Density Calculator
Calculate density, mass, or volume from the other two values.
Common densities at 20 °C (g/cm³) — click to use
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What it does
The Density Calculator solves the density relationship in any direction: density from a measured mass and volume, the mass that a known volume of a substance will weigh, or the volume that a given mass will occupy. Mass, volume and density each carry their own unit selector, so a handbook value quoted in kg/m³, a volume measured in litres and a mass in milligrams can all be entered as they are. A table of common densities is provided to check a result against, which is faster than opening a handbook. Everything runs in the browser.
How it works
Density is mass per unit volume, so density equals mass divided by volume, which rearranges to mass equals density times volume and volume equals mass divided by density. Every input is converted to a base of grams, millilitres and g/mL before the arithmetic, so the unit selectors change how a value is entered and reported without changing the underlying answer. Those units are worth keeping straight because g/mL and g/cm³ are numerically identical, since one millilitre is exactly one cubic centimetre, while kg/m³ is a factor of a thousand smaller and kg/L is numerically the same as g/mL. Water at 1.000 g/mL is therefore 1.000 g/cm³, 1000 kg/m³ and 1.000 kg/L at the same time. Results are formatted to six significant figures, switching to scientific notation below 1e-3 or at 1e9 and above, and the tool will not compute from an empty, zero or negative input.
Worked example
A metal block weighing 25.0 g that displaces 3.20 mL of water has a density of 25.0 / 3.20 = 7.8125 g/mL. Comparing that against a table, iron is 7.87, zinc 7.14, copper 8.96 and lead 11.34, so the sample sits close to iron but not on it, and the discrepancy is itself informative. A small bubble clinging to the block raises the apparent volume and lowers the calculated density, and the sensitivity is worth appreciating: at this scale a 0.1 mL error in the reading moves the answer by about 0.25 g/mL. Running the equation the other way, 50.0 g of ethanol at 0.789 g/mL occupies 50.0 / 0.789 = 63.371 mL, which is the volume to measure out if no balance is available. For reference, water is 0.99705 g/mL at 25 C but 1.00000 g/mL at 4 C, a difference of about 0.3 percent that only matters once four significant figures are being reported.
When to use it
Use it whenever a protocol gives one quantity and the equipment measures another, for example converting a weight-based recipe into a volume to pipette, or working out what a 250 mL bottle of a reagent should weigh on the bench. Three cautions come from the physics rather than the software. Units are selectable rather than fixed, so a density quoted in kg/m³ or a volume measured in litres can be entered as it stands and the answer comes back in whichever unit is selected, but the selector does not know what the substance is: it converts units, it does not tell you which density to use. A density obtained by dividing a weighed mass by a volume read from a cylinder is a bulk or apparent density, not the true density of the material, and that distinction matters most for powders and porous solids: a tapped pharmaceutical powder can read 0.4 g/mL while the true density of its particles is 1.4 g/mL. Finally, density is a function of temperature, since liquids expand when warm, so a handbook value quoted at 20 C used alongside a measurement taken at 30 C will be wrong in the third figure. For accurate work, measure mass and volume at the same temperature and allow for the buoyancy of air if the sample is weighed in a large container.
FAQ
- How do I calculate density from mass and volume?
- Divide the mass by the volume: density = mass / volume. A 25.0 g block that displaces 3.20 mL gives 25.0 / 3.20 = 7.8125 g/mL. For a liquid, weigh the container empty and full to obtain the mass of liquid, and read the volume from the same graduated cylinder or from the calibration of the container.
- What units does the calculator use?
- Any of the listed ones. Density can be given in g/mL, g/cm³, kg/m³ or kg/L; mass in g, kg or mg; volume in mL, cm³, L or µL. Every input is converted to a base of grams, millilitres and g/mL before the arithmetic, and the answer is reported in the unit selected for the unknown. Because one millilitre equals one cubic centimetre, g/mL and g/cm³ are interchangeable, while kg/m³ is a thousand times smaller: water is 1.000 g/mL, 1.000 g/cm³, 1000 kg/m³ and 1.000 kg/L at once. Watch for the trap of entering a kg/m³ figure while the selector still says g/mL, which understates the density by three orders of magnitude.
- What is the difference between bulk density and true density?
- Bulk density, sometimes called apparent density, is the mass of a sample divided by the volume it occupies including the voids between particles, so it depends on how the powder was poured or tapped. True density is the density of the solid material itself, measured by helium pycnometry or with a density bottle. A powder can show 0.4 g/mL bulk and 1.4 g/mL true density, so state which one is meant before comparing with a table.
- Why does my measured density differ from the handbook value?
- Four common reasons: temperature, since liquids expand and the density of water falls from 1.00000 g/mL at 4 C to 0.99705 at 25 C; trapped air bubbles, which inflate the volume and lower the result; an impure or hydrated sample, where absorbed water changes the mass; and container or meniscus errors of a few tenths of a millilitre. At the scale of a 3 mL measurement, 0.1 mL of error moves the answer by roughly 0.25 g/mL.