Density, Mass & Volume

How Density, Mass, and Volume Relate

Density measures how much mass is packed into a given volume — it’s why a bowling ball is so much heavier than a beach ball of the same size. Enter any two of density, mass, or volume, and this calculator finds the third.

The Formula

$$\vC{\text{Density}} = \frac{\vA{\text{Mass}}}{\vB{\text{Volume}}}$$ $$\vA{\text{Mass}} = \vC{\text{Density}} \times \vB{\text{Volume}}$$ $$\vB{\text{Volume}} = \frac{\vA{\text{Mass}}}{\vC{\text{Density}}}$$

Mass and volume each have their own unit picker (kg/g/lb and m³/L/ft³) — when solving for density, the result is shown as a compound unit built directly from whichever mass and volume units you picked (for example lb/ft³), so it always matches the units you actually entered.

Worked Example

A sample weighing 500 grams with a volume of 200 liters:

1. Convert to canonical SI units: $\vA{500}\text{ g} = \vA{0.5}\text{ kg}$ and $\vB{200}\text{ L} = \vB{0.2}\text{ m}^3$ (since 1 m³ = 1,000 L).
2. Density: $\vA{0.5} \div \vB{0.2} = \vC{2.5}$ kg/m³.

Key Factors to Consider

• Temperature and pressure both affect a material’s true density, especially for gases and liquids. Most published density reference values are given at a specific standard temperature (often 20°C or 25°C) — an object measured at a very different temperature can have a meaningfully different actual density than the reference value suggests, since materials generally expand slightly when heated.
• Solids are generally much less compressible than liquids, and liquids much less than gases. This is why a gas’s density changes dramatically with pressure while a solid’s barely changes at all — density comparisons across different states of matter need to account for this if precision matters.
• An irregularly shaped object’s volume is trickier to measure directly than its mass. Weighing an object is usually straightforward with a scale, but finding its volume often requires water displacement or a geometric calculation — the accuracy of a calculated density is only as good as the least precise of the two measurements that go into it.
• Specific gravity (relative density) compares a substance’s density to water’s, as a simple ratio. A specific gravity greater than 1 means denser than water (it sinks); less than 1 means less dense than water (it floats) — this is a related, unitless way some fields express the same underlying property this calculator computes directly.

Common Mistakes

• Mixing up mass and weight. Mass (kg, g, lb as a mass unit) is how much matter an object has; weight is the force gravity exerts on that mass. The density formula uses mass — on Earth the two track closely enough in everyday use that this rarely causes a wrong answer, but it’s worth knowing they’re not actually the same thing.
• Forgetting that a hollow or porous object’s overall density is lower than its material’s true density. A solid steel ball and a hollow steel sphere are made of the same material, but the hollow one has less mass for the same outer volume — this calculator reports whatever density the entered mass and volume actually imply, not a material’s textbook reference value.
• Entering an object’s outer dimensions’ volume instead of its own displaced volume. For an irregular or partially hollow object, the volume that matters for density is the actual space the material occupies, not the bounding box around it — water-displacement measurement captures this correctly, a quick length × width × height estimate often doesn’t.

Useful to Know

This calculator always keeps mass and volume in whatever units you actually entered, converting internally to SI (kilograms and cubic meters) only to do the math and then converting the result back — so a density result in lb/ft³ or g/cm³ reflects your own units, not a forced conversion to kg/m³. If you need to compare against a published reference density (often given in g/cm³ or kg/m³), it’s usually easiest to switch your mass and volume units to grams and cubic centimeters (or kilograms and cubic meters) before comparing, rather than converting the final answer by hand.