Density Unit Conversion: Formulas, Factors and Examples

Density Unit Conversion: Formulas, Factors and Examples

To convert density between units, multiply by a conversion factor that equals one. The most common switch is the simplest: 1 g/cm³ equals 1000 kg/m³, so you multiply by 1000 going from g/cm³ to kg/m³ and divide by 1000 going back. For pounds per cubic foot, pounds per gallon or specific gravity, the same method applies with a different factor. This guide gives every factor you are likely to need, worked examples with real materials, and the checks that catch the usual errors.

TL;DR

• Density is mass divided by volume, so every density unit is a mass unit over a volume unit. Convert the mass part and the volume part, or use one ready-made factor.
• g/cm³ to kg/m³: multiply by 1000. kg/m³ to g/cm³: divide by 1000. g/mL is the same number as g/cm³.
• lb/ft³ to kg/m³: multiply by 16.01846. Water is about 1 g/cm³, 1000 kg/m³ or roughly 62.4 lb/ft³.
• Keep full precision during the calculation and round only the final answer, then ask whether the magnitude makes sense.

Table of Contents

• What density is and why so many units exist
• The core conversion: kg/m³ and g/cm³
• Other density units you will meet
• Quick reference table
• A method that works for any density conversion
• Worked examples
• Mistakes that cost accuracy
• Our perspective
• Convert density instantly
• FAQ
• Sources

What density is and why so many units exist

Density is mass per unit volume, written ρ = m/V. In the SI system the unit is kilograms per cubic meter (kg/m³), and the older cgs system uses grams per cubic centimeter (g/cm³), as OpenStax University Physics explains. Because the definition is a ratio, any mass unit divided by any volume unit is a valid density unit. That is why you meet kg/m³, g/cm³, g/mL, g/L, mg/L, lb/ft³ and lb/gal in different fields.

Each field settled on the unit that gives comfortable numbers. OpenStax Chemistry notes that g/cm³ is commonly used for solids and liquids, while g/L is often used for gases. Engineers working in SI prefer kg/m³ because it fits directly into force, pressure and flow equations. In the United States, pounds per cubic foot and pounds per gallon still appear in construction, shipping, brewing and fluid handling.

The practical effect is that a single material can appear as 2.7, 2700 or about 168.6, depending on who wrote the datasheet. All three describe the same aluminum. Converting correctly is how you compare them.

The core conversion: kg/m³ and g/cm³

The relationship behind the most searched density conversion is short:

Why the factor is 1000

The factor is not arbitrary. It comes from two separate conversions that combine:

• 1 g = 0.001 kg, so the mass in the numerator gets 1000 times smaller.


• 1 cm³ = 0.000001 m³ (one millionth), so the volume in the denominator gets a million times smaller.

1 g/cm³ = (0.001 kg) / (0.000001 m³) = 1000 kg/m³

If you ever forget the direction, redo this two-step check. It takes ten seconds and removes the guesswork.

g/cm³ to kg/m³: multiply by 1000

kg/m³ to g/cm³: divide by 1000

Suppose a fuel datasheet lists 850 kg/m³. Divide by 1000 and you get 0.85 g/cm³. That is lighter than water, which matches what you would expect from a fuel that floats on it. The shortcut is to move the decimal point three places to the left.

Other density units you will meet

g/mL and g/L

One milliliter is exactly one cubic centimeter, so g/mL and g/cm³ are the same number. A liquid at 0.92 g/mL is 0.92 g/cm³ and 920 kg/m³.

Grams per liter is smaller by a factor of 1000 in volume terms: 1 L equals 0.001 m³ and 1 g equals 0.001 kg, so 1 g/L equals 1 kg/m³. That makes g/L and kg/m³ interchangeable, which is handy for gases, where the numbers in g/L are small and easy to read. Likewise 1 g/mL equals 1000 g/L.

mg/L

Milligrams per liter appear in water quality and lab work. Since 1 mg is 0.000001 kg and 1 L is 0.001 m³, 1 mg/L equals 0.001 kg/m³. A concentration of 250 mg/L is therefore 0.25 kg/m³ or 0.25 g/L. Strictly, this is a mass concentration rather than the density of the material, but the unit arithmetic is identical.

lb/ft³ and lb/gal

For U.S. customary units, Perry's Chemical Engineers' Handbook lists these factors:

• 1 lbm/ft³ = 16.01846 kg/m³ = 0.01601846 g/cm³


• 1 lbm/U.S. gal = 119.8264 kg/m³ = 0.1198264 g/cm³

Running the first factor backward, 1 g/cm³ equals 1000 ÷ 16.01846, or about 62.428 lb/ft³. Note that "lb" here is the pound as a unit of mass. In everyday American usage that is what the density figure means.

Specific gravity

Specific gravity is the ratio of a material's density to the density of water, according to OpenStax University Physics, which also gives water's reference density as 1000 kg/m³, or 1 g/cm³. It has no unit. Because water is 1 g/cm³, the specific gravity of a liquid equals its density in g/cm³ (or g/mL) at that reference condition. A fluid with specific gravity 0.85 has a density of 0.85 g/cm³, or 850 kg/m³. To get specific gravity from kg/m³, divide by 1000.

Quick reference table

A method that works for any density conversion

The NIST unit conversion guide describes a method that handles every case in this article, including ones with no ready-made factor. In short:

• Identify the starting unit and the target unit. For example, lb/ft³ to g/cm³.


