F_b = ρVg — Buoyant Force (Archimedes' Principle)

Archimedes' buoyant force — the weight of displaced fluid — with a worked boat example.

F_b = \rho V g

Buoyant force equals fluid density times displaced volume times g.

What it means

The upward buoyant force equals the weight of the fluid the object displaces — not the object's own weight. Denser fluids push harder (easier to float in the Dead Sea), and larger submerged volumes push harder (why ships are hollow). Float when $F_b$ equals your weight.

Variables

Symbol	Name	Unit	Meaning
$F_b$	Buoyant force	N	Upward force from the fluid
$ρ$	Fluid density	kg/m³	Fluid's mass per unit volume
$V$	Displaced volume	m³	Volume of fluid pushed aside
$g$	Gravity	m/s²	Gravitational acceleration

Assumptions

Object fully or partially submerged in a static fluid
Fluid density uniform
Negligible surface tension effects

Worked example

Problem

A boat displaces 2.5 m³ of seawater (ρ = 1025 kg/m³). What is the buoyant force?

Given:

V = 2.5 m³ (submerged volume)
ρ = 1025 kg/m³ (seawater)
g = 9.81 m/s²

Write the principle: $F_b = \rho V g$
Substitute: $F_b = 1025 \times 2.5 \times 9.81$
Calculate: $F_b = 1025 \times 24.525 = 25{,}138\ \mathrm{N} \approx 2.51\times10^4\ \mathrm{N}$

≈ 2.51×10⁴ N

The water pushes up with about 25,100 N — enough to support roughly 2,560 kg of mass. A floating object sinks exactly until the displaced water weighs as much as it does.