Density Calculator

Density calculator at a glance#

What is the formula for density?#

Density is mass divided by volume: ρ = m ÷ V, where ρ (the Greek letter rho) is density (the calculator writes it as p), m is mass and V is volume. A block with a mass of 270 g and a volume of 100 cm³ has a density of 270 ÷ 100 = 2.7 g/cm³. Pick Density, Mass or Volume at the top of the calculator, enter the other two values with their units, and choose the unit you want the answer in.

What is the density of an object with a mass of 100 g and a volume of 50 cm³?#

It's 100 ÷ 50 = 2 g/cm³. That's twice the density of water, so the object sinks in water.

How do you find mass or volume from density?#

Rearrange the formula. Mass is density times volume, m = ρ × V, and volume is mass divided by density, V = m ÷ ρ. A metal with a density of 2.7 g/cm³ that fills 15 cm³ has a mass of 2.7 × 15 = 40.5 g. A kilogram of gold, at 19.32 g/cm³, takes up 1,000 ÷ 19.32 = 51.76 cm³.

What density tells you#

Density measures how much mass is packed into a given space. OpenStax College Physics defines it as mass per unit volume, with the SI unit kg/m³. Two blocks of the same size can feel completely different in your hand. A 100 cm³ block of aluminum has a mass of 270 g, while the same block in lead has a mass of 1,130 g, because lead's density is 11.3 g/cm³.

Density belongs to the material, not the object. Cut the aluminum block in half and each half has half the mass and half the volume, so the density stays 2.7 g/cm³. That's why density helps identify what something is made of.

How to find density step by step#

The example on this page is a solid metal block, 5 cm long, 5 cm wide and 4 cm tall, with a mass of 270 g.

1. Weigh the object on a scale: 270 g.
2. Find its volume. For a rectangular block, multiply length × width × height: 5 × 5 × 4 = 100 cm³.
3. Divide the mass by the volume: 270 g ÷ 100 cm³ = 2.7 g/cm³.
4. Compare the result with a density table. Aluminum is 2.7 g/cm³, so the block is very likely aluminum.

Keep the units matched. Grams over cubic centimeters give g/cm³, and kilograms over cubic meters give kg/m³. The calculator converts for you, so you can enter the mass in pounds and the volume in cubic inches and still read the answer in g/cm³. For shapes other than a box, the volume calculator finds the volume of a cylinder, sphere, cone and more, and the cylinder volume calculator handles cans, pipes and tanks.

Irregular objects: the water displacement method#

A rock or a key has no simple length, width and height. Measure its volume with water instead. Fill a graduated cylinder partway, read the level, lower the object in and read it again. The rise is the object's volume, and since 1 mL equals 1 cm³ you can use it directly.

Say the water climbs from 50.0 mL to 65.0 mL. The object's volume is 15 cm³. If it's made of a metal with a density of 2.7 g/cm³, its mass is 2.7 × 15 = 40.5 g. Weigh it to check, or go the other way: a measured 40.5 g over 15 cm³ gives 2.7 g/cm³.

Solving for mass or volume#

The density formula links three quantities, so knowing any two gives you the third. A formula triangle makes the rearranging easy to remember: mass sits on top, density and volume sit side by side underneath. Cover the one you want and the other two show the operation.

The calculator's Find switch does the same thing. Choose Mass and enter density and volume, or choose Volume and enter mass and density. Each mode has its own unit menus, so you can enter a density in kg/m³ and a volume in liters and get the mass in pounds.

Two more examples: a cubic foot of water at 62.43 lb/ft³ has a mass of 62.43 lb, and a 1 kg gold bar at 19.32 g/cm³ has a volume of 51.76 cm³. The calculator prints the full decimal, 51.75983436853002 cm³ in that case, so round to match how precisely you measured. The significant figures calculator rounds to any number of figures.

Mass and weight aren't the same. Weight is the force gravity puts on a mass, w = m × g, so a 270 g block weighs about 0.270 kg × 9.80 m/s² = 2.6 N on Earth. The force calculator works with mass, acceleration and force in many units.

Density units and conversions#

Because 1 mL is exactly 1 cm³ and 1 L is 1,000 cm³, several density units are the same size. These are all equal:

• 1 g/cm³ = 1 g/mL = 1 kg/L
• 1 g/cm³ = 1,000 kg/m³ = 1,000 g/L
• 1 g/cm³ = 62.43 lb/ft³ = 0.0361 lb/in³

So aluminum at 2.7 g/cm³ is 2,700 kg/m³ or about 168.56 lb/ft³. The calculator's density menus cover g/cm³, kg/m³, g/mL, g/L, kg/L, lb/in³ and lb/ft³, its mass menus g, kg, oz and lb, and its volume menus mL, cm³, m³, L, ft³ and in³.

Will it float?#

Compare the object's density with the liquid's. Water has a density of 1.000 g/cm³ at 4 °C, so anything less dense floats in it and anything denser sinks. Ice, at 0.917 g/cm³, floats. Most wood, at 0.3 to 0.9 g/cm³, floats too. The 2.7 g/cm³ aluminum block sinks, even though a boat made of aluminum floats, because the boat's hull encloses a lot of air and its overall density ends up below that of water.

Densities of common substances#

Values in g/cm³ come from Table 11.1 of OpenStax College Physics 2e. The other columns are converted from them.

Sources#

• OpenStax, College Physics 2e, section 11.2: Density (Table 11.1)

Frequently asked questions#

What are the units of density?#

The SI unit is kilograms per cubic meter, kg/m³. In labs and classrooms you'll mostly see grams per cubic centimeter, g/cm³, which is the same as g/mL. In US customary units, density is often given in pounds per cubic foot, lb/ft³.

What is the density of water?#

Water has a density of 1.000 g/cm³ at 4 °C, which is 1,000 kg/m³ or about 62.43 lb/ft³. It changes slightly with temperature, which is why reference tables give one.

How do you calculate density from mass and volume?#

Divide the mass by the volume. A block with a mass of 36 g and a volume of 9 cm³ has a density of 36 ÷ 9 = 4 g/cm³. Make sure the mass and volume units match the density unit you want.

How do you convert g/cm³ to kg/m³?#

Multiply by 1,000. A density of 2.7 g/cm³ is 2,700 kg/m³, and 0.917 g/cm³ is 917 kg/m³. To go back, divide by 1,000.

Is density the same as weight?#

No. Density is mass per unit volume and doesn't depend on how much material you have. Weight is a force, mass times the acceleration of gravity, and it grows with the size of the object.

Does density change if you cut an object in half?#

No. Each half has half the mass and half the volume, so the ratio stays the same. A half block of aluminum is still 2.7 g/cm³.