# Buoyancy Calculator (Archimedes, F = ρ·V·g)

Compute buoyant force, fluid density, or displaced volume from any two, with optional float/sink analysis

> Canonical page: https://elysiatools.com/en/tools/buoyancy-calculator

- **Category:** Math & Numbers

- **Keywords:** buoyancy, archimedes, buoyant force, fluid density, displaced volume, float, sink, apparent weight, physics, fluid mechanics

## Overview

Archimedes' principle: the upward buoyant force on a body in a fluid equals the weight of the fluid it displaces.

Equations (given any two of F, ρ, V — the third follows):
- Buoyant force:  F = ρ · V · g
- Fluid density:  ρ = F / (V · g)
- Volume:         V = F / (ρ · g)

With object density ρ₀:
- Object weight:    W = ρ₀ · V · g
- Apparent weight:  W − F
- ρ₀ < ρ floats (submerged fraction = ρ₀/ρ); ρ₀ = ρ neutral; ρ₀ > ρ sinks.

g defaults to 9.80665 m/s².

## Inputs

- **Solve For** (select)
- **Buoyant Force (F, N)** (number): leave blank when solving for force
- **Fluid Density (ρ, kg/m³)** (number): water 1000, seawater 1025, mercury 13534
- **Volume (V, m³)** (number): leave blank when solving for volume
- **Gravity (g, m/s²)** (number): 9.80665 (Earth)
- **Object Density (ρ₀, kg/m³)** (number): optional — for float/sink analysis (e.g. iron 7870, wood 600)

## When to use

- When calculating the upward buoyant force acting on a submerged or floating object.
- When determining the required displaced volume of a vessel or pontoon to support a specific load.
- When analyzing whether an object will float, sink, or remain neutrally buoyant in a given fluid.

## How it works

- Select the target variable you want to solve for: Buoyant Force (F), Fluid Density (ρ), or Volume (V).
- Input the two known values along with the local acceleration due to gravity (g), which defaults to 9.80665 m/s².
- Optionally enter the object's density (ρ₀) to calculate its actual weight, apparent weight, and submerged fraction.
- Click calculate to instantly view the solved variable and the flotation analysis.

## Use cases

- Designing marine hulls, pontoons, and buoys to ensure proper flotation and load capacity.
- Solving physics homework problems and verifying fluid mechanics equations.
- Estimating the density or volume of irregular objects using hydrostatic weighing methods.

## Frequently asked questions

### What is Archimedes' principle?

It states that the upward buoyant force on an object in a fluid equals the weight of the fluid it displaces.

### How is apparent weight calculated?

It is calculated by subtracting the upward buoyant force (F) from the object's actual weight (W = ρ₀ · V · g).

### What units should I use for the inputs?

Use standard SI units: Newtons (N) for force, kg/m³ for density, and m³ for volume.

### Can I calculate buoyancy on other planets?

Yes, you can adjust the gravity (g) field to match the gravitational acceleration of other celestial bodies.

### How does the tool determine if an object floats or sinks?

It compares the object density (ρ₀) to the fluid density (ρ). If ρ₀ is less than ρ, the object floats.

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