Compute density, mass, or volume with ρ = m ÷ V — plus an instant float-or-sink check against water. Free and mobile-friendly.
Choose the unknown: **density**, **mass**, or **volume**. The density triangle — ρ = m ÷ V, m = ρ × V, V = m ÷ ρ — covers all three. Enter the two known values, pick sensible units (grams with cm³, kilograms with liters, pounds with in³), and press **Calculate**.
The tool converts everything to grams and cm³ internally, computes, and converts the answer to your chosen density unit. A bonus line compares the result to water (1 g/cm³) and tells you whether the object floats or sinks. **Reset** restores the water defaults: 1000 g in 1000 cm³ = 1 g/cm³.
Watch the unit pairings: density in g/cm³ goes with mass in grams and volume in cm³; kg/m³ pairs with kg and m³. The dropdowns keep the common pairings one click away.
Who relies on it? Jewelers testing metal authenticity, brewers tracking fermentation, engineers selecting materials by strength-to-weight, teachers demonstrating Archimedes’ principle, and students checking lab results — anyone for whom mass and volume must agree.
Density (ρ, the Greek letter rho) is mass per unit volume — how much “stuff” is packed into a given space. A kilogram of feathers and a kilogram of steel have the same mass but wildly different densities, because the steel occupies far less volume.
The SI unit is kilograms per cubic meter (kg/m³), but everyday science uses grams per cubic centimeter (g/cm³): water is 1 g/cm³ = 1000 kg/m³. Reference points: air ≈ 0.0012 g/cm³, ice 0.917, aluminum 2.7, iron 7.87, lead 11.34, gold 19.32. Anything above 1 sinks in water; below 1 floats.
Density is an intensive property: it does not depend on how much material you have. Half a gold bar has the same density as the whole bar — which is exactly why jewelers and archaeologists test density to spot fakes.
All three are one relation rearranged. The subtlety is units: mass ÷ volume only yields a meaningful density when the units are a matched pair — grams with cm³, kg with m³, lb with in³. Mixing grams with liters gives g/L (valid but unusual); mixing grams with m³ gives a number 1,000,000× off.
Temperature matters for precision work: most materials expand when heated, so the same mass occupies more volume and density falls. Water is the famous exception near freezing — ice (0.917 g/cm³) floats on liquid water (1.0 g/cm³), which is why lakes freeze top-down.
Pressure matters too, mainly for gases: squeeze air to half its volume and its density doubles, which is why compressed-air tanks and scuba cylinders hold so much in so little space. For solids and liquids pressure effects are tiny enough to ignore outside the laboratory, so tables quote their densities at standard conditions without fuss.
A bar sold as gold weighs 1,000 g and displaces 60 cm³ of water. Its density: ρ = 1000 ÷ 60 ≈ 16.67 g/cm³. Real gold is 19.32 g/cm³ — this bar is too light for its size. It might be tungsten-plated or alloyed; either way, the density test caught it without scratching the surface.
Second scenario: you need the mass of 2.5 L of olive oil (ρ ≈ 0.91 g/cm³). Convert: 2.5 L = 2500 cm³, then m = 0.91 × 2500 = 2,275 g ≈ 2.28 kg. Recipes and shipping both live on this calculation.
A third scenario from the workshop: a machinist needs 800 g of aluminum (ρ = 2.70 g/cm³) for a part. The required volume is V = 800 ÷ 2.70 ≈ 296 cm³ — so a billet roughly 10 × 6 × 5 cm (300 cm³) covers it with a small machining allowance. Ordering stock by volume instead of guessing saves both money and scrap.
Unit mismatch. Dividing grams by m³ instead of cm³ inflates the error by a million. Match the pair.
Confusing density with weight. Density is mass ÷ volume; weight is mass × gravity. A denser object is not automatically heavier — size matters.
Ignoring temperature. Hot air is less dense than cold air — the entire basis of hot-air balloons.
Forgetting displacement subtleties. Porous objects absorb water, understating volume; coat them or use dry methods.
Assuming 1 g/cm³ for all liquids. Only pure water at 4°C is exactly 1; seawater is ~1.025, oil ~0.91.
Iceberg: 1,000,000 kg of ice (ρ 917 kg/m³) → V = 1,000,000 ÷ 917 ≈ 1,090 m³.
Lead weight: 500 cm³ of lead (11.34 g/cm³) → m = 5,670 g = 5.67 kg.
Air in a room: 50 m³ × 1.2 kg/m³ = 60 kg of air — heavier than most people guess.
Concrete slab: 2 m × 1 m × 0.1 m = 0.2 m³ of concrete (ρ ≈ 2400 kg/m³) → m = 480 kg — plan the lifting crew accordingly.
Float check: wood at 0.6 g/cm³ in water → floats with 60% submerged.
