Calculate Mass and Volume: Formulas and Examples

To calculate mass, multiply an object’s density by its volume; to calculate volume, divide its mass by its density. Enter the known values in consistent units, and the calculator returns mass and volume, with density used to connect the two.

Formula

The relationship between mass, density, and volume is:

• Mass: m = ρ × V
• Volume: V = m ÷ ρ
• Density: ρ = m ÷ V

Here, m is mass in kilograms (kg), ρ is density in kilograms per cubic metre (kg/m³), and V is volume in cubic metres (m³). The calculator’s first result is mass calculated from the entered density and volume. Its second result is volume calculated from the entered mass and density.

The example density, 1,000 kg/m³, is approximately the density of water under ordinary conditions. The two calculations use the default volume of 0.001 m³ and default mass of 1 kg. These are separate calculations using the same density, rather than a requirement that the entered mass and volume describe the same object.

Worked Example

Using the calculator’s defaults:

• Density = 1,000 kg/m³
• Mass = 1 kg
• Volume = 0.001 m³

Mass from density and volume:
m = ρ × V
m = 1,000 kg/m³ × 0.001 m³ = 1.000 kg

Volume from mass and density:
V = m ÷ ρ
V = 1 kg ÷ 1,000 kg/m³ = 0.001000 m³

The units cancel as they should: kg/m³ multiplied by m³ gives kg, while kg divided by kg/m³ gives m³.

What Mass and Volume Mean

Mass describes how much matter an object contains. It is commonly measured in grams (g), kilograms (kg), ounces (oz), or pounds (lb). Weight is a force caused by gravity, so it is not technically the same as mass, even though everyday conversation often treats the words as interchangeable. A scale typically reports mass in familiar units, although its physical operation involves forces.

Volume describes the space occupied by a substance or object. Metric units include millilitres (mL), litres (L), cubic centimetres (cm³), and cubic metres (m³). US customary volume units include teaspoons, cups, quarts, and gallons; solid dimensions may instead be stated in cubic inches or cubic feet. Density is mass per unit volume, so it tells you how much mass is packed into a given space.

For example, a litre of water has a volume of 1 L and a mass close to 1 kg under ordinary conditions. A litre of a denser liquid has greater mass, even though the volume is unchanged. Conversely, equal masses of different materials can occupy different volumes.

How to Choose the Calculation

Use the equation that matches the information you have and the quantity you need:

• You know density and volume: multiply them to find mass.
• You know mass and density: divide mass by density to find volume.
• You know mass and volume: divide mass by volume to find density.

If density is not known, you must measure it or obtain a suitable value for the material and conditions. A material name alone may not be enough: temperature, pressure, composition, moisture, and trapped air can affect density. For mixtures or irregular objects, a single published density may not accurately represent the sample.

Units and Practical Conversions

Before using a formula, make sure the mass, volume, and density units are compatible. If density is in kg/m³ and volume is in m³, the mass result is in kg. If mass is in grams and volume in cubic centimetres, density is in g/cm³. These density units have the same numerical value: 1 g/cm³ = 1,000 kg/m³.

• 1 L = 0.001 m³ = 1,000 cm³.
• 1 mL = 1 cm³.
• 1 kg = 1,000 g, approximately 2.205 lb.
• 1 US gallon is approximately 3.785 L; an imperial gallon is approximately 4.546 L.
• 1 cubic foot is approximately 0.02832 m³.

Do not mix US gallons with imperial gallons, or fluid ounces with ounces of mass. A fluid ounce is a volume unit; an ounce used to weigh something is a mass unit. If converting between customary and metric values, convert each input before substituting it into the formula, or use a consistent set of units throughout.

Measurements, Assumptions, and Common Errors

The equations are straightforward, but the result is only as reliable as the measurements. For a rectangular solid, volume is length × width × height, with all dimensions expressed in the same length unit. For a cylinder, volume is π × radius² × height. Irregular objects can be measured by displacement: note the liquid’s initial volume, submerge the object if appropriate, then subtract the initial reading from the final reading.

Displacement is unsuitable if the object dissolves, absorbs the liquid, reacts with it, or cannot be safely submerged. It can also be inaccurate for objects that trap air or float unless the measurement method accounts for those effects. For porous or granular materials, decide whether the intended volume includes gaps between particles; bulk density and the density of the solid material are not necessarily the same.

• Use the radius, not the diameter, in a cylinder’s volume formula.
• Convert centimetres to metres before calculating cubic metres; cubic units scale by the conversion factor cubed.
• Do not round intermediate values too early. Round the final answer to match the precision of the measurements.
• Check that density is positive and that the units describe mass per volume.

The formula assumes the chosen density applies to the whole volume and remains effectively uniform. It does not determine an unknown density, account for changing conditions, or correct faulty measurements. If a material’s density varies across a sample, the simple calculation may require separate regions or a measured average density.

Frequently Asked Questions

How do I calculate mass from volume?
Multiply volume by density: mass = density × volume. For example, 0.002 m³ of a material with density 800 kg/m³ has a mass of 1.6 kg.

How do I calculate volume from mass?
Divide mass by density: volume = mass ÷ density. A 2 kg sample with density 1,000 kg/m³ occupies 0.002 m³, or 2 L.

Can I calculate mass without knowing density?
Not from volume alone. You need density or another measurement that supplies equivalent information, such as weighing the object directly.

Is mass the same as weight?
No. Mass measures matter and is commonly expressed in kilograms or pounds-mass; weight is gravitational force, measured in newtons in SI units. Everyday scales and speech often blur the distinction.

Why does the calculated mass differ from what I measured?
Check unit conversions, the volume measurement, and whether the density matches the material’s composition and conditions. Trapped air, moisture, temperature, and rounding can also explain differences.

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in dens | Density | kg/m³ | 1000 | 0
in mass | Mass | kg | 1 | 0
in vol | Volume | m³ | 0.001 | 0
out calc_mass | Mass from density and volume | kg | dens * vol | 3
out calc_vol | Volume from mass and density | m³ | mass / dens | 6