Who needs this?
Density comes up whenever someone knows the size of a thing and needs its weight:
- Haulers and boatersFuel, water and cargo tanks are sold in gallons, but trailers and boats are rated in pounds.
- Fabricators and buildersA steel plate or a concrete pour has to be lifted and supported, and its weight comes from its volume.
- BakersA cup of flour and a cup of sugar fill the same cup and weigh very different amounts.
- HomeownersA big aquarium, a hot tub or a waterbed puts a surprising load on a floor.
- Students and lab workDensity, specific gravity and buoyancy are staples of intro chemistry and physics.
- 3D printing and hobby castingFilament and resin are sold by weight, while models are designed by volume.
How density works
Picture two identical shoeboxes, one full of feathers and one full of sand. Same volume, but the sand box is far heavier because more mass is packed into every cubic inch. That ratio, mass per unit of volume, is density.
- The formula is density = mass ÷ volume, so mass = volume × density and volume = mass ÷ density.
- Water is the yardstick. The metric system was built around it, so pure water is almost exactly 1 g/cm³ (1 kg/L, 1,000 kg/m³) at about 4 °C, where it's densest. At room temperature (20 °C) it's about 998 kg/m³, a difference that only matters in a lab.
- In US units water is about 62.4 lb/ft³ and about 8.34 lb per US gallon.
- Floating is a density contest. Anything less dense on average than the liquid around it floats. Ice is about 0.917 g/cm³, so it floats with roughly 92% of its volume under the surface in fresh water (about 89% in seawater, which is where "the tip of the iceberg" comes from).
- Specific gravity is density divided by water's density. Since water is so close to 1 g/cm³, it's the same number as the density in g/cm³, minus the units: steel is about 7.85 either way.
Converting, step by step
Between density units
The metric units are powers of ten apart: g/cm³ to kg/m³ is just × 1,000. The US units need real factors: 1 g/cm³ is about 62.43 lb/ft³ and about 8.345 lb per US gallon.
From volume to weight
Multiply the volume by the density, with matching units. Here's a US gallon of gasoline at about 0.74 kg/L:
- Turn the volume into liters
1 US gal = 3.785 L - Multiply by the density
3.785 × 0.74 = 2.801 kg - Convert to pounds if you need them
2.801 ÷ 0.4536 = 6.18 lb
From weight to volume
Divide instead. How much space do 500 g of honey take up, at about 1.42 g/ml?
- Divide by the density
500 ÷ 1.42 = 352 ml - Convert to cups if you need them
352 ÷ 236.6 = 1.49 cups
Real situations, worked out
Gasoline is about 0.74 kg/L, which works out to about 6.18 lb per US gallon. 15 × 6.18 = 92.6 lb of fuel, before the tank itself. The blend and temperature move it a little, so call it about 93 lb. The fuel economy guide shows how far that weight of fuel takes you.
15 gal of gasoline ≈ 93 lbVolume first: 48 × 96 × 0.25 = 1,152 in³, and 1,152 ÷ 1,728 = 0.667 ft³. Steel is about 490 lb/ft³, so 0.667 × 490 = 327 lb. The same sheet in aluminum (about 169 lb/ft³) weighs about 112 lb, roughly a third as much.
steel plate ≈ 327 lb · aluminum ≈ 112 lb55 × 8.34 = about 460 lb of water alone. With glass, stand and gravel, the total easily passes 600 lb on about 4 square feet. For anything bigger, like a hot tub, a structural engineer or contractor should look at the floor.
55 US gal of water ≈ 460 lbHalf a US cup is 118.3 ml. Water would weigh 118 g, but honey is about 1.42 g/ml: 118.3 × 1.42 = 168 g.
1/2 cup of honey ≈ 168 gDoing it in your head
For liquids, pounds per US gallon ≈ density in kg/L × 8⅓. The true factor is 8.345, so the shortcut always runs about 0.15% low, far closer than any label or measuring cup.
| Liquid | kg/L | Exact lb/gal | × 8⅓ | Off by |
|---|---|---|---|---|
| Gasoline | 0.74 | 6.18 | 6.17 | 0.01 |
| Olive oil | 0.91 | 7.59 | 7.58 | 0.01 |
| Water (4 °C) | 1.00 | 8.35 | 8.33 | 0.02 |
| Seawater | 1.025 | 8.55 | 8.54 | 0.01 |
| Milk | 1.03 | 8.60 | 8.58 | 0.02 |
| Honey | 1.42 | 11.85 | 11.83 | 0.02 |
A pint's a pound. The old rhyme says a US pint of water weighs a pound. It's really about 1.04 lb, close enough for hauling water. A liter of water weighs about 2.2 lb, the same number as the kilogram-to-pound factor, because a liter of water is a kilogram.
