Archimedes' Principle Calculator — Buoyant Force
Find the upward buoyant force acting on any object submerged in a fluid. Enter the fluid's density, the submerged volume, and local gravity — the calculator applies Archimedes' principle to give you the buoyant force and the mass of fluid displaced.
kg/m³
m³
m/s²
Upward force the fluid exerts on the submerged object
- 1
Mass of displaced fluid
1,000 × 0.001 = 1Fluid density × submerged volume gives the mass of fluid pushed aside. - 2
Buoyant force F = mass × g
1 × 9.81 = 9.8100
How does this calculator work?
Archimedes' principle: buoyant force F_b = ρ × V × g, where ρ is fluid density (kg/m³), V is submerged volume (m³), and g is gravity (m/s²). Water has ρ = 1000 kg/m³. An object floats when F_b equals its weight, sinks when F_b is less, and rises when F_b is greater.
Formula
How this is calculated
Archimedes' principle states that any object fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. The formula is F_b = ρ × V × g, where ρ is the fluid density in kg/m³, V is the volume of fluid displaced in m³, and g is gravitational acceleration (≈ 9.81 m/s² at Earth's surface). The displaced fluid weighs ρ × V × g newtons — and the buoyant force equals exactly that weight, regardless of the object's material.
Whether an object sinks, floats or rises depends on comparing F_b to the object's own weight. If F_b equals the object's weight it floats in equilibrium; if F_b is greater it rises; if less it sinks. This is why a hollow steel ship floats — its hull-plus-air cavity displaces a large volume of water, making the average density of the whole vessel less than water. A solid steel ball of the same mass displaces far less water and sinks.
This calculator computes only the magnitude of the buoyant force. It does not account for the object's own weight or shape — to determine flotation, compare F_b to the object's weight (mass × g). The volume input is the submerged portion only; for a partially floating object, enter just the submerged fraction of its total volume.
Frequently asked questions
Archimedes' principle states that a submerged object experiences an upward buoyant force equal to the weight of the fluid it displaces: F_b = ρ × V × g. If this force equals the object's weight, the object floats; if less, it sinks; if greater, it rises.
A ship's hollow hull encloses a large volume of air, so the total average density of the ship (steel + air) is less than water. A solid steel ball has no air, so its average density far exceeds water. Buoyancy depends on the volume of water displaced, not just the raw weight.
The calculator uses SI units — volume in cubic metres (m³). One litre = 0.001 m³; one cubic centimetre (1 cm³) = 0.000001 m³. To convert litres to m³, divide by 1000.
Also known as
TG we-Calculate Editorial Team. (2026). Archimedes' Principle Calculator — Buoyant Force [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/archimedes-principle-calculator
TG we-Calculate Editorial Team. "Archimedes' Principle Calculator — Buoyant Force." TG we-Calculate. 2026. https://we-calculate.com/calculator/archimedes-principle-calculator.
TG we-Calculate Editorial Team, "Archimedes' Principle Calculator — Buoyant Force," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/archimedes-principle-calculator
@misc{wecalculate_archimedes_principle_calculator, title = {Archimedes' Principle Calculator — Buoyant Force}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/archimedes-principle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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