Calculation
ρ = m / V
Density is mass per volume and affects weight, buoyancy and inertia.
ρ = m/V
Density Calculator from Mass and Volume
Density is mass per volume and affects weight, buoyancy and inertia.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Density ρ — Mass per cubic metre of the substance – a material property that determines how heavy a given volume is. Source: material table/datasheet (typical values: structural steel ≈ 7850 kg/m³, water at 4 °C = 1000 kg/m³, aluminium ≈ 2700 kg/m³) or computed from your own weighing and volume measurement. Valid only at the stated temperature.
- Mass m — The mass of the sample or part whose density is being found. Source: weigh it on a scale; for liquids, weigh the empty and the filled container and use the difference.
- Volume V — The geometric or displaced volume belonging to the entered mass m. Source: calculate it from dimensions (cylinder, box) or measure it by displacement in a liquid. Must belong to the same sample as m.
Example
7.85 kg / 0.001 m³ = 7,850 kg/m³ (steel-like value).
Assumptions and limits
Homogeneous material at constant temperature.
Understand Density Calculator from Mass and Volume
This calculator finds the missing quantity among mass m, volume V and density ρ from the other two. It helps identify materials, estimate part weight, or check mixing ratios. The article explains the difference between mass and weight, why water's density depends on temperature, and how equally sized parts of different materials can differ hugely in weight.
What does this quantity describe?
The density ρ of a substance is its mass m relative to the volume V it occupies: ρ = m/V. It is a material property that, for many substances, also depends on temperature and pressure, especially for liquids and gases.
Two equally sized 1-litre cubes of aluminium and steel show the effect clearly: the aluminium cube weighs about 2.7 kg at a density of roughly 2,700 kg/m³, while the steel cube weighs about 7.8 kg at roughly 7,800 kg/m³ — nearly three times as much for identical volume.
Formula and variables
ρ = m / V
ρ = m / Vm = ρ · VV = m / ρ
| Symbol / input | Meaning |
|---|---|
| Density ρ | Mass per cubic metre of the substance – a material property that determines how heavy a given volume is. Source: material table/datasheet (typical values: structural steel ≈ 7850 kg/m³, water at 4 °C = 1000 kg/m³, aluminium ≈ 2700 kg/m³) or computed from your own weighing and volume measurement. Valid only at the stated temperature. |
| Mass m | The mass of the sample or part whose density is being found. Source: weigh it on a scale; for liquids, weigh the empty and the filled container and use the difference. |
| Volume V | The geometric or displaced volume belonging to the entered mass m. Source: calculate it from dimensions (cylinder, box) or measure it by displacement in a liquid. Must belong to the same sample as m. |
Choose the inputs correctly
Enter two of the three quantities. Density requires mass and volume, mass requires density and volume, volume requires mass and density. For liquids and gases, use a density value for the actual temperature, not a generic table value at 20 °C.
How to use the calculator
Select the target quantity and enter the two known values with units. For liquids, check that the density value matches the actual temperature, since water in particular has an unusual temperature dependence.
Worked example
Given m = 7.85 kg and V = 0.001 m³ (1 litre), substitution gives ρ = 7.85 kg / 0.001 m³ = 7,850 kg/m³, a typical value for structural steel. For comparison, aluminium is about 2,700 kg/m³, roughly a third of that.
Understand the result and units
A density of 7,850 kg/m³ means one cubic metre of this material weighs 7,850 kg. For a part with known volume, this directly estimates mass; for weight force, multiply additionally by gravitational acceleration (weight force = mass · g).
The SI unit is kg/m³. Laboratories and chemistry commonly use g/cm³, where 1 g/cm³ = 1,000 kg/m³. Water reaches its maximum density of about 999.97 kg/m³ near 4 °C; at 20 °C it is about 998.2 kg/m³, and at 100 °C only about 958.4 kg/m³.
Why does water's density change with temperature?
Water has its highest density, about 999.97 kg/m³, near 4 °C. Both warming it further and cooling it below 4 °C reduce its density — unusual behaviour for a liquid, caused by the hydrogen-bonded structure that forms as it approaches the freezing point. This is why ice is lighter than liquid water and floats, whereas for most other substances the solid phase is denser than the liquid.
Typical applications
Density calculations are used for material identification, estimating part and shipping weight, sizing buoyancy and floatation, and checking mixing ratios in process engineering.
Assumptions, limits and common mistakes
The formula assumes a homogeneous material and a clearly defined volume. For porous, layered or strongly temperature-dependent substances, density is valid only for the stated conditions; for gases it also changes noticeably with pressure.
Common mistake: Do not confuse mass and weight force: mass in kg is location-independent, while weight force in newtons depends on gravitational acceleration. A density value without a stated temperature is incomplete for liquids, since water, for example, does not have a constant density between 0 °C and 100 °C.
Frequently asked questions
What is the difference between mass and density?
Mass is the absolute amount of matter in a body, in kg. Density relates that mass to volume and is therefore a material property independent of part size.
Why does water have its highest density at 4°C?
This is due to the particular structure of hydrogen bonds. Density decreases both when warming above and cooling below 4°C.
Can density identify a material?
Approximately, if mass and volume are measured precisely. When several materials have similar densities, additional tests are needed.
How do I convert g/cm³ to kg/m³?
Multiply the value in g/cm³ by 1,000 to get kg/m³.