Common mistakes
Treating every liquid like water. "A gallon weighs 8.34 lb" is only true for water. A gallon of milk is about 8.6 lb, a gallon of gasoline about 6.2 lb and a gallon of honey nearly 12 lb. Look up the density of the actual liquid.
Confusing fluid ounces with ounces. A fluid ounce is volume; an ounce is weight. A 12 oz honey jar (12 oz net weight, 340 g) holds only about 8 fl oz, about a cup. The labels only line up for water and liquids close to it.
Mixing up g/cm³ and kg/m³. They're 1,000 apart. Steel at 7.85 g/cm³ is 7,850 kg/m³. Plug 7.85 kg/m³ into a weight calculation and the beam comes out a thousand times too light.
Using solid density for loose material. Flour, sugar, gravel and mulch have air between the grains, so what counts is their bulk density, which changes with how they're packed. A spooned cup of all-purpose flour is about 120 g and a cup of granulated sugar about 198 g. The cooking guide covers why bakers weigh instead.
A bit of history
The link between water and metric units is deliberate: the system's designers built mass out of length and water.
- c. 250 BCArchimedes is said to have checked whether King Hiero's crown was pure gold by comparing the water it displaced with that of an equal weight of gold. It's a story told by the Roman architect Vitruvius about two centuries later, and the "Eureka" bath may be legend, but the idea behind it is sound.
- 1795A French law defines the gram as the mass of one cubic centimeter of pure water at the temperature of melting ice.
- 1799The "Kilogram of the Archives", a platinum cylinder meant to match a liter of water at its densest (about 4 °C), becomes the standard.
- 1964The liter, which had been defined since 1901 as the volume of 1 kg of water (about 1.000028 dm³), is redefined as exactly one cubic decimeter.
- 2019The kilogram is redefined from the Planck constant, so it no longer depends on water or on any metal artifact.
Reference table
Typical values at room temperature unless noted; natural materials vary.
| Material | g/cm³ (kg/L) | kg/m³ | lb/ft³ | lb/US gal |
|---|---|---|---|---|
| Air (sea level, 20 °C) | 0.0012 | 1.2 | 0.075 | 0.01 |
| Gasoline | 0.74 | 740 | 46.2 | 6.18 |
| Oak, dry (varies by species) | 0.6 to 0.9 | 600 to 900 | 37 to 56 | n/a |
| Olive oil | 0.91 | 910 | 56.8 | 7.59 |
| Ice | 0.917 | 917 | 57.2 | 7.65 |
| Water (20 °C) | 0.998 | 998 | 62.3 | 8.33 |
| Water (4 °C) | 1.000 | 1,000 | 62.4 | 8.35 |
| Seawater | 1.025 | 1,025 | 64.0 | 8.55 |
| Milk | 1.03 | 1,030 | 64.3 | 8.60 |
| Honey | 1.42 | 1,420 | 88.6 | 11.85 |
| Concrete | 2.4 | 2,400 | 150 | 20.0 |
| Aluminum | 2.70 | 2,700 | 169 | 22.5 |
| Steel | 7.85 | 7,850 | 490 | 65.5 |
| Gold | 19.32 | 19,320 | 1,206 | 161 |
Questions people ask
How much does a gallon of water weigh?
About 8.34 lb per US gallon. Cold water near 4 °C is about 8.35 lb and room-temperature water about 8.33 lb. A UK (imperial) gallon is bigger and holds about 10 lb.
Why does ice float?
Water expands as it freezes, so ice (about 0.917 g/cm³) is less dense than the liquid water around it. That's also why lakes freeze from the top down.
How does a steel ship float if steel sinks?
What floats is the whole ship, and its hull is mostly air. As long as the average density of hull plus contents stays below water's, it floats. Let water in and the average climbs.
What's the difference between density and specific gravity?
Density has units (g/cm³, lb/ft³). Specific gravity is the ratio to water, so it has none. In g/cm³ they're the same number; in lb/ft³, multiply specific gravity by 62.4.
Why does a cup of flour weigh less than a cup of sugar?
Flour grains are fine and fluffy and trap a lot of air, so a spooned cup weighs about 120 g. Sugar crystals pack tighter, about 198 g per cup. Same volume, different bulk density.