What is Archimedes' principle?
The buoyant force on an object equals the weight of the fluid it displaces: F = ρVg.
Buoyancy Force Calculator
F = ρVg
Archimedes' buoyancy calculator — find the upward force on a submerged object. F = ρVg.
Calculate
Enter values above to calculate
How it calculates
1
Archimedes' principle: F = ρ × V × g
2
ρ = fluid density, V = displaced volume, g = 9.81 m/s²
3
Result is the upward buoyant force in newtons
Formula
F = ρVg
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| F | Buoyant force | N |
| ρ | Fluid density | kg/m³ |
| V | Displaced fluid volume | m³ |
| g | Gravitational acceleration | m/s² |
How to Use This Calculator
This buoyancy force calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.
Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.
Assumptions and Limits
The formula F = ρVg is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.
Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.
Worked Example
An object displaces 0.01 m³ of water (ρ=1000). Find buoyant force.
Step 1: F = ρVg
Step 2: F = 1000 × 0.01 × 9.81
Answer: F = 98.1 N upward
Common Mistakes
- V is the volume of fluid displaced, not the object's total volume (unless fully submerged)
- An object floats if buoyant force ≥ its weight
- Buoyancy explains why steel ships float — they displace enough water
Related
Frequently Asked Questions
Why do ships float?
A steel hull displaces a large volume of water, generating a buoyant force greater than the ship's weight, even though steel is denser than water.