What this calculator does
Change a density from one unit to another, like g/cm³ to pounds per cubic foot. Density is how much mass fits in a given space: mass divided by volume. So its units are always a mass unit over a volume unit. That gives many ways to write the same thing. A lab notebook says 1.00 g/cm³ for water, and an engineering table says 1,000 kg/m³. A builder's reference says 62.4 lb/ft³, and a fuel spec says 8.34 lb per US gallon. They all describe the same liquid.
This converter changes a density from any of 16 units to any other. Every unit is set exactly from the official definitions of the pound, the meter and the gallon. So nothing gets rounded along the way. It shows the working through the standard metric (SI) unit, kilograms per cubic meter. It also shows a table of the same density in every unit at once.
Where it's used
Why this math matters outside the classroom:
- Shipping weight. A shipper finds that a 1 ft³ crate of steel at 490 lb/ft³ weighs about 490 lb, far over a parcel limit.
- Fuel loads. Pilots and boaters use about 6 lb per US gallon for gasoline when converting fuel volume to weight.
- Lab reports. Chemistry students convert a measured 0.789 g/mL for ethanol to 789 kg/m³ for an SI data table.
- Concrete estimates. Contractors convert 2,400 kg/m³ for concrete to about 149.8 lb/ft³ to use US load tables.
- Floating objects. Students compare pine at about 500 kg/m³ with water at 1,000 kg/m³ to see why the wood floats.
Grade level and standards: Grades 6–7; Common Core State Standards for Mathematics 6.RP.A.3.d. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Enter the density you have. Decimals are fine, and zero is allowed.
- Choose the unit it's in, then the unit you want.
- Read the converted value, or open the table to see the density in every unit. The working shows how big each unit is in kg/m³.
What the inputs mean
- Density
- Density is a size only, so negative values aren't accepted. Some typical values: air is about 1.2 kg/m³ and water is 1,000 kg/m³ (1 g/cm³). Aluminum is 2,700 kg/m³ and steel is about 7,850 kg/m³.
- From
- g/cm³, g/mL, kg/L and t/m³ are all the same size. So are kg/m³, g/L and mg/mL. Converting within either group leaves the number unchanged.
Formula and method
value in kg/m³ = value × (size of the starting unit in kg/m³) result = value in kg/m³ ÷ (size of the target unit in kg/m³) 1 g/cm³ = 1,000 kg/m³ 1 lb/ft³ = 0.45359237 kg ÷ 0.028316846592 m³ ≈ 16.0184634 kg/m³ 1 lb/US gal = 0.45359237 kg ÷ 0.003785411784 m³ ≈ 119.826427 kg/m³
Each unit is a mass divided by a volume, and every one of those has an exact official size. The pound is exactly 0.45359237 kg, and the foot is exactly 0.3048 m. The US gallon is exactly 231 cubic inches, and the imperial gallon is exactly 4.54609 liters. So every factor here is an exact ratio.
The calculator goes through one home-base unit, kg/m³. That means only two numbers matter. The first is how many kg/m³ one starting unit is worth. The second is how many kg/m³ one target unit is worth. Multiply by the first and divide by the second.
Worked example
A steel supplier lists a density of 7.85 g/cm³. What is that in pounds per cubic foot?
- Convert to the SI unit: 7.85 g/cm³ × 1,000 = 7,850 kg/m³.
- One pound per cubic foot is 16.018463374 kg/m³.
- Divide: 7,850 ÷ 16.018463374 = 490.0594905 lb/ft³.
Result: 7.85 g/cm³ is about 490.06 lb/ft³. That's close to the 490 lb/ft³ often listed for steel in US tables.
Understanding the result
Comparing a density with water's tells you whether something floats. Water is 1 g/cm³, 62.43 lb/ft³ or 8.345 lb per US gallon. Anything less dense than water floats in it.
The same number means very different things in different units. 1 kg/m³ is a thin gas, while 1 g/cm³ is water, a thousand times denser. So always check the unit before comparing values.
Assumptions and limitations
- US and imperial units use the international pound, foot and inch agreed in 1959. They also use today's US and imperial gallon definitions.
- The slug is the US engineering unit of mass, 1 lbf·s²/ft. It's based on standard gravity.
- Converting units doesn't account for temperature. A real material's density changes as it warms up or gets squeezed, so note the conditions with the value.
- Specific gravity (density compared with water) and API gravity are ratios, not units, so they aren't included.
- The bulk density of loose materials, such as gravel or grain, depends on how tightly they pack and how damp they are, not just the unit.
Frequently asked questions
How do I convert g/cm³ to kg/m³?
Multiply by 1,000. A cubic meter holds a million cubic centimeters, and a kilogram is a thousand grams. So 1 g/cm³ = 1,000,000 g ÷ 1,000 per m³ = 1,000 kg/m³. Water at 1 g/cm³ is 1,000 kg/m³.
Is g/mL the same as g/cm³?
Yes. One milliliter is exactly one cubic centimeter, so the numbers are identical. kg/L and t/m³ are the same size again.
How many pounds per gallon is water?
About 8.345 lb per US gallon and 10.022 lb per imperial gallon at 1 g/cm³. Real water at room temperature is slightly less dense, about 0.998 g/cm³. That gives about 8.33 lb per US gallon.
Why does the table show some units with the same value?
Several metric units are the same size. g/cm³, g/mL, kg/L and t/m³ are all 1,000 kg/m³, and g/L and mg/mL both equal 1 kg/m³. They're listed separately because different fields use different ones.
How this calculator is checked
Method: Exact unit definitions: international pound 0.45359237 kg, foot 0.3048 m, inch 0.0254 m, US gallon 231 in³, imperial gallon 4.54609 L, slug 1 lbf·s²/ft with standard gravity 9.80665 m/s². The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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