Density
Solve density, mass, or volume with the standard density relationship. Free online calculator with formulas and step-by-step solutions.
Key formula
rho = m / V
How do you calculate density?
Density is ρ = m / V. Divide mass by volume. Rearrange to m = ρ V or V = m / ρ. Fresh water is about 1000 kg/m³ (or 1 g/cm³). Objects denser than the surrounding fluid tend to sink when fully submerged.
About this tool
Density measures how much mass sits in a given volume. This page keeps ρ = m/V visible so you can solve for density, mass, or volume without mixing g/cm³ with kg/m³.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: 12 kg in 0.003 m³
ρ = m/V = 12 / 0.003 = 4000 kg/m³ — denser than water (1000 kg/m³).
Example 2: find mass from steel-like density
ρ = 7800 kg/m³, V = 0.002 m³. m = ρ V = (7800)(0.002) = 15.6 kg.
Example 3: find volume of 2.0 kg of water
ρ = 1000 kg/m³. V = m/ρ = 2.0/1000 = 0.002 m³ = 2.0 L.
Frequently asked questions
What is the density formula?
ρ = m / V, where m is mass and V is volume. Rearrangements are m = ρV and V = m/ρ.
What units should I use for density?
SI density is kg/m³. Lab work often uses g/cm³. Convert with 1 g/cm³ = 1000 kg/m³. Do not mix grams with cubic metres.
What is the density of water?
Fresh water is usually taken as 1000 kg/m³ or 1.00 g/cm³ near room temperature. Use the value on the exam if it differs slightly.
How does density relate to floating?
If an object’s average density is less than the fluid’s density, it floats. Buoyant force Fb = ρ_fluid V_displaced g uses fluid density, not object density.
Is density the same as weight?
No. Density is mass per volume (kg/m³). Weight is a force W = mg (newtons). You need both ideas for float/sink problems.