Skip to content
Calcapedia
Menu
Science

Buoyancy Calculator

Find the upward push a liquid or gas gives a submerged object, or check whether an object floats and how much of it sits below the surface.

Level: Grades 8–9

Printable worksheet

Buoyancy Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Calculate

Only the part of the object below the fluid surface counts.

Result

Buoyant force

488.8615 N

The buoyant force is 488.8615 N.

In kilonewtons
0.4889 kN
In pounds-force
109.9004 lbf
Mass of fluid displaced
49.85 kgThis is also the most mass this force can hold up

See the step-by-step solution ↓

Step-by-step solution

  1. Use the density of fresh water at 25 °C (typical)

    ρ=997 kg/m³

  2. Use the surface gravity of Earth (standard gravity)

    g=9.80665 m/s²

  3. Change submerged volume to m³, the standard unit the formula uses (1 L = 0.001 m³)

    50 L×0.001=0.05 m³

  4. Find the upward push: fluid density × volume below the surface × gravity. This is the weight of the fluid pushed aside (Archimedes' principle)

    997×0.05×9.80665=488.861503 N

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how hard water, or any fluid, pushes up on an object, and whether that object will float. This upward push is called the buoyant force. Archimedes' principle says it equals the weight of the fluid the object pushes aside. As a formula, the buoyant force is F = ρ × V × g. Here ρ (the Greek letter rho) is the fluid's density, meaning how heavy it is for its size. V is the volume of the object below the surface, and g is the pull of gravity. The push exists because fluid pressure grows with depth. So the push on the bottom of the object is bigger than the push on its top.

This calculator works in two ways. In buoyant-force mode, it finds the upward force on any volume under the surface. In "Will it float?" mode, you enter an object's mass and total volume. It compares the object's average density with the fluid's to tell you whether it floats, sinks or hovers. It also shows how much of the object sits below the surface. For a floating object, it shows how much extra load it could carry.

Where it's used

Why this math matters outside the classroom:

  • Boat design. Boat builders check that a 2,000 kg boat floats once its hull pushes aside about 2 m³ of fresh water.
  • Floating ice. Ice at about 917 kg/m³ floating in seawater of about 1,025 kg/m³ sits roughly 89% below the surface.
  • Scuba weighting. Divers add lead weights until their weight balances the buoyant force from the water their body and gear displace.
  • Science class. Students lower a 100 cm³ block into water and find a buoyant force of about 0.98 N, the weight of 100 g of water.

How to use it

  1. Choose "Buoyant force" or "Will it float?".
  2. Pick the fluid: fresh water, seawater or a custom density.
  3. Enter the volume under the surface, or the object's mass and total volume.
  4. Leave gravity at Earth's standard value, unless you're working on another planet or moon.

What the inputs mean

Fluid
The presets are typical values. Fresh water is about 997 kg/m³ at 25 °C, closer to 1,000 kg/m³ when cold. Surface seawater is about 1,025 kg/m³, and it varies with saltiness and temperature. Use a custom density for other liquids or gases.
Fluid density (ρ)
For example about 1.2 kg/m³ for air at room temperature, or about 13,530 kg/m³ for mercury.
Submerged volume (V)
For an object that's only partly under, count only the part below the surface. Only that part pushes fluid aside.
Total volume of the object
The volume inside the object's outer surface. A hollow or air-filled object counts its sealed air spaces. That's how steel ships float.
Custom gravitational acceleration
For example 9.81 or 9.8 m/s² to match a textbook, or 32.174 ft/s².

Formula and method

Buoyant force F = ρ_fluid × V_submerged × g
Object density ρ_object = m ÷ V_object
Floats if ρ_object < ρ_fluid
Fraction submerged = ρ_object ÷ ρ_fluid (when floating)
Apparent weight when sunk = m × g − ρ_fluid × V_object × g

F is the buoyant force. ρ_fluid is the fluid's density and ρ_object is the object's average density. V_submerged is the volume below the surface, and V_object is the object's whole volume. The letter m is the object's mass, and g is the pull of gravity.

The calculator changes volumes to cubic meters and densities to kg/m³, so the force comes out in newtons. A floating object sinks until it has pushed aside its own weight in fluid. That's why the share under water is just the ratio of the two densities. This ratio doesn't depend on gravity. An ice cube would float at the same depth on the Moon.

An object denser than the fluid sinks. It still feels the full buoyant force, so it seems lighter underwater. This apparent weight is its real weight minus the buoyant force.

Worked example

A sealed 80-liter container with a total mass of 60 kg is put in fresh water (997 kg/m³).

  1. Change the volume to cubic meters: 80 L × 0.001 = 0.08 m³.
  2. Object density = 60 ÷ 0.08 = 750 kg/m³. That's less than 997 kg/m³, so it floats.
  3. Share under water = 750 ÷ 997 ≈ 75.2257%.
  4. Extra load before it goes under = (997 − 750) × 0.08 = 19.76 kg.

Result: The container floats with about 75.23% of its volume under water. It could carry about 19.76 kg more before sinking.

Understanding the result

The same object floats higher in seawater than in fresh water, because seawater is denser. Something that barely floats in the sea can sink in a lake.

When an object's average density exactly matches the fluid, it's called neutrally buoyant. It stays at whatever depth you put it. Submarines and fish change their density to do this.

Assumptions and limitations

  • The fluid has the same density all the way through, and it's still.
  • The object is rigid, so its volume doesn't change with depth.
  • Surface tension, the slight "skin" on water, is small enough to ignore. That's reasonable for objects bigger than a few centimeters.
  • It doesn't check whether a floating object stays upright. That depends on stability: where its center of gravity and its center of buoyancy sit.
  • Squeezable objects, such as a diver's wetsuit or a balloon, change volume with depth.
  • In gases, buoyancy is small but real. Precise weighing corrects for the buoyancy of air.

Frequently asked questions

Why does a steel ship float if steel sinks?

The ship's hull holds a large volume of air. So the average density of the whole ship, steel plus air, is lower than water's. If the hull floods, the average density rises and the ship sinks.

How much of an iceberg is under water?

Ice is about 917 kg/m³ and seawater is about 1,025 kg/m³. So roughly 917 ÷ 1,025 ≈ 89.5% of a floating iceberg is below the surface.

Does the depth of a submerged object change the buoyant force?

Not for a rigid object in a fluid with the same density throughout. The pressure difference between its top and bottom stays the same at any depth. So the buoyant force does too.

Is buoyancy weaker on the Moon?

The buoyant force is smaller, because gravity (g) is weaker. But the object's weight shrinks by the same amount. So whether it floats, and how deep it sits, doesn't change.

How this calculator is checked

Method: Archimedes' principle (F = ρVg) and the floating condition from equating weight with displaced-fluid weight. Fluid presets are typical values. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

Embed this calculator

Put this Buoyancy Calculator on your own website or blog for free. Paste this code where you want it to appear: