Density Calculator: Mass, Volume and Density
MathChoose what you want to find: density, mass or volume, then enter the other two values with their units. The calculator converts to SI units, applies ρ = m / V and shows the answer in kg/m³ and g/cm³, in kg and g, or in L, cm³ and m³.
Step by step
920 g / 1 L = 920 kg/m³
- Convert the mass to kg and the volume to m³: m = 0.92 kg and V = 0.001 m³.
- Divide mass by volume, ρ = m / V: the result is 920 kg/m³.
- For g/cm³, divide by 1,000: 0.92 g/cm³.
Once every entry is valid, you’ll see each step of the calculation here.
Formula
- ρ
- density, in kg/m³ or g/cm³
- m
- mass, in kg or g
- V
- volume, in m³, L or cm³
How it works
Density is how much mass a material has in a given volume: density = mass ÷ volume, written ρ = m / V with the Greek letter rho. The SI unit is kilograms per cubic meter (kg/m³). Grams per cubic centimeter (g/cm³) is the other unit you see most often, and it gives a number 1,000 times smaller: 1 g/cm³ = 1,000 kg/m³ = 1 kg/L = 1 t/m³. Liquid water is about 1 g/cm³, so a milliliter of water has a mass of about 1 gram.
The calculator solves all three forms of the formula. To find density, enter the mass and the volume: 54 g that fill 20 cm³ give 54 ÷ 20 = 2.7 g/cm³, or 2,700 kg/m³, which is the density of aluminum. To find mass, enter the density and the volume: m = ρ × V. To find volume, enter the mass and the density: V = m ÷ ρ. Choose the unit you measured in for each value (g, kg or t; cm³, mL, L or m³; kg/m³ or g/cm³) and everything is converted to SI units before the calculation.
In the US, density is often given in pounds per cubic foot (lb/ft³): 1 g/cm³ = 62.428 lb/ft³, so water is about 62.4 lb/ft³ and aluminum about 169 lb/ft³. This calculator uses metric units, so convert first. For weights, use the grams to pounds converter for pounds and ounces and the pounds to kilograms converter for larger amounts; for liquids, the mL to oz converter for fluid ounces and the gallons to liters converter for US gallons. For volumes measured in inches or feet, 1 in³ = 16.387064 cm³ and 1 ft³ = 28.316846592 L, both exact because an inch is exactly 2.54 cm and a foot exactly 0.3048 meter. Density changes with temperature and pressure, especially for gases, so tables state the conditions, often 20 °C (68 °F).
The formula
Density is a ratio, so the three formulas are one relationship written three ways. Internally the calculator works in SI units: mass in kilograms (1 g = 0.001 kg, 1 t = 1,000 kg), volume in cubic meters (1 cm³ = 1 mL = 0.000001 m³, 1 L = 0.001 m³) and density in kg/m³ (1 g/cm³ = 1,000 kg/m³). It then converts the result back to the units you usually read. The t in the mass menu is the metric ton of 1,000 kg, not the US short ton of 2,000 lb.
For a pure, uniform material the density does not depend on the amount: 54 g of aluminum fill 20 cm³ and 540 g fill 200 cm³, and both give 2.7 g/cm³. The results assume one uniform material at the temperature and pressure of the measurement. Bulk materials such as sand or sugar hold air gaps, so mass divided by the volume you measure gives their bulk density, which is lower than the density of the material itself.
Example
What is the density of a 54 g sample that fills 20 cm³?
- Convert to SI units: 54 g = 0.054 kg and 20 cm³ = 0.00002 m³.
- Divide mass by volume: 0.054 kg / 0.00002 m³ = 2,700 kg/m³.
- In g/cm³, divide by 1,000: 2,700 / 1,000 = 2.7 g/cm³, the density of aluminum.
- In pounds per cubic foot, multiply g/cm³ by 62.428: 2.7 × 62.428 = 168.6 lb/ft³.
A mass of 54 g that fills 20 cm³ has a density of 2,700 kg/m³, which is 2.7 g/cm³.
Load this example into the calculatorFrequently asked questions
What is density?
Density is the mass of a material per unit of volume, written ρ = m / V. It tells you how much matter is packed into a given space: 1 cm³ of water has a mass of about 1 g, 1 cm³ of aluminum about 2.7 g and 1 cm³ of gold about 19.3 g. The SI unit is kg/m³, and g/cm³ is also widely used.
What is the density formula?
Density equals mass divided by volume: ρ = m / V. Rearranged, mass equals density times volume (m = ρ × V) and volume equals mass divided by density (V = m / ρ). Keep the units consistent: grams with cm³ give g/cm³, kilograms with m³ give kg/m³.
How do you calculate density?
Measure the mass with a scale, find the volume, then divide mass by volume. For a regular shape, work out the volume from its dimensions: length × width × height for a box and π × radius² × height for a cylinder. For an irregular solid that sinks, lower it into a graduated cylinder of water: the level rises by the object’s volume, and 1 mL equals 1 cm³. If 54 g raises the level by 20 mL, the density is 54 / 20 = 2.7 g/cm³. Choose “Density” above and enter the two values to check it.
How do you find mass from density and volume?
Multiply the density by the volume: m = ρ × V. Cooking oil is about 0.92 g/cm³, so 3.5 L (3,500 cm³) of it has a mass of 0.92 × 3,500 = 3,220 g, or 3.22 kg. Choose “Mass” above, enter the volume and the density, and the calculator does the unit conversions for you.
How do you find volume from mass and density?
Divide the mass by the density: V = m / ρ. A 1 kg (1,000 g) block of iron at 7.87 g/cm³ has a volume of 1,000 / 7.87 = 127.06 cm³. Mass and density must use matching units, or you can let the calculator convert them under “Volume”.
How do you convert g/cm³ to kg/m³ and lb/ft³?
Multiply g/cm³ by 1,000 to get kg/m³: 2.7 g/cm³ is 2,700 kg/m³. For pounds per cubic foot, multiply g/cm³ by 62.428: 2.7 g/cm³ is about 168.6 lb/ft³. To go back, divide by 1,000 or by 62.428. The units kg/L, g/mL and t/m³ have the same number as g/cm³.
What is the density of water?
Water is about 1 g/cm³ or 1,000 kg/m³, which is 62.4 lb/ft³. Its density is 999.972 kg/m³ at 4 °C and 998.207 kg/m³ at 20 °C (68 °F). A liter of water therefore has a mass of about 1 kg, and a US gallon about 8.3 lb.
What is the difference between density and specific gravity?
Specific gravity, also called relative density, is a material’s density divided by the density of water, so it has no unit. Because water is about 1 g/cm³, a solid or liquid has nearly the same specific gravity as its density in g/cm³: aluminum is about 2.7. A specific gravity below 1 means the material floats on water.
Does density change with temperature?
Yes. Most materials expand when heated, so the same mass takes up more volume and the density drops. The change is small for solids and liquids and large for gases. Tables therefore name the temperature, often 20 °C (68 °F). Water is an exception between 0 °C and 4 °C, where it gets denser as it warms.
- The International System of Units (SI Brochure, 9th edition): mass density in kg m⁻³, the liter and the metric ton (tonne) (Bureau International des Poids et Mesures (BIPM))
- NIST Guide to the SI, Appendix B.8: conversion factors for g/cm³, lb/ft³, the inch, foot, cubic inch and cubic foot, the metric ton and the short ton (National Institute of Standards and Technology (NIST))
- Density: definition, units, specific gravity, and the density of water and common materials (Wikipedia)