Buoyancy Calculator

What is a buoyant force?

When an object sits in a liquid or a gas, the fluid pushes up on it. That upward push is the buoyant force, also called upthrust. It exists because pressure grows with depth: the bottom of a submerged object is squeezed harder than its top, and the difference is a net force pointing up.

Archimedes' principle gives the size of that force in a neat way: the buoyant force equals the weight of the fluid that the object pushes out of the way. A ship floats, even though steel sinks, because its hull displaces a large volume of water whose weight matches the weight of the ship.

Buoyant force formula

F = ρ × V × gρ is the fluid density, V the volume of fluid displaced, and g the gravitational acceleration.

Multiplying density by volume gives the mass of displaced fluid, m = ρ × V. Multiplying that mass by g gives its weight, which is the buoyant force. The calculator therefore reports both numbers.

Use the volume that is actually under the surface. A fully submerged object displaces its whole volume; a floating one displaces only the part below the waterline.

• Volume: choose from mm³, cm³, m³, ml, litres, US gallons, fluid ounces, cubic inches, cubic feet or cubic yards. The volume converter can translate other units first.
• Fluid density: default 1024 kg/m³, typical of sea water. Fresh water is close to 1000 kg/m³ (998 kg/m³ at 20 °C).
• Gravity: default 1 g, which is 9.80665 m/s². Switch to m/s² to enter another planet's value.

Calculating the buoyant force: examples

A cubic metre of sea water. With ρ = 1,024 kg/m³ and g = 9.80665 m/s², F = 1,024 × 1 × 9.80665 ≈ 10,042 N, or 10.042 kN. The displaced mass is 1,024 kg, which is 1.024 tonnes.

A submerged 2.5 litre bottle in fresh water. The volume is 0.0025 m³, so the displaced mass is 1,000 × 0.0025 = 2.5 kg and F = 2.5 × 9.80665 ≈ 24.52 N.

A small boat. A hull that sinks until it displaces 8 m³ of sea water pushes aside 8 × 1,024 = 8,192 kg of water. F = 8,192 × 9.80665 ≈ 80,336 N, so the boat and its load have a combined mass of about 8.19 tonnes.

A person swimming. A 75 kg person with an average body density of about 985 kg/m³ has a volume of 75 ÷ 985 ≈ 0.0761 m³. Fully submerged in fresh water, the upthrust would be 0.0761 × 1,000 × 9.80665 ≈ 747 N, just above their weight of 735 N, so they float with only a little of the body out of the water.

Another world. On the Moon, where g is about 1.62 m/s², the same cubic metre of sea water produces only 1,024 × 1.62 ≈ 1,659 N. Buoyancy depends on gravity, but so does the weight of the object, which is why things still float or sink in the same way.

Density of water and other common fluids

A denser fluid pushes harder on the same volume. The table lists approximate densities near room temperature and the upthrust on one fully submerged cubic metre at standard gravity.

Density also changes with temperature and with the amount of dissolved salt, so for accurate work measure it or take the value for your exact conditions. The density calculator helps when you know a mass and a volume instead.

Will it float or sink?

Compare the average density of the object with the density of the fluid. If the object is less dense, the buoyant force from full submersion would exceed its weight, so it rises and floats. If it is denser, it sinks.

A floating object settles where the buoyant force equals its weight, which means the submerged fraction equals the ratio of the two densities: submerged fraction = ρ_object ÷ ρ_fluid. Ice at 917 kg/m³ has about 91.7% of its volume under fresh water and about 89.6% under sea water (917 ÷ 1,024). A wooden board of 600 kg/m³ sits 60% submerged in fresh water, so a 0.15 m thick board has a draft of 0.09 m.

For a heavy item that sinks, the useful figure is the net downward force: weight minus buoyant force. One litre of aluminium (about 2,700 kg/m³) weighs 26.48 N in air, loses 9.81 N to the water, and so presses down with about 16.67 N.

How the results are shown

• Force: newtons up to 1,000, then kilonewtons, meganewtons and giganewtons as the value grows. The thresholds are inclusive, so exactly 1,000 N is shown as 1,000 N.
• Mass: grams (with pounds) below 1 kg, kilograms (with pounds) from 1 kg up to, but not including, 1,000 kg, and tonnes (with short tons) from 1,000 kg. Here a tonne is 1,000 kg and a ton is 2,000 lb.
• The calculator uses 2.20462 lb per kg and 1.10231 short tons per tonne.
• Values are rounded to six decimals for force and three for mass, with unneeded trailing zeros removed.

Results assume a still fluid of uniform density and are idealised figures. Do not rely on them alone for lifejackets, boat loading, diving equipment or other safety-critical decisions; see the disclaimer.