• Choose linking conversion factors, each written as a fraction equal to one, such as 453.59237 g / 1 lb.


• Arrange the fractions so unwanted units cancel. Write the units next to the numbers and strike them out as you go.


• Calculate with full precision.


• Repeat the calculation as a check, ideally in a different order.


• Ask whether the result makes sense. Is the magnitude physically reasonable for this material?

Worked examples

Example 1: a steel part in g/cm³ to kg/m³

A drawing lists steel at 7.9 g/cm³. Multiply by 1000: 7.9 × 1000 = 7900 kg/m³. Sanity check: steel is nearly eight times denser than water, and 7900 is nearly eight times 1000. It passes.

Example 2: a fuel in kg/m³ to g/cm³

A safety sheet gives 850 kg/m³. Divide by 1000 to get 0.85 g/cm³. The specific gravity is 0.85. The value is below 1, so the fuel floats on water.

Example 3: water in lb/ft³ to kg/m³

Water is commonly quoted at about 62.4 lb/ft³. Multiply by 16.01846: 62.4 × 16.01846 ≈ 999.55 kg/m³. That lands very close to the 1000 kg/m³ reference value, and the small gap comes from rounding 62.4. This is a good reminder that the lb/ft³ figure was already rounded before you started.

Example 4: water in lb/gal to kg/m³

The often-quoted 8.34 lb/gal for water gives 8.34 × 119.8264 ≈ 999.35 kg/m³, again very near 1000.

Example 5: aluminum in kg/m³ to lb/ft³

Start with 2700 kg/m³ and divide by 16.01846: 2700 ÷ 16.01846 ≈ 168.56 lb/ft³. A quick check: multiply 168.56 by 16.01846 and you should get about 2700. You do.

Example 6: from density to mass

Density conversion usually serves a bigger calculation. Say you need the mass of an aluminum cylinder with a radius of 2 cm and a height of 10 cm. The volume is π × 2² × 10 ≈ 125.66 cm³ (our cylinder volume formula guide covers that step). With aluminum at 2.7 g/cm³, the mass is 125.66 × 2.7 ≈ 339.3 g. Staying in g/cm³ avoids a conversion entirely, because the volume is already in cm³. Had you used 2700 kg/m³, you would have needed the volume in m³ (0.00012566 m³) and the answer would come out as 0.3393 kg. Same result, different units. Match the unit system of the density to the unit system of the volume before you multiply.

Mistakes that cost accuracy

Our perspective

Most density conversion errors we see in questions people send are not arithmetic mistakes. They are unit-bookkeeping mistakes: a number copied without its unit, a volume in liters multiplied by a density in kg/m³, or a rounded factor reused ten steps later. That is why we build our converters around internationally recognized standards and show the factor behind each result, so you can see what was multiplied and decide if it fits your situation.

Our advice for students, engineers and cooks alike is the same. Write the units on every line. Keep the unrounded numbers until the end. Look at the answer and ask whether a steel part really should weigh that much. A converter is fastest when you already know roughly what the answer should be, and it is safest when you check it against that expectation.

— Nkosi

Convert density instantly

If you would rather skip the arithmetic, our free tools on MetriqaHub handle length, mass, temperature and volume conversions with no registration, and they pair well with density work: convert the volume first, then apply the density. For the other side of the calculation, our ratio to percentage guide is useful when you need to express a density comparison, such as a mixture ratio, as a percentage.

Every converter returns a result immediately, so you can check your hand calculation against it and keep working.

FAQ

How do you convert density from g/cm³ to kg/m³?

Multiply the value by 1000. For example, 7.9 g/cm³ × 1000 = 7900 kg/m³. The factor comes from 1 g being 0.001 kg and 1 cm³ being one millionth of a cubic meter. To go back, divide by 1000.

What is the unit for density in g/mL?

Grams per milliliter is a density unit meaning grams of mass in each milliliter of volume. Because 1 mL is the same as 1 cm³, g/mL and g/cm³ give the same number. A liquid at 1.2 g/mL is also 1.2 g/cm³ and 1200 kg/m³.

How do you convert density to pounds per cubic foot?

Divide the density in kg/m³ by 16.01846, which is the number of kg/m³ in 1 lb/ft³. For 2700 kg/m³, that gives about 168.56 lb/ft³. If you start in g/cm³, multiply by about 62.428 instead.

Is 1 g/L the same as 1 kg/m³?

Yes. One gram is 0.001 kg and one liter is 0.001 m³, so the two factors cancel and the numbers match. This is why gas densities are often written in either unit with identical values.

What does specific gravity tell you compared with density?

Specific gravity compares a material's density with water's, so it has no unit. With water at 1 g/cm³, a material with a specific gravity of 0.85 has a density of 0.85 g/cm³, or 850 kg/m³. A value above 1 means the material is denser than water and sinks in it.

Sources

• 14.1 Fluids, Density, and Pressure, University Physics Volume 1 (OpenStax)
• 1.4 Measurements, Chemistry 2e (OpenStax)
• Conversion Factors and Mathematical Symbols, Perry's Chemical Engineers' Handbook, 7th edition
• Density, IGCSE Physics (BBC Bitesize)
• NIST Guide to the SI, Appendix B.9: Factors for units listed by kind of quantity
• Unit Conversion (NIST)

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