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Physics

Buoyancy Calculator

F = ρ V g. Free online Buoyancy Calculator. Calculate buoyancy online — fast, accurate, mobile-friendly, no signup needed.

Fb = ρ·V·g (Archimedes’ principle).
Buoyant force (N)
981

Derivation

  1. ├── 01Givenrho = 1000, V = 0.1
  2. ├── 02Formulae.rho × e.V × 9.81
  3. ├── 03Substitutee.1000 × e.0.1 × 9.81
  4. └── 04Compute Buoyant force (N)981
Did you know?

Archimedes discovered the buoyancy principle in a public bath in Syracuse (~250 BCE) and is said to have run naked through the streets shouting "Eureka!".

§01What is

Understanding the Buoyancy Calculator

The Buoyancy Calculator computes Buoyant force (N) from 2 inputs: fluid density (kg/m³), displaced volume (m³). F = ρ V g.

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Buoyancy Calculator sits in that toolkit — it F = ρ V g. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

e.rho × e.V × 9.81

Where

rho
Fluid density (kg/m³)
V
Displaced volume (m³)
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Fluid density (kg/m³) = 1000, Displaced volume (m³) = 0.1.

  1. 01Start by noting the input — Fluid density (kg/m³): 1000.
  2. 02Start by noting the input — Displaced volume (m³): 0.1.
  3. 03Substitute these values into the formula: e.rho × e.V × 9.81
  4. 04Compute Buoyant force (N): the calculator returns 981.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Buoyancy Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Fluid density (kg/m³) halved

rho = 500 (from 1000)

Keep every other input at its default and halve the fluid density (kg/m³). See how buoyant force (n) responds.

  1. 01New Fluid density (kg/m³): 500
  2. 02Baseline Buoyant force (N): 981
  3. 03New Buoyant force (N): 490.5
  4. 04Buoyant force (N) decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Fluid density (kg/m³) doubled

rho = 2000 (from 1000)

Keep every other input at its default and double the fluid density (kg/m³). See how buoyant force (n) responds.

  1. 01New Fluid density (kg/m³): 2000
  2. 02Baseline Buoyant force (N): 981
  3. 03New Buoyant force (N): 1962
  4. 04Buoyant force (N) increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Displaced volume (m³) halved

V = 0.05 (from 0.1)

Keep every other input at its default and halve the displaced volume (m³). See how buoyant force (n) responds.

  1. 01New Displaced volume (m³): 0.05
  2. 02Baseline Buoyant force (N): 981
  3. 03New Buoyant force (N): 490.5
  4. 04Buoyant force (N) decreases by 50% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Displaced volume (m³) doubled

V = 0.2 (from 0.1)

Keep every other input at its default and double the displaced volume (m³). See how buoyant force (n) responds.

  1. 01New Displaced volume (m³): 0.2
  2. 02Baseline Buoyant force (N): 981
  3. 03New Buoyant force (N): 1962
  4. 04Buoyant force (N) increases by 100% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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