Density Calculator

What density is and the three ways to use it

Density is how much mass fits into a given volume. Divide mass by volume and you have it. A cubic centimeter of water has a mass of about 1 gram, a cubic centimeter of aluminum about 2.7 grams, and a cubic centimeter of gold about 19.3 grams. The number tells you how tightly the material packs matter into space.

The formula has three faces, and the one you need depends on what is missing. To find density, divide mass by volume. To find the mass of a known volume, multiply density by volume. To find the volume that holds a known mass, divide mass by density. The calculator on this page does all three, and it also converts the answer into the units people buy and ship in.

Units matter more here than in most formulas. Density is usually written in grams per cubic centimeter (g/cm3) or kilograms per cubic meter (kg/m3). In the US, weight per volume shows up as pounds per cubic foot for concrete, gravel and soil, and pounds per gallon for liquids. All of those describe the same property, and the calculator prints all four so the number matches the quote you were given.

The densities below come from the HyperPhysics table of common substances at Georgia State University, rounded to two or three figures. One caution before the numbers: density is not weight. A kilogram of water has the same mass on the Moon, where it would weigh about a sixth as much. The tables and formulas here use mass in kilograms and grams, then convert to pounds, which is the everyday weight unit in the US.

The units that cause trouble

Most mistakes with density come from mixing a volume unit with a weight unit, or from converting one but not the other.

The gallon is the trap. A US gallon is 231 cubic inches, which is 3,785.41 cubic centimeters, and a US fluid ounce is 29.57 milliliters. An ounce of weight is 28.35 grams. Those are different ounces, and a recipe that says 8 oz of liquid means fluid ounces while a package that says 8 oz means weight.

Water is the handy bridge between the systems. One liter of water has a mass of about 1 kilogram, and one US gallon weighs about 8.35 pounds. Those two facts let you sanity check almost any liquid number: if a calculator says a gallon of milk weighs 12 pounds, something went wrong, because milk is only about 3 percent denser than water.

Worked example: an aluminum plate

A plate measures 12 inches by 12 inches by 0.5 inch. First find the volume in cubic inches: 12 x 12 x 0.5 = 72 cubic inches. Then convert to cubic centimeters with the factor 16.387, because a cube one inch on each side holds 16.387 milliliters.

72 x 16.387 = 1,179.9 cm3. Aluminum is 2.70 g/cm3, so the mass is 1,179.9 x 2.70 = 3,185.6 g, which is 3.19 kg or 7.02 lb.

There is a shorter route once you know the density in pounds per cubic inch. Aluminum is 0.0975 lb/in3, so 72 x 0.0975 = 7.02 lb. Same answer, one step, and it is the version a machinist would use.

The gap between aluminum and steel is what makes this worth calculating. A steel plate of the same size at 7.85 g/cm3 would weigh 20.4 lb, almost three times as much, which is why aircraft parts and truck beds use aluminum despite the higher price per pound.

Worked example: a concrete slab

Concrete is quoted in pounds per cubic foot, with 150 lb/ft3 as the usual figure for cured normal weight concrete. That works out to 2,400 kg/m3, or 2.4 g/cm3.

A patio 10 ft by 10 ft and 4 inches thick: the area is 100 square feet, and 4 inches is 0.333 ft. Volume is 100 x 0.333 = 33.33 cubic feet. Multiply by 150 and the slab weighs 5,000 lb, or 2.5 tons.

The bag count matters for a weekend pour. An 80 lb bag of concrete mix yields about 0.60 cubic feet, according to the manufacturer's data sheet, so this slab needs 56 bags, which is roughly 4,480 lb of material to move by hand. At that size most people order a ready mix truck instead, since one cubic yard is 27 cubic feet and the slab needs 1.23 cubic yards.

Do not confuse the density of cured concrete with the density of the wet mix in the truck. Fresh concrete is ordered by volume, and the 150 lb/ft3 figure describes what the slab weighs once it sets.

Water is the reference, and it changes with temperature

Water is the reference because 1 cm3 of it weighs about 1 gram, which makes the numbers easy to remember. The exact value depends on temperature, and the USGS water density page publishes the table below.

Water is densest at about 4 C, not at freezing. That is why a lake freezes from the top: the coldest water at the surface is less dense than the 4 C water below it, so it floats and freezes while the fish keep swimming in the denser layer.

For everyday work the rounding is fine. A five gallon bucket of water weighs 5 x 8.345 = 41.7 lb at room temperature, and the difference between 60 F and 100 F is about 0.6 percent, which is 4 ounces on that bucket. Where the difference does matter is in brewing, pool chemistry and any process that measures water by weight instead of volume. The USGS facts about water page lists the density at both ends of that range.

Specific gravity and what a hydrometer reads

Specific gravity is density divided by the density of water. It has no units, and it is how brewers, winemakers and pool owners describe a liquid. A reading of 1.025 means the liquid is 2.5 percent denser than water.

Seawater at 1.025 means one liter has a mass of 1,025 grams, and a cubic foot weighs about 64.0 lb instead of 62.4. That extra density is what makes a person float more easily in the ocean than in a lake.

Gasoline is the other direction. At 0.70 g/cm3 a gallon weighs 5.84 lb, so a 15 gallon tank holds 87.6 lb of fuel rather than the 125 lb a water-sized guess would suggest. It also explains why gasoline floats on water and why a fuel spill spreads across a wet floor instead of sinking.

A hydrometer works by floating at a depth that depends on the liquid's density. The scale is printed so that the reading at the surface gives specific gravity directly, which is why the instrument needs no power and no calibration beyond a clean test jar.

Will it float?

The rule is simple: an object floats in water if its average density is less than 1.0 g/cm3, and sinks if it is more. Ice at 0.917 g/cm3 floats, which is why ice cubes sit at the surface of a glass.

Floating objects do not sit on top of the water. They sink until the mass of the water they push aside equals their own mass. For ice, that happens when 91.7 percent of the cube is below the surface, leaving 8.3 percent above. That is the same ratio you see in an iceberg, and it is why most of an iceberg is out of sight.

A steel ship floats because the hull encloses air. The average density of hull plus air is far below 1.0, so the ship floats even though the steel itself would sink as a solid block. The same idea explains why a concrete canoe can float while a concrete block cannot.

Buoyancy also changes with the liquid. An object with a density of 1.02 g/cm3 sinks in fresh water and floats in seawater at 1.025, which is a small margin that matters to anyone loading a boat near its limit.

Mistakes worth avoiding

Using ounces for both weight and volume. A fluid ounce is 29.57 milliliters, and an ounce of weight is 28.35 grams. The two are close for water, which is where the confusion started, but they diverge as soon as the liquid is heavier or lighter.

Assuming one density for a bulk material. A cubic yard of gravel weighs about 1.4 tons, while a cubic yard of mulch weighs far less because most of that volume is air. Soil, sand and wood chips are sold by volume but priced by the truckload, and the conversion depends on how the material is packed and how wet it is.

Forgetting temperature for liquids. Gasoline, oil and water all change density as they warm. A tank measured at 40 F holds more mass than the same tank at 90 F, which is why fuel is sold by volume with a temperature correction in commercial trade.

Treating gases like solids. Air at sea level is about 0.0012 g/cm3, roughly 800 times less dense than water, and it changes with pressure and altitude. The same formulas apply, but the numbers move a lot.

Rounding in the middle. Convert units at the end, not at every step. The aluminum plate above gives 7.02 lb when you carry full precision, and 7.0 lb if you round the cubic centimeters to 1,180 first. Both are fine, but the first one matches a scale more closely.