Density Calculator – Density, Mass or Volume From Any Two

Floats or sinks — your density against water

Water is the world’s reference: 1,000 kg/m³, exactly 1 g/cm³. Anything less dense floats, anything denser sinks, and anything right at water’s density just hovers. The block in the tank below sits where your numbers put it — a floating block even submerges by exactly its density ratio, which is why 91.7% of an iceberg hides underwater.

Keep exploring

Density starts with a volume — these measure the space itself.

How it works in three steps

How density is worked out

Going deeper

Material library — densities by category

Density is most useful as a comparison: one number means little until you hold it next to the materials it might be. The table below gathers the values a density reading is most often checked against, grouped the way the competitor-style material pickers group them — metals, liquids, gases, everyday solids, and the bodies of the solar system. Every value is a typical figure at ordinary room conditions (gases at sea level), not a certified measurement of any particular sample: alloys vary with composition, woods vary with species and moisture, and rocks vary with porosity, so treat a match within a few percent as a strong lead, exactly as the page’s own material rows do.

Two habits make the table far more useful than a bare list. First, compare in the same units — grams per cubic centimetre for bench-sized objects, kilograms per cubic metre for anything bigger — and remember the bridge between them is exactly 1,000. Second, use the table backwards as well as forwards: if you know the material, you can predict the mass of a part before you make it (volume times density), and if you know the mass and the volume, the table can name the material for you.

Sources and cautions: solid and liquid values are the typical room-temperature figures carried by standard reference tables such as the Engineering ToolBox material-density tables and the CRC Handbook of Chemistry and Physics; planetary mean densities are NASA Planetary Fact Sheet values. Saturn is the showpiece of the astronomy rows: at 0.69 g/cm³ it is less dense than water, so a big enough ocean would float the whole planet — a thought experiment, not a practical test, since no such ocean exists. Gases are quoted at sea-level pressure because their density is set by temperature and pressure as much as by composition; double the pressure and you roughly double the density, which is why a scuba tank holds far more air than its size suggests. For engineering, shipping or safety decisions, measure the actual material rather than trusting any table, including this one.

To use a row in the calculator, tap the matching material in the floats-or-sinks panel, or open Advanced options below the main form and pick it from the category library there — either route loads the density into the main calculator, where the three solve modes take over.

Volume from dimensions — boxes, cylinders and spheres

Many density problems stall before the formula, because the volume is not given — only the shape and a few measurements. The Advanced panel’s volume helper covers the three shapes that account for nearly all of them, and each one is a single formula worth knowing by heart. A cuboid (a box) is length × width × height. A cylinder is π × radius² × height. A sphere is (4 ÷ 3) × π × radius³. Measure all the lengths in the same unit and the volume comes out in that unit cubed: centimetres give cubic centimetres, metres give cubic metres.

Three worked examples, each checked the way the calculator checks itself. A cuboid measuring 10 cm × 5 cm × 2 cm has a volume of 10 × 5 × 2 = 100 cm³; a 72 g block of that size is oak-like at 72 ÷ 100 = 0.72 g/cm³. A cylinder of radius 5 cm and height 10 cm has a volume of π × 25 × 10 = 785.4 cm³; a 2,120 g cylinder of that size has a density of 2,120 ÷ 785.4 = 2.70 g/cm³, essentially aluminium. A sphere of radius 3 cm has a volume of (4 ÷ 3) × π × 27 = 113.1 cm³; a 100 g sphere of that size is 100 ÷ 113.1 = 0.88 g/cm³, so it floats. Notice the recurring trap in the cylinder and sphere cases: the formulae want the radius, not the diameter — halving a diameter first is the single most common volume error, and it changes a cylinder’s volume by a factor of four.

Converting the result is mechanical. Cubic centimetres divided by 1,000 give litres, and divided by 1,000,000 give cubic metres; the volume helper shows all three so the number can go straight into the main calculator, which accepts cubic centimetres, cubic metres, litres, millilitres, cubic inches, cubic feet and US gallons. For awkward shapes that match none of the three formulae, fall back to water displacement — the method described in the FAQ — which measures any volume directly, however irregular the object.

