Density Calculator - rho = m / V, and What It Is Made Of

Density in one page, from air to osmium

Weigh something, measure how much room it takes up, and the ratio tells you what it is made of. This page holds the whole picture: the arithmetic in three directions, a ladder of 27 materials spanning a factor of 18,000 from room air to osmium, the conversions between kg/m³, g/cm³ and lb/ft³, and the one rule that decides whether a thing floats. A pebble of 390 g displacing 50 cm³ of water comes out at 7,800 kg/m³, which is steel to within 0.6 percent, and it sinks.

1,000

kg/m³ of fresh water, the line between floating and sinking

62.43

lb/ft³ of that same water, the number US tables use

22,590

kg/m³ of osmium, the densest element on the shelf

From a kitchen scale to a number you can look up

Three of the boxes below are always enough. Whichever one you leave out is the one the calculator hands back.

1
Say which of the three you want. Density from a mass and a volume, a mass from a density and a volume, or a volume from a mass and a density. The fields rearrange themselves around the choice.
2
Weigh the object dry. Grams, kilograms, ounces or pounds. A kitchen scale reading to 1 g is enough for anything bigger than a coin, and each unit has its own selector so nothing needs converting by hand.
3
Get the volume. A regular shape gives it up to a ruler. Anything else goes into a measuring jug of water, and the rise in level is the answer, because 1 mL of displacement is 1 cm³.
4
Read the three tiles. Specific gravity, the closest material on record, and whether the thing floats. The ladder underneath places your figure between its neighbors so you can see how far off a guess was.

What the ratio actually measures

Density is mass per unit of volume, written rho = m / V, and it is a property of the material rather than of the object. Half a brick has half the mass and half the volume, so it keeps the same density. That is what makes it useful for identification: a number that does not care how big your sample is can be compared against a table that nobody measured your sample for.

The metric system was built around one of these values on purpose. A cubic centimeter of water at its densest weighs one gram, which is why water sits at exactly 1,000 kg/m³ and why specific gravity, the ratio of a density to water's, reads as the same digits as g/cm³. A hydrometer floating in a brine tank and a spec sheet quoting 1.150 g/cm³ are saying the identical thing.

Temperature moves the figure, though rarely enough to matter for a solid. Water is heaviest near 4 degrees C and loses about 0.7 percent by the time it reaches body temperature. Gases are the opposite case: room air at 1.204 kg/m³ is around 830 times lighter than the water beside it, which is why the same object that sinks like a stone in a pool is effectively weightless in the breeze above it.

The oldest way to get a volume is still the best one for an awkward shape. Lower the object into a jug of water and read the rise, or hang it from a scale and weigh it twice, once in air and once submerged. The difference between those two readings in grams is the volume in cubic centimeters, exactly, with no ruler involved. That is the trick attributed to Archimedes, and it is the reason a jeweler can check a ring without cutting it open.

Materials by the weight of one liter

The column that makes this concrete is the last one: how much a single liter of the stuff weighs in pounds. A liter of gold is heavier than most people can lift with one hand comfortably, and a liter of osmium is heavier again than that.

Material	kg/m³	g/cm³	lb/ft³	1 liter weighs
Air at room temperature	1.204	0.0012	0.08	0.04 oz
Styrofoam	25	0.025	1.56	0.88 oz
Cork	180	0.180	11.24	0.40 lb
Pine	530	0.530	33.09	1.17 lb
Oak	720	0.720	44.95	1.59 lb
Gasoline	750	0.750	46.82	1.65 lb
Ice	917	0.917	57.25	2.02 lb
Olive oil	920	0.920	57.43	2.03 lb
Fresh water	1,000	1.000	62.43	2.20 lb
Seawater	1,025	1.025	63.99	2.26 lb
Concrete	2,400	2.400	149.83	5.29 lb
Glass	2,500	2.500	156.07	5.51 lb
Aluminum	2,700	2.700	168.56	5.95 lb
Granite	2,750	2.750	171.68	6.06 lb
Titanium	4,507	4.507	281.36	9.94 lb
Steel	7,850	7.850	490.06	17.31 lb
Iron	7,874	7.874	491.56	17.36 lb
Brass	8,500	8.500	530.64	18.74 lb
Copper	8,960	8.960	559.35	19.75 lb
Silver	10,490	10.490	654.87	23.13 lb
Lead	11,340	11.340	707.93	25.00 lb
Mercury	13,546	13.546	845.65	29.86 lb
Tungsten	19,250	19.250	1,201.74	42.44 lb
Gold	19,300	19.300	1,204.86	42.55 lb
Platinum	21,450	21.450	1,339.08	47.29 lb
Iridium	22,560	22.560	1,408.37	49.74 lb
Osmium	22,590	22.590	1,410.25	49.80 lb

Values are for solid material at room temperature with no voids in it. A cast part with porosity, a board with grain and knots, or a powder with air between the grains will all read lower than the row above, and that gap is itself a measurement: it tells you what fraction of the sample is empty space.

