Free Density Calculator
Calculate density, mass, or volume from the relation ρ = m / V. Enter any two values and this tool solves the third instantly, showing the answer in both kg/m³ and g/cm³.
ρ = m / V. Enter mass in kilograms and volume in cubic meters so density comes out in kg/m³. Divide kg/m³ by 1000 to read g/cm³ (water ≈ 1000 kg/m³ = 1 g/cm³).
Quick answer
Density is mass divided by volume: ρ = m / V. With mass in kilograms and volume in cubic meters, density is expressed in kilograms per cubic meter (kg/m³); divide by 1000 to convert to grams per cubic centimeter (g/cm³). For example, 1000 kg in 1 m³ gives a density of 1000 kg/m³, which equals 1 g/cm³ — the density of liquid water.
Formula & method
Density
ρ = m / V
- ρ — density (kg/m³)
- m — mass (kg)
- V — volume (m³)
Rearrange to find the missing quantity: mass is m = ρ × V, and volume is V = m / ρ. Volume must be non-zero to compute density, and density must be non-zero to compute volume.
Unit conversion
ρ (g/cm³) = ρ (kg/m³) ÷ 1000
1 g/cm³ equals exactly 1000 kg/m³ because 1 g = 0.001 kg and 1 cm³ = 0.000001 m³. Water is about 1000 kg/m³ = 1 g/cm³ at 4 °C.
Examples
- Input
- Mass m = 2700 kg, Volume V = 1 m³, solve for ρ
- Result
- ρ = 2700 kg/m³ = 2.7 g/cm³
- Why
- ρ = m / V = 2700 ÷ 1 = 2700 kg/m³. Dividing by 1000 gives 2.7 g/cm³, the textbook density of solid aluminium.
- Input
- Density ρ = 13534 kg/m³, Volume V = 0.5 m³, solve for m
- Result
- m = 6767 kg
- Why
- Rearranging ρ = m / V gives m = ρ × V = 13534 × 0.5 = 6767 kg. Mercury is extremely dense, so even half a cubic meter weighs nearly 6.8 tonnes.
- Input
- Mass m = 500 kg, Density ρ = 789 kg/m³, solve for V
- Result
- V ≈ 0.633714 m³ (≈ 633.7 L)
- Why
- V = m / ρ = 500 ÷ 789 = 0.633714 m³. Multiplying by 1000 converts to 633.7 liters, the space 500 kg of ethanol would fill.
- Input
- Mass m = 1000 kg, Volume V = 1 m³, solve for ρ
- Result
- ρ = 1000 kg/m³ = 1 g/cm³
- Why
- ρ = m / V = 1000 ÷ 1 = 1000 kg/m³. This is the reference density of liquid water and the basis of the metric definition of the kilogram-per-liter.
When to use this tool
- Identifying or verifying a material by comparing its measured density against known reference values (e.g. distinguishing gold from a gold-plated fake).
- Converting between the mass and volume of a substance when you know its density — for shipping weights, tank capacities, or recipe scaling.
- Checking buoyancy: an object floats in a fluid only if its average density is lower than the fluid's density.
- Engineering and lab work where you need consistent SI density (kg/m³) but also want the familiar g/cm³ figure for quick intuition.
Common mistakes
- Mixing unit systems — using grams for mass but cubic meters for volume. Keep mass in kg and volume in m³ to get kg/m³, then divide by 1000 for g/cm³.
- Confusing density with weight or mass. Density is mass per unit volume; a small lead pellet is denser than a large foam block even though the foam block weighs more.
- Forgetting that 1 g/cm³ = 1000 kg/m³, not 1. The factor is 1000 because both the gram-to-kilogram and cm³-to-m³ conversions compound.
- Entering a volume of zero (or a density of zero when solving for volume), which makes the division undefined — the calculator returns a blank result to avoid dividing by zero.
Frequently asked questions
What is the formula for density?
Density equals mass divided by volume: ρ = m / V. To find mass, multiply density by volume (m = ρ × V); to find volume, divide mass by density (V = m / ρ).
What units does this density calculator use?
It uses SI base units: mass in kilograms (kg) and volume in cubic meters (m³), giving density in kilograms per cubic meter (kg/m³). When you solve for density it also shows the result in grams per cubic centimeter (g/cm³), which is kg/m³ divided by 1000.
How do I convert kg/m³ to g/cm³?
Divide the kg/m³ value by 1000. For example, 7870 kg/m³ (iron) ÷ 1000 = 7.87 g/cm³. The conversion factor is exactly 1000 because 1 g/cm³ equals 1000 kg/m³.
What is the density of water?
Pure liquid water is about 1000 kg/m³, or 1 g/cm³, at 4 °C — the temperature where it is densest. It drops slightly with temperature (about 997 kg/m³ at 25 °C) and is the default reference point for floating and sinking.
Can I calculate mass or volume instead of density?
Yes. Use the "Solve for" selector to choose Mass or Volume. Enter the other two values and the tool rearranges ρ = m / V automatically — mass becomes ρ × V and volume becomes m / ρ.
Why does the calculator refuse to compute when volume is zero?
Density is mass per unit volume, so dividing by a volume of zero is mathematically undefined. The calculator guards against this and leaves the result blank until you enter a non-zero volume (and likewise a non-zero density when solving for volume).
Sources & references
External references open in a new tab. We are independent and not affiliated with these organizations.
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Provided “as is” for general information only — results may be inaccurate, so verify before you rely on them. No warranty; use at your own risk.
Built and reviewed by HIFreeTools against the formula shown above and any authoritative references cited on this page. See our methodology and editorial standards.
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