Water at every temperature — and whether you float

The floats-or-sinks test on this page uses plain water at 1,000 kg/m³, which is a superb round-number reference and very nearly true. But water’s density is not a constant: it rises as cold water warms towards 4 °C, peaks there, then falls steadily as it warms further, and the Advanced panel’s temperature check uses the standard table below rather than the round number. The differences look small — a few kilograms per cubic metre — yet they decide borderline cases, and they explain why the same object can behave differently in a cold lake and a warm sea.

Values are the standard Kell (1975) water-density table, rounded to two decimals; the Advanced tool interpolates linearly between neighbouring rows, which is accurate to a fraction of a kilogram per cubic metre across these intervals, and it clamps outside 0–100 °C rather than inventing values. Buoyancy itself is Archimedes’ principle: a floating body displaces its own weight of water, so the fraction submerged equals the object’s density divided by the water’s density. Oak at 720 kg/m³ in 20 °C water (998.21 kg/m³) sits 720 ÷ 998.21 = 72.1% submerged. Ice at 917 kg/m³ is 91.7% submerged against the round 1,000 kg/m³ reference and 91.9% submerged in 20 °C water — the same iceberg, a slightly different waterline, purely because the water changed.

Borderline cases are where temperature earns its keep. An object at 1.01 g/cm³ (1,010 kg/m³) sinks in fresh water at any temperature in the table, because it is denser than every row — yet it floats in seawater at 1,025 kg/m³, with about 98.5% submerged. Salt, not temperature, rescues it there: the Dead Sea, at roughly 1,240 kg/m³, floats a human body high out of the water for the same reason. Conversely, a body at exactly water’s density hovers, neither rising nor sinking — the neutral-buoyancy state that submarines and scuba divers trim themselves into, and that the main calculator reports as “Hovers” when the density lands within half a kilogram per cubic metre of 1,000.

Unit conversions at a glance

Density problems fail more often on units than on arithmetic, because three quantities each carry several common units and the formula only works when they agree. The calculator’s own rule — convert everything to kilograms and cubic metres first, then present the answer in your units — is the safest habit to copy by hand, and the table below collects the exact factors it uses. The pound is exactly 0.45359237 kg and the inch exactly 2.54 cm by definition, so the imperial conversions below are exact, not approximate; the gallon is the US gallon (3.785411784 litres), not the larger imperial gallon.

One conversion deserves a warning: the density unit g/cm³ and the numerically identical g/mL are the same physical quantity, because 1 cm³ is exactly 1 mL, so laboratory densities quoted per millilitre can be used directly. The same is not true of specific gravity, which is a ratio and has no units at all — a specific gravity of 2.7 is 2,700 kg/m³, but writing “2.7 kg/m³” would be wrong by a factor of a thousand.

Worked examples — five densities solved by hand

Example 1 — finding density. A metal block weighs 270 g and measures 100 cm³. Density = 270 ÷ 100 = 2.7 g/cm³, which is 2,700 kg/m³. The material table points at aluminium (2.70), and the block sinks, since 2.7 is well above water’s 1.0.

Example 2 — finding mass. An iron plate has a volume of 500 cm³ and iron’s density is 7.87 g/cm³. Mass = 7.87 × 500 = 3,935 g, or 3.935 kg — a plate the size of a paperback that weighs nearly four kilograms, which is why iron feels so unexpectedly heavy for its size.

Example 3 — finding volume. Ten kilograms of aluminium at 2.70 g/cm³ takes up 10,000 ÷ 2.70 = 3,703.7 cm³, about 3.7 litres of solid metal. This is the Volume mode of the calculator, and it is the calculation behind every “how big a block do I need” workshop question.

Example 4 — density from dimensions. A cylinder of radius 5 cm and height 10 cm weighs 2,120 g. Its volume is π × 5² × 10 = 785.4 cm³, so its density is 2,120 ÷ 785.4 = 2.70 g/cm³ — aluminium again, which cross-checks the measurement: if the answer had come out at 2.4 or 3.0, something (probably the radius) would have been mis-measured.

