Buoyant Force Calculator
An object submerged in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid — Archimedes' principle. Choose a mode below: compute the buoyant force, the apparent weight of a submerged object, or what percent of the object's volume is submerged while floating.
For an object floating in equilibrium: submerged volume fraction = ρobject / ρfluid.
How it works — worked example
- Take the fluid density: fresh water ρ = 1000 kg/m³.
- Submerged volume V = 0.5 m³, gravity g = 9.80665 m/s².
- Fb = ρ × V × g = 1000 × 0.5 × 9.80665 = 4903.32 N (≈ 500 kgf).
Assumptions: static (non-flowing) fluid with uniform density; surface tension and compressibility ignored. See the FAQ for detailed limitations.
Frequently asked questions
What is Archimedes' principle?
Archimedes' principle states that an object submerged (partially or fully) in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid: F_b = ρ × V × g, where ρ is the fluid density (kg/m³), V the submerged volume (m³), and g gravity (9.80665 m/s²). This principle was formulated by Archimedes of Syracuse in the 3rd century BC.
How do I calculate buoyant force?
Multiply the fluid density by the submerged volume and gravity. Example: a 0.5 m³ block fully submerged in fresh water (ρ = 1000 kg/m³) with g = 9.80665 m/s² → F_b = 1000 × 0.5 × 9.80665 = 4903.32 N. Enter your numbers in the 'Buoyant force' mode above for an instant result.
What is apparent weight and how do I calculate it?
Apparent weight is the weight measured while an object is submerged: true weight minus buoyant force (W − F_b). Example: a 10 kg object with volume 0.005 m³ fully submerged in fresh water → true weight W = 10 × 9.80665 = 98.0665 N; buoyant force F_b = 1000 × 0.005 × 9.80665 = 49.0332 N; apparent weight = 98.0665 − 49.0332 = 49.0332 N. Object density = 10 / 0.005 = 2000 kg/m³, greater than water, so its status is sinking.
Why does ice float in sea water?
Ice (ρ = 917 kg/m³) is lighter than sea water (ρ = 1025 kg/m³), so it floats. The submerged volume fraction = 917 / 1025 = 0.8946, meaning 89.5% of the ice's volume is below the surface and 10.5% sticks out above — the origin of the 'tip of the iceberg' expression.
When does an object float, hover, or sink?
Compare the object's density with the fluid's density: object ρ < fluid ρ → floats; exactly equal → hovers (neutral), e.g., a 1025 kg/m³ object in sea water; greater → sinks. The 'Apparent weight' mode shows this status automatically from the mass and volume you enter.
What units does this calculator support?
Volume: m³, L, mL, cm³, ft³, US gal, and in³. Mass: kg, g, ton, lb, and oz. Force: N, kN, kgf, lbf, and dyn. Exact reference values: 1 ft³ = 0.028316846592 m³; 1 US gallon = 0.003785411784 m³; 1 lb = 0.45359237 kg; 1 lbf = 4.4482216152605 N.
Does air also produce buoyant force?
Yes, but small. One cubic meter of displaced air at sea level (ρ = 1.225 kg/m³) gives F_b = 1.225 × 1 × 9.80665 = 12.0131 N (about 1.225 kgf). This effect is ignored in most problems but matters for hot-air balloons and precision measurements.
What are this calculator's limitations?
The calculator assumes a static (non-flowing) fluid with uniform density, and ignores surface tension and fluid compressibility. For very small objects, moving fluids, or compressible fluids like high-pressure gases, results are approximate.
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