Density also explains layering: pour honey (1.4), water (1.0), and oil (0.91) into a glass and they stack in order — a classic classroom demo of ρ = m ÷ V made visible. Shake it and the layers separate again, because each fluid returns to its density level — immiscible liquids sort themselves by density every single time without exception, which makes it a reliable classroom demonstration.
A 100,000-tonne cargo ship floats because its average density — steel hull plus mostly air inside — is below water’s 1.025 g/cm³ (seawater). The hull displaces a volume of water whose weight equals the ship’s weight: V = 100,000,000 kg ÷ 1025 kg/m³ ≈ 97,561 m³ submerged. Load it past its Plimsoll line and the displaced volume can’t grow enough — average density crosses the threshold, and down it goes. Every loading decision is a density calculation.
Density is mass ÷ volume — an intensive property, same for a chip or a bar of the same material.
Water at 1 g/cm³ is the universal float/sink benchmark.
Match unit pairs: g with cm³, kg with m³ — or convert first.
Rearrange freely: m = ρ × V, V = m ÷ ρ.
Geology reads Earth’s history in density: continental crust (~2.7 g/cm³) floats higher on the mantle (~3.3 g/cm³) than dense oceanic crust (~3.0 g/cm³) — isostasy, the reason continents stand proud of the oceans. Prospectors hunt ore bodies by their density anomalies.
Medicine uses density daily: bone densitometry (DEXA scans) diagnoses osteoporosis by measuring grams of mineral per cm², and urine specific gravity — a density ratio — flags dehydration in seconds.
Brewing runs on density: fermenting wort’s specific gravity falls as yeast converts dense sugars into lighter alcohol. Brewers track the hydrometer reading to know exactly when fermentation finishes — density as a progress bar.
Aerospace obsesses over it: every gram saved is fuel saved. Aluminum (2.7), titanium (4.5), and carbon composites (~1.6 g/cm³) are chosen by strength-to-density ratio, not strength alone.
Oceanography maps currents by density: cold salty water (denser) sinks and drives the global conveyor belt that regulates climate. A 0.1% density difference moves oceans.
Try these, then check the answers — keep unit pairs matched.
1. 250 g of copper (ρ = 8.96 g/cm³). Volume? Answer: V = 250 ÷ 8.96 ≈ 27.9 cm³.
2. 2 L of mercury (ρ = 13.6 g/cm³). Mass in kg? Answer: V = 2000 cm³; m = 27,200 g = 27.2 kg.
3. A 54 g block measures 3×2×1 cm. Density? Float in water? Answer: V = 6 cm³; ρ = 9 g/cm³ — sinks.
4. Ice (0.917 g/cm³): what fraction of an iceberg sits below water? Answer: 91.7% submerged.
5. 5 kg of air at 1.2 kg/m³. Volume? Answer: V = 5 ÷ 1.2 ≈ 4.17 m³.
The most famous density experiment in history began with a fraud investigation. King Hiero II of Syracuse suspected his goldsmith had mixed silver into a “golden” crown. He asked Archimedes to find out — without melting the crown.
Archimedes realized in the bathhouse that a submerged body displaces its own volume of water — the “Eureka!” moment. He weighed the crown, then measured its volume by water displacement, and computed density: mass ÷ volume. Pure gold’s density was known; the crown’s came up short. The smith had indeed cheated.
Whether the legend is literally true, the method is real and still used: hydrostatic weighing remains the gold standard (pun intended) for density measurement. Museums authenticate artifacts, customs officers check metal shipments, and students repeat the experiment — all running ρ = m ÷ V on a 2,300-year-old idea.
The Density Calculator solves ρ = m ÷ V, m = ρ × V, V = m ÷ ρ, converting inputs to g and cm³ internally and reporting density in g/cm³, kg/m³, or lb/in³, with a float/sink verdict against water (1 g/cm³). Key facts: density is intensive (independent of sample size); match unit pairs (g with cm³); temperature shifts density via thermal expansion.
Density = mass ÷ volume (ρ = m ÷ V). Rearranged: mass = density × volume, and volume = mass ÷ density.
Pure water is 1 g/cm³ (1000 kg/m³) at 4°C. Seawater is about 1.025 g/cm³ because of dissolved salts.
Weigh it for mass, then submerge it in water and measure the displaced volume (Archimedes’ method). Divide mass by that volume.
Objects less dense than the fluid float; denser ones sink. A steel ship floats because its hull encloses air, making its average density below water’s.
Osmium, at about 22.6 g/cm³ — more than twice as dense as lead.
Usually yes: heating expands most materials, lowering density. Water is unusual — it is densest at 4°C, which is why ice floats.
Specific gravity is density relative to water (unitless). A material with density 2.7 g/cm³ has specific gravity 2.7.
Pure gold is 19.32 g/cm³. A bar that weighs right but displaces too much water (lower density) is fake or diluted — a non-destructive authenticity test.
Cite this page as: Density Calculator. Sigma Calculator. Retrieved October 11, 2026, from https://sigmacalculator.net/math-calculators/density-calculator/
Last updated: October 11, 2026