Density Calculator

What is a density calculator?

A density calculator solves the equation ρ = m/V, returning density, mass or volume when you supply the other two values. Density measures how much mass is packed into a given volume of a substance. Chemistry and physics students, lab technicians, engineers and machinists use it to identify materials, check buoyancy and convert between mass and volume.

What is the density formula?

The density formula is ρ = m / V — density equals mass divided by volume. It links three quantities, and knowing any two gives the third. Each symbol stands for a measurable property:

• ρ (rho) — density, expressed as a mass unit over a volume unit (kg/m³, g/cm³, kg/L).
• m — mass, in any unit of mass (kg, g, lb).
• V — volume, in any unit of volume (m³, cm³, L).

The calculator works with any consistent units: kilograms with cubic metres give an answer in kg/m³, while grams with cubic centimetres give g/cm³. It does not convert units for you, so match them yourself before entering values.

To solve for a single unknown, the tool rearranges the formula algebraically. The three forms are:

Solve for	Rearranged formula
Density (ρ)	ρ = m / V
Mass (m)	m = ρ · V
Volume (V)	V = m / ρ

Because volume and density appear as divisors, both must be positive — you cannot divide by zero or a negative volume. The result is reported to six significant figures.

Worked examples

Each example below uses only the rearrangements above, so you can reproduce every answer by entering the same two values into the calculator.

Example 1 — solve for density (ρ)

A container holds m = 1000 kg of fresh water filling V = 1 m³. Find the density.

ρ = m / V = 1000 / 1 = 1000 kg/m³

The result, 1000 kg/m³, is the textbook density of water — equivalent to 1 g/cm³.

Example 2 — solve for mass (m)

You have V = 1 m³ of water with a known density ρ = 1000 kg/m³. Find the mass.

m = ρ · V = 1000 × 1 = 1000 kg

One cubic metre of water weighs 1000 kg (one tonne), confirming Example 1 in reverse.

Example 3 — solve for volume (V)

A sample of water has mass m = 1000 kg and density ρ = 1000 kg/m³. Find the volume it occupies.

V = m / ρ = 1000 / 1000 = 1 m³

The 1000 kg of water takes up exactly 1 m³, closing the loop on the first two examples.

Example 4 — using g/cm³ (gold)

A pure gold cube has mass m = 19.3 g and volume V = 1 cm³. Find its density.

ρ = m / V = 19.3 / 1 = 19.3 g/cm³

Gold’s density of 19.3 g/cm³ (19,300 kg/m³) is why a small gold bar feels surprisingly heavy.

Density of common substances

This chart lists approximate densities at about 20–25°C in both common unit systems. Note that 1 g/cm³ equals exactly 1000 kg/m³, which makes water the convenient reference point.

Substance	Density (g/cm³)	Density (kg/m³)
Air (sea level)	0.00120	1.20
Cork	0.24	240
Ethanol	0.789	789
Ice (0°C)	0.917	917
Water (fresh)	1.00	1000
Seawater	1.025	1025
Aluminium	2.70	2700
Iron	7.87	7870
Lead	11.3	11,300
Mercury	13.6	13,600
Gold	19.3	19,300

Anything less dense than the surrounding fluid floats: ice (917 kg/m³) floats on water (1000 kg/m³), and a substance under 1000 kg/m³ floats in fresh water.

Common uses

The density formula appears anywhere mass and volume meet:

• Chemistry and physics homework — finding density to identify an unknown substance from a data table.
• Exam and lab problems — solving for mass or volume when density and one other value are given.
• Material identification — comparing a measured density against reference values to tell brass from gold or steel from aluminium.
• Buoyancy and floating — deciding whether an object floats by comparing its density to water’s 1000 kg/m³.
• Engineering and manufacturing — estimating the weight of a part from its volume, or the volume of a tank from a known mass of fluid.

Tips and common mistakes

• Keep units consistent. Mass and volume must belong to the same system: kg with m³, or g with cm³. Mixing grams with cubic metres produces a number that is off by a factor of a million.
• Watch the g/cm³ to kg/m³ jump. To convert g/cm³ to kg/m³, multiply by 1000 (water: 1 g/cm³ = 1000 kg/m³). To go back, divide by 1000.
• Volume and density must be positive. They sit in the denominator when you solve for density or volume, so a value of zero or below is rejected — that is the division-by-zero guard of this tool.
• Use the right volume of an irregular object. For odd shapes, measure volume by water displacement rather than guessing, or the density will be wrong even if the arithmetic is perfect.
• Mind significant figures. The display shows six sig figs, but your answer is only as accurate as the least precise measurement you typed in.
• Specific gravity is unitless. Divide your density by water’s 1000 kg/m³ to get specific gravity; do not leave units on it.

Limitations and accuracy

The calculator does pure arithmetic on the values you enter, so the math is exact, but the physical density of a real substance depends on temperature and pressure. The reference chart above assumes roughly room temperature (20–25°C) and ordinary atmospheric pressure; water peaks near 1000 kg/m³ at 4°C and is slightly less dense when warmer. Gases are especially sensitive — air’s density changes markedly with altitude, temperature and humidity. The tool also assumes a uniform, non-porous material: a foam or a powder with trapped air has a lower bulk density than its solid material. Treat it as an education and estimation aid, and confirm critical figures against measured data for your exact conditions.

For more science tools, try the combined gas law calculator for how gas volume and pressure shift with temperature, the kinetic energy calculator for the energy of a moving mass, or the pH calculator — and browse more in the chemistry and physics category.