Density_as_a_conversion_factor)
• Density, reference page

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• Ratio to Percentage Conversion: Formulas and Worked Examples
• Volume of a Cylinder Formula: V = πr²h Explained
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