Density ↔ Volume Converter
Solve for mass, volume, or density using ρ = m/V — enter any two of the three and get the third, with steps. Or flip it around: enter a density and identify which common substance it likely is, from air to osmium.
Background
Density relates how much matter (mass) is packed into a given amount of space (volume): ρ = m / V. Because it's a fixed property of a pure substance under given conditions, density is also a fingerprint — measure an object's mass and volume, and the density you calculate can tell you what it's likely made of.
How to use this calculator
- Choose Solve for m, V, or ρ when you know two of the three quantities and need the third.
- Choose Identify a Substance when you've already calculated (or measured) a density and want to know what material it likely is.
- Pick what you're solving for, or enter your density value, then choose matching units.
- Click Calculate to see the visual, the full result, and a step-by-step explanation.
How density works
Density (ρ) packs mass and volume into a single number: ρ = m / V. It answers "how much stuff is squeezed into this space?"
Rearranged, the same relationship gives mass (m = ρ × V) or volume (V = m / ρ) whenever the other two quantities are known.
Density is intensive — it doesn't depend on how much of the substance you have. A gram of gold and a kilogram of gold have the same density, unlike mass or volume, which are extensive.
Because density is a fixed property of a pure substance (at a given temperature and pressure), measuring it is one way to help identify an unknown material.
An object floats in a fluid if its density is lower than the fluid's, and sinks if it's higher — this is why ice (0.92 g/cm³) floats on water (1.00 g/cm³), but a copper coin does not.
1 mL and 1 cm³ are exactly the same volume, which is why g/mL and g/cm³ are interchangeable density units.
Formulas & Equations Used
Density: ρ = m / V
Mass: m = ρ × V
Volume: V = m / ρ
Unit equivalence: 1 mL = 1 cm³, 1 g/mL = 1 g/cm³ = 1 kg/L = 1,000 kg/m³
Example Problems & Step-by-Step Solutions
Example 1 — Solving for density
A block of metal has a mass of 54 g and a volume of 20 cm³.
Step: ρ = m / V = 54 ÷ 20.
Result: ρ = 2.70 g/cm³ — this matches aluminum almost exactly.
Example 2 — Solving for mass
You have 250 mL of water (density 1.00 g/mL).
Step: m = ρ × V = 1.00 × 250.
Result: m = 250 g.
Example 3 — Solving for volume
A 100 g sample of a liquid has a density of 0.79 g/mL (ethanol).
Step: V = m / ρ = 100 ÷ 0.79.
Result: V ≈ 126.6 mL.
Example 4 — Identifying an unknown metal
A 350 g sample fills exactly 39 cm³.
Step: ρ = 350 ÷ 39 ≈ 8.97 g/cm³.
Result: That's within 0.2% of copper (8.96 g/cm³) — a strong match.
Example 5 — Why ice floats
Ice has a density of about 0.92 g/cm³; liquid water is 1.00 g/cm³.
Step: Compare the two densities directly — no formula needed once both are known.
Result: Since 0.92 < 1.00, ice is less dense than water and floats.
Example 6 — Converting density units
Seawater is often quoted as 1,025 kg/m³. Express this in g/cm³.
Step: 1,025 kg/m³ × 0.001 = 1.025 g/cm³.
Result: Seawater is about 1.025 g/cm³ — slightly denser than fresh water.
Frequently Asked Questions
Do I need to enter mass, volume, and density all at once?
No. Pick what you're solving for and only the other two fields matter — the calculator computes the third from ρ = m/V.
How does identifying a substance from density actually work?
Pure substances have characteristic densities at a given temperature. Your entered value is compared against a reference table, and the closest match (within about 5%) is reported. It's a strong clue, not absolute proof — alloys, impurities, and temperature can shift real-world measurements slightly.
Why are g/mL and g/cm³ treated as the same unit?
Because 1 milliliter and 1 cubic centimeter are defined to be exactly the same volume, so a density expressed in either unit has the identical numeric value.
Why can't volume or density be zero or negative?
Density is mass divided by volume, so a zero volume makes the calculation undefined (division by zero), and negative volume or density has no physical meaning for a real object.
Does density change with temperature?
Yes, slightly for solids and more noticeably for liquids and gases, since volume typically expands as temperature rises while mass stays constant. The reference values used here are standard room-temperature approximations.
What does it mean if my density value doesn't match anything in the table?
It likely falls between two reference substances, or outside the whole range (lighter than hydrogen gas or denser than osmium) — the result will tell you which known substances it falls near.
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