buoyancy formulas and interpretation
Buoyant force equals the weight of fluid displaced by an immersed object.
The calculator preserves shape-based volume assistance, fluid presets, and float-or-sink interpretation.
How to use the buoyancy calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
Archimedes’ principle states that buoyant force equals displaced fluid weight.
Fb = ρfluid g Vdisplaced- Fb — Buoyant force
- Upward fluid force (N)
- ρfluid — Fluid density
- Fluid mass per volume (kg/m³)
- g — Gravity
- Local gravitational acceleration (m/s²)
- V — Displaced volume
- Submerged fluid volume (m³)
Submerged volume example
An object displaces 0.01 m³ of fresh water.
- Density
- 1000 kg/m³
- Volume
- 0.01 m³
- Fb = 1000 × 9.80665 × 0.01
- Fb = 98.0665 N
Result: Buoyant force is about 98.07 N.
Compare this upward force with object weight to assess vertical tendency.
Understanding your results
Interpreting the result
An object floats in equilibrium when buoyant force balances its weight.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.