Buoyant Force Calculator

Buoyant Force from Fluid Density and Displaced Volume

Buoyant Force Formula

Formula

\[ F_b = \rho_{\text{fluid}} \cdot V \cdot g \]

Where:

\(F_b\) — buoyant force (N), the upward push of the fluid
\(\rho_{\text{fluid}}\) — density of the fluid (kg/m³)
\(V\) — volume of fluid displaced by the object (m³)
\(g\) — gravitational acceleration (m/s², 9.81 on Earth)

This is Archimedes' principle: the buoyant force equals the weight of the fluid the object pushes aside. If you also know the object's weight in air \(W\), its apparent weight in the fluid is \(W_{\text{app}} = W - F_b\).

If \(W_{\text{app}} > 0\) the object sinks; if \(W_{\text{app}} = 0\) it is neutrally buoyant; if \(W_{\text{app}} < 0\) it floats, displacing only enough fluid to balance its weight.

Buoyant Force – Calculation Example

Example: a fully submerged object displaces 2 L of fresh water (density 1000 kg/m³). Standard gravity is 9.81 m/s² and the object weighs 25 N in air.

\[ F_b = 1000 \ \tfrac{\text{kg}}{\text{m}^3} \times 0.002\ \text{m}^3 \times 9.81\ \tfrac{\text{m}}{\text{s}^2} = 19.62\ \text{N} \]

\[ W_{\text{app}} = 25\ \text{N} - 19.62\ \text{N} = 5.38\ \text{N} \]

Result: the buoyant force is 19.62 N and the apparent (underwater) weight is 5.38 N. Because the buoyant force is smaller than the weight, the object sinks; it would need an upward pull of 5.38 N to hold it still.

How to use the calculator

Enter the Fluid density (ρ) and pick a unit. Fresh water is about 1000 kg/m³, sea water about 1025 kg/m³.
Enter the Displaced volume (V) — the volume of fluid the object pushes aside — and choose its unit (m³, L, cm³, ft³, in³, or gal). For a fully submerged object, this is simply the object's volume.
Set the Gravitational acceleration (g). Use 9.81 m/s² for Earth unless you are working on another planet or in a textbook problem that specifies a different value.
Optionally enter the Object weight in air (W). Leave it blank to get only the buoyant force; enter it to also get the apparent weight, the object's average density, and a float/sink verdict.
Read the results: the buoyant force in newtons plus kN, kgf, and lbf equivalents, the apparent weight if you provided \(W\), and the formulas with your values plugged in.

What is buoyant force?

Buoyant force is the upward force a fluid exerts on any object immersed in it. It exists because pressure in a fluid increases with depth: the pressure pushing up on the bottom of an object is greater than the pressure pushing down on its top. The net effect is an upward force equal to the weight of the fluid the object displaces — a rule discovered by Archimedes of Syracuse over 2200 years ago.

What matters is only the displaced fluid, not the object itself. A steel ship floats because its hull encloses a huge volume, displacing water whose weight exceeds the ship's weight. A solid steel block of the same mass sinks because it displaces far less water. This is why comparing densities is the quickest way to predict the outcome: an object with an average density less than the fluid's density floats, a denser one sinks, and an exactly equal one is neutrally buoyant.

The apparent weight is what the object "feels like" when held underwater — it is also what a scale would read if you weighed it while submerged. Divers experience this directly: a properly weighted diver is close to neutral buoyancy, so \(W \approx F_b\) and hovering takes almost no effort. The same principle governs hot-air balloons (where the "fluid" is air), hydrometers, and the loading lines marked on ship hulls.

Assumptions, limitations, and tips

Full submersion is assumed. When you enter a weight, the calculator takes the displaced volume as the object's full volume. A floating object displaces only part of its volume, which the calculator reports in the float verdict.
The fluid is incompressible and uniform. In practice, density varies slightly with temperature, salinity, and depth. For seawater, values between 1020 and 1030 kg/m³ are typical.
Surface tension and currents are ignored. For small objects (a needle resting on water) surface tension can matter, and it is not included here.
Remember that 1 L = 0.001 m³ and 1 g/cm³ = 1000 kg/m³ — two conversions that cause most unit mistakes in buoyancy problems.
If the object floats, its apparent weight is zero at equilibrium, not negative; the calculator reports the reduced volume it actually displaces when floating.

If you are analyzing the full force picture on a submerged object, you may also find our Force and Tension in Ropes calculators useful, for example to find the rope tension needed to lift the underwater object, or the Atwood Machine calculator for connected-mass problems.

Frequently Asked Questions

Does buoyant force change with depth?

No — as long as the object is fully submerged and the fluid is incompressible, the buoyant force stays the same at any depth. Only the displaced volume and fluid density matter, and neither changes when you push an object deeper. In reality water is very slightly compressible, so density increases a tiny amount with depth, but the effect is negligible for everyday calculations.

Why does an object float in sea water but sink in fresh water?

Sea water contains dissolved salt, making it denser (about 1025 kg/m³ versus 1000 kg/m³ for fresh water). A denser fluid weighs more per unit displaced, so it pushes up harder. An object whose average density falls between these two values — for example around 1010 kg/m³ — floats in the ocean but sinks in a lake. This is also why swimming is noticeably easier in very salty water like the Dead Sea.

Can I use mass in kg instead of weight in newtons?

Be careful here. The formula requires weight (a force) in newtons. If you only know the object's mass in kilograms, first convert: multiply mass by gravitational acceleration, for example a 10 kg object weighs about 98.1 N on Earth. A common mistake is typing 10 into a field expecting newtons — this underestimates the weight by roughly a factor of 10 and flips the float/sink verdict.

How do I find the volume of an irregular object for the displaced volume?

Submerge the object in a full container of water and measure the overflow, or note the water level rise in a graduated container — the volume of that water equals the object's volume. Alternatively, use the formula for a regular shape (cube, sphere, cylinder). If the object is fully waterproof, its volume is exactly what you enter as the displaced volume.

Does buoyancy work in air, not just water?

Yes — any fluid, including air, produces buoyant force. Air at sea level has a density of about 1.225 kg/m³, so a person displacing roughly 0.07 m³ of air feels an upward push of less than 1 N. It is small but real, and precision scales correct for it. Hot-air balloons exploit exactly this: the warm air inside is less dense than the surrounding air, so the displaced air weighs more than the balloon.

What is the difference between buoyant force and upthrust?

There is no difference — upthrust is simply another common name for the buoyant force, especially in UK textbooks. Both refer to the same upward force equal to the weight of displaced fluid, given by \(F_b = \rho \cdot V \cdot g\). You may also see it called the Archimedes force. All these terms are interchangeable in buoyancy problems.

How do I calculate buoyancy on the Moon or Mars?

Change the gravitational acceleration: about 1.62 m/s² on the Moon and 3.71 m/s² on Mars. The buoyant force scales directly with g, so the same object in the same fluid experiences a smaller buoyant force there. Interestingly, whether it floats or sinks does not change, because both the weight and the buoyant force shrink by the same factor.