Converting between the three units without losing a zero

Three units are in daily use and they differ by factors that are easy to fumble. The middle column is the one to memorize, because it is the only conversion most people ever need in both directions.

Going from	To	Multiply by	Where you meet it
g/cm³	kg/m³	1,000	lab data sheets into engineering tables
lb/ft³	kg/m³	16.0185	US building specs into metric software
kg/m³	lb/ft³	0.062428	anything imported reading in metric
oz/in³	kg/m³	1,730.0	machinist tables and casting weights
specific gravity	g/cm³	1	hydrometers, brewing, battery acid

Things this number quietly settles

Air weighs more than the room suggests. A living room of 12 by 12 by 10 ft holds 1,440 ft³ of air, and at 1.204 kg/m³ that comes to 49.1 kg, or 108 lb. You do not feel it because you are floating in it, held up by the same principle that keeps a cork on a pond.

Ice floats with almost all of itself hidden. At 917 against water's 1,000, exactly 91.7 percent of an ice cube sits below the waterline and 8.3 percent above. In seawater at 1,025 the submerged share drops to 89.5 percent, which is the difference between a floating cube in a glass and an iceberg in the North Atlantic.

Gold and tungsten are nearly twins. 19,300 against 19,250 is a gap of 0.26 percent, which is why a tungsten core is the classic way to fake a gold bar and why density alone cannot settle that question. Anything that fits inside the sampling error of your scale needs a second test, not a second weighing.

A liter is a convenient unit of shopping-bag weight. One liter of water is 2.20 lb, of concrete 5.29 lb, of steel 17.31 lb and of lead 25.00 lb. That last number is the one that surprises people who have never handled a lead brick: a box the size of a carton of milk that you can barely lift with one arm.

Reading the verdict: floats, sinks, or hovers

The float rule has no arithmetic in it at all: below 1,000 kg/m³ a thing floats in fresh water, above it the thing sinks, and the fraction that stays under the surface is just the density divided by the water's. Oak at 720 rides with 72 percent of itself wet. Gasoline at 750 sits on top of a puddle rather than mixing into it, which is why a fuel spill spreads instead of sinking. Pure aluminum at 2,700 sinks in water and floats in mercury, a fluid five times heavier again.

Where the rule misleads is with objects rather than materials. A steel hull floats because the shape encloses air, so the density that matters is the whole vessel's, not the plate's. Run the calculator on a boat's total mass and total displaced volume and you will get a figure below 1,000 every time it is still afloat.

What the reading does not tell you

My result came out between two materials. Which one is it?

Possibly neither. Density narrows the field, it does not identify a sample. A reading of 8,700 kg/m³ sits between brass and copper and could be either, or a bronze, or a copper part with a cavity in it. The calculator only claims a match inside 15 percent and says so plainly when nothing is close, because a confident wrong name is worse than no name.

How accurate does the volume have to be?

The error in the volume passes straight through to the density. Measuring 50 cm³ to the nearest 1 cm³ is a 2 percent uncertainty, which is enough to tell steel from aluminum and nowhere near enough to tell gold from tungsten. Displacement in a narrow jug beats a wide one for the same reason a tall thermometer reads finer than a squat one.

Why does my wood reading come out under the table value?

Because the table lists the material and you measured an object. Wood holds air in the grain and water in the fiber, so a kiln-dried oak board can read 600 kg/m³ against a table entry of 720 and still be oak. The same gap appears in cast metal with porosity and in any powder, where you are partly measuring the space between the grains.

Is specific gravity the same thing as density?

It is the density divided by water's, so it carries no unit at all. The convenience is that it reads as the same digits as g/cm³: a specific gravity of 1.150 is 1,150 kg/m³. Brewing, battery testing and mineralogy all quote it that way, and a hydrometer measures it directly by how deep it floats.

Does temperature change the answer enough to worry about?

For solids and liquids, rarely. Water loses about 0.7 percent between its densest point and body temperature, and most metals move by well under a percent across a normal workshop range. For gases it changes everything: the same air at twice the absolute temperature has half the density, which is the whole working principle of a hot air balloon.

Can I get the volume without a measuring jug?

For a regular shape, yes: length times width times height for a block, and the usual formulas for a cylinder or sphere. For anything else, weigh the object in air and again while it hangs submerged. The difference in those two readings, in grams, is the volume in cubic centimeters, because the water pushes back with the weight of exactly what the object displaced.

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