Example 5 — the float test with temperature. A wooden toy boat of density 0.72 g/cm³ goes into 20 °C water at 998.21 kg/m³. It floats, with 720 ÷ 998.21 = 72.1% of its volume submerged and 27.9% riding above the waterline. Heat that water to 80 °C (971.80 kg/m³) and the same boat sits deeper — 720 ÷ 971.80 = 74.1% submerged — because the water got lighter while the boat stayed the same. Small change, visible consequence, and exactly the effect the temperature check in Advanced options quantifies.

Where density decides things

In geology, density is how prospectors and geophysicists see underground: a gravity survey detects buried ore because dense rock pulls slightly harder, and a hand specimen’s density, measured by displacement, can separate minerals that look identical — gold at 19.32 g/cm³ against iron pyrite (“fool’s gold”) at about 5.0 g/cm³ is a difference no eye can miss once weighed. In the oceans, density drives the planet’s circulation: cold, salty water is denser, sinks, and crawls along the seafloor for centuries, while warm surface water flows back above it — the thermohaline conveyor that moves more water than all the world’s rivers combined.

In engineering, density is a trade between weight and strength. Aircraft skins use aluminium at 2.70 g/cm³ where steel at 7.85 would triple the mass for the same volume; racing yachts use lead keels at 11.34 g/cm³ precisely because the density is a virtue there, holding the boat upright in a small volume. In shipping, ballast water is pumped in and out to trim a vessel, and a ship’s load line — the Plimsoll mark — is set differently for fresh water, seawater and tropical seawater, because the same ship floats at different depths in water of different density. In the kitchen, the same physics separates oil from water in a dressing (0.91 against 1.00) and tells a cook that honey at 1.42 pours slowly for a structural reason, not just a sticky one.

Two distinctions keep density honest. Bone mineral density, the DEXA-scan quantity, is an areal density (grams per square centimetre of projected bone), not the volumetric density of this page — the units look similar and the quantities are different, so they must never be swapped. And in medicine, specific gravity of urine (typically 1.005–1.030) is a genuine density ratio used as a concentration check, which shows how far one ratio reaches: from a ship’s load line to a laboratory test, the question is always the same — how much mass is packed into the space, and what does it float in.

Measuring density at home: a scale, a jug, and displacement

Density needs two measurements, and both can be taken in a kitchen: mass on a scale, and volume by the water the object pushes aside.

Weigh the object first, in grams, on a kitchen scale. Then fill a measuring jug with enough water to cover the object, note the level in millilitres, lower the object in gently on a thread, and note the new level. The rise in millilitres is the volume in cubic centimetres, because 1 mL is exactly 1 cm³, and the density is the mass divided by that volume. A rock weighing 240 g that raises the level by 90 mL has a volume of 90 cm³ and a density of 240 divided by 90, which is 2.67 g/cm³ — denser than water, which is why it sinks, and in the range of ordinary rock. The method is Archimedes displacement, and it is the same method the laboratory uses, with better glassware: the principle does not change with the equipment, only the precision.

Three conditions keep the measurement honest. The object must sink: a floating object pushes aside only its own weight of water, not its full volume, so a piece of wood measured this way gives the submerged volume only, and a floating object needs a sinker of known volume to hold it under, with the sinker volume subtracted afterwards. The object must not absorb water: a sponge or an unglazed pot soaks up water as it is measured, the level rise understates the volume, and the density comes out too high, so porous objects need sealing or a different method. And the water must be still and the jug read at eye level, at the bottom of the meniscus, because a reading taken from above, or while the water is still sloshing, can be out by several millilitres, which on a 90 mL rise is several percent. With those conditions met, a kitchen measurement lands within a few percent of the true value, which is close enough to identify a material from the library above, and close enough to check a homework answer, though never a substitute for a laboratory measurement where the figure matters.

Temperature enters the measurement through the water, not through the object: water at room temperature is about 0.998 g/cm³ rather than the 1.000 g/cm³ it reaches at 4 °C, so a displacement measurement that treats the water as exactly 1.000 carries a 0.2% error, which is smaller than the reading error on most jugs and can be ignored for kitchen purposes. The thermal expansion of the object itself is smaller still for solids over a kitchen temperature range. The companion guide derives the formula from first principles and works five densities by hand, including the displacement case, for readers who want the method in full.

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