Density calculator

A density calculator works out how much mass is packed into each unit of volume. Density = mass ÷ volume, written ρ = m/V. Our Density Calculator finds density from mass and volume, or uses a known density to find the mass or the volume, and tells you which common materials are nearest and whether your object would float in water.

This page is about the density of materials in physics and chemistry. Searches such as density altitude, freight density or population density use the same idea of an amount per unit, but different formulas.

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Density Calculator

Find density, mass or volume and compare materials

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How to use the density calculator

1. Choose what to find: Density, Mass or Volume.
2. Choose your units. Mass can be in g, kg, tonnes or lb; volume in mm³, cm³, mL, L or m³; and density in kg/m³, g/cm³, g/L, kg/L or lb/ft³.
3. Type the two values you know. When density is an input, you can pick a material instead, from air to gold.
4. Read the answer, with the formula and the numbers put in, and the answer in other units underneath.
5. Check the comparison: how many times denser than water it is, whether it floats or sinks, and the nearest materials either side of it.

A scale of common materials, from air to gold, marks where your density sits. For practice, Practice and help sets density, mass and volume questions, plus questions on floating and on what happens to density when an object is cut in half.

The density formula

Rearranged, mass = density × volume (m = ρV) and volume = mass ÷ density (V = m/ρ). A formula triangle with m on top and ρ and V underneath gives all three.

Density units

To change g/cm³ to kg/m³, multiply by 1,000: water is 1 g/cm³, or 1,000 kg/m³. Pick g/cm³ in the calculator and it converts for you.

Worked examples you can check in the calculator

Example 1: finding density

A metal bar has a mass of 81 g and takes up 30 cm³. What is its density, and what might it be made of?

In the calculator, set the units to g and cm³ and type 81 and 30. It gives 2,700 kg/m³ and says this is the same as aluminium in its list, and that the bar sinks in water.

Example 2: finding mass

A steel beam has a volume of 0.05 m³. Steel's density is 7,850 kg/m³. What is its mass?

Choose Mass, pick Steel as the material, and type 0.05 m³.

Example 3: finding volume

What volume does 1.5 kg of petrol take up? Petrol's density is 750 kg/m³.

Example 4: an irregular object

To find the volume of an odd shape, lower it into a measuring cylinder of water and see how far the level rises. A metal nut raises the water from 50.0 mL to 62.5 mL, so its volume is 12.5 cm³, and its mass is 112 g:

That matches copper in the calculator's list. This is the displacement method, used in school practicals to measure the density of solids.

Check you have the formula:

Will it float? Density and water

An object floats in water if its average density is less than water's, 1,000 kg/m³, and sinks if it is more. The calculator says "Floats" or "Sinks" for every result.

These are the values in the calculator's materials list. Ice floats, but only just: its density is 917 ÷ 1,000 = 0.917 times water's, so about 92% of a block of ice sits under fresh water. A steel ship floats because its average density, including all the air inside its hull, is less than water's.

Density does not change when you cut something

Density is a property of the material, not of the object. Cut a block in half and both its mass and its volume halve, so mass ÷ volume stays the same. Changes of temperature or state do change density: most substances are less dense as liquids than as solids, but water is unusual, because ice is less dense than liquid water.

Common mistakes

• Dividing the wrong way. Density is mass ÷ volume, not volume ÷ mass.
• Mixing units. Grams with m³, or kilograms with cm³, gives an answer off by a factor of 1,000 or a million. Match the units, or set them in the calculator.
• Getting the g/cm³ conversion backwards. 1 g/cm³ = 1,000 kg/m³, so 2.7 g/cm³ is 2,700 kg/m³, not 0.0027.
• Using the water level, not the rise. In the displacement method, the volume is the change in level.
• Thinking heavy things always sink. Floating depends on density, not on mass. A huge log floats; a small pebble sinks.

Practise density in a short timed paper

Density comes up in High School Physics and Grade 8 Physical Science practice, and in GCSE Physics Higher in the UK. Each daily paper is a short timed paper of 8 questions worth 25 to 35 marks, and the papers mix topics. For pressure in liquids, which uses density too, try the Pressure Calculator.

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