Buoyancy Calculator
Calculate buoyancy calculator calculate Archimedes buoyant force Fb from fluid density rho, displaced volume V, and gravity g (Fb = rho * V * g). Accurate physics formulas and unit conversions for engineers, students & technicians.
Calculate Archimedes Buoyant Force (F_b = ρ · V · g)
Enter your physical parameters below to compute verified buoyant force metrics.
Calculation Results
Calculated using verified physical methodology: Archimedes Buoyant Force: F_b = \rho_{fluid} \cdot V_{displaced} \cdot g
Displaced Fluid Mass: m_{displaced} = \rho_{fluid} \cdot V_{displaced}
Quick Summary
The Buoyancy Calculator applies Archimedes' Principle ($F_b = \rho_{fluid} \cdot V_{displaced} \cdot g$) to compute upward buoyant force in Newtons (N), kilonewtons (kN), lbf, and maximum supported floating cargo mass.
Formula Explanation
Archimedes Buoyant Force: F_b = \rho_{fluid} \cdot V_{displaced} \cdot g
Displaced Fluid Mass: m_{displaced} = \rho_{fluid} \cdot V_{displaced}
How It Works
The Buoyancy Calculator multiplies fluid density ($\rho_{fluid}$ in $\text{kg/m}^3$) by displaced volume ($V$ in $\text{m}^3$) and Earth gravity ($g = 9.80665\text{ m/s}^2$). It outputs upward buoyant force ($F_b$), displaced fluid mass, and maximum floating payload tonnage.
Step-by-Step Worked Example
Practical Problem: Calculate upward buoyant force acting on a boat displacement hull displacing $V = 2.0\text{ m}^3$ of seawater ($\rho = 1,025.0\text{ kg/m}^3$).
- Step 1: Identify Input Parameters: Seawater Density $\rho = 1,025.0\text{ kg/m}^3$, Displaced Volume $V = 2.0\text{ m}^3$, $g = 9.80665\text{ m/s}^2$.
- Step 2: Calculate Displaced Fluid Mass ($m_{displaced}$): $m_{displaced} = 1,025.0 \times 2.0 = 2,050.0\text{ kg}$.
- Step 3: Apply Archimedes' Principle Formula: $F_b = \rho \cdot V \cdot g$.
- Step 4: Execute Numeric Multiplication: $F_b = 2,050.0\text{ kg} \times 9.80665\text{ m/s}^2 = 20,103.63\text{ Newtons (N)}$.
- Step 5: Convert and Interpret Imperial & Payload Tonnes: Buoyant Force $F_b = 20,103.63\text{ N} = 20.10\text{ kN} = 4,519.48\text{ lbf}$. Max Floating Payload Mass = $2,050.0\text{ kg} = 2.05\text{ metric tonnes}$.
Real-World Calculation Examples
Scenario 1: Small Boat Seawater Hull
Parameters: $\rho = 1,025\text{ kg/m}^3$, $V = 2.0\text{ m}^3$, $g = 9.81\text{ m/s}^2$
Result: $F_b = 20.10\text{ kN}$ (4,519 lbf, 2.05 tonnes buoyancy). Boat hull support.
Scenario 2: Hot Air Balloon Atmospheric Lift
Parameters: $\rho = 1.225\text{ kg/m}^3$ (Air), $V = 2,000.0\text{ m}^3$, $g = 9.81\text{ m/s}^2$
Result: $F_b = 24.03\text{ kN}$ (5,401 lbf, 2,450 kg gross air displacement). Balloon buoyancy.
Scenario 3: Cargo Ship Ocean Liner Hull
Parameters: $\rho = 1,025\text{ kg/m}^3$, $V = 50,000.0\text{ m}^3$, $g = 9.81\text{ m/s}^2$
Result: $F_b = 502.59\text{ MN}$ (51,250 tonnes cargo capacity). Ocean freighter displacement.
Scenario 4: Submarine Ballast Tank
Parameters: $\rho = 1,025\text{ kg/m}^3$, $V = 500.0\text{ m}^3$, $g = 9.81\text{ m/s}^2$
Result: $F_b = 5.03\text{ MN}$ (512.5 tonnes lift). Submarine ballast buoyancy.
Key Benefits of Using This Calculator
Archimedes' Law Precision
Calculates exact upward buoyant force equal to the weight of displaced fluid.
Max Cargo Payload Capacity
Computes maximum supported floating cargo mass ($m = \rho \cdot V$) in tonnes.
Multi-Unit Readouts
Outputs buoyant force in Newtons, kilonewtons (kN), and Imperial lbf.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is Archimedes' Principle?
Archimedes' Principle states that any body completely or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the body (Fb = rho_fluid * V_displaced * g).
What is the formula for buoyant force?
Fb = rho_fluid * V_displaced * g.
What causes buoyant force in fluids?
Hydrostatic fluid pressure increases with depth (P = rho*g*h), creating a net upward pressure force on the bottom surface of submerged objects.
When does an object float vs sink?
If buoyant force Fb > object weight W, the object accelerates upward and floats; if Fb < W, it sinks; if Fb = W, it maintains neutral buoyancy.
What is the difference between freshwater and seawater buoyancy?
Seawater is denser (rho = ~1025 kg/m³) than freshwater (rho = 1000 kg/m³), providing ~2.5% more buoyant force for identical displaced volume.
Does buoyant force depend on object material density?
No, buoyant force depends strictly on FLUID density and DISPLACED VOLUME, regardless of object composition mass.
How does a steel ship float if steel is 7.85 times denser than water?
Because the hollow shape of the ship hull encloses large air spaces, making average overall density of ship + air lower than water density (rho_average < 1000 kg/m³).
How do submarines control buoyancy to dive or surface?
Submarines flood ballast tanks with water to increase total mass (W > Fb) for diving, and use compressed air to blow water out to decrease mass (W < Fb) for surfacing.
What is apparent weight in water?
Apparent Weight W_apparent = W_actual - Fb = (rho_object - rho_fluid) * V * g.
Does buoyant force exist in gases?
Yes, hot air balloons and helium blimps rise because atmospheric air provides upward buoyant force Fb = rho_air * V * g according to Archimedes' principle.