Calculate buoyant force, sink-or-float status, or dock float count from fluid density, volume, mass, and load in fresh water, seawater, or air.
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Float Weight Formula
The calculator uses three formulas, one per tab.
Buoyant force tab. Archimedes' principle gives the upward force on a submerged or partly submerged object.
B = ρ × V × g
- B = buoyant force (N)
- ρ = fluid density (kg/m³)
- V = submerged or displaced volume (m³)
- g = gravitational acceleration, 9.80665 m/s² at Earth's surface
Inputs are converted to SI before the math runs. The result is shown in newtons, pounds-force, and kilograms-force. The displaced fluid mass equals ρ × V.
Sink or float tab. The object floats when its average density is less than the fluid density.
ρ_object = m / V f_submerged = ρ_object / ρ_fluid
- m = object mass (kg)
- V = total object volume (m³)
- ρ_object = average object density (kg/m³)
- ρ_fluid = fluid density (kg/m³)
- f_submerged = fraction of volume below the surface at equilibrium
If f_submerged is less than 1, the object floats and that fraction sits below the waterline. If it is greater than 1, the object sinks. The tool also reports the net upward force at full submersion, which is (ρ_fluid − ρ_object) × V × g.
Dock floats tab. The number of floats needed is the required buoyancy divided by the capacity per float, rounded up.
N = ceil( (L × W × q) / C )
- L = dock length (ft)
- W = dock width (ft)
- q = required buoyancy per square foot (lb/ft²)
- C = buoyancy capacity of one float (lb)
- N = number of floats
The preset values for q bundle the dead load of common framing and decking with a reserve so the deck rides above the waterline under foot traffic. Pick "Custom load" if you have engineered numbers for your build.
Reference Tables
Use these values when you do not have a measured number for density or float capacity.
| Fluid | Density (kg/m³) | Density (lb/ft³) |
|---|---|---|
| Fresh water (4 °C) | 1000 | 62.4 |
| Seawater | 1025 | 64.0 |
| Gasoline | 740 | 46.2 |
| Engine oil (SAE 30) | 900 | 56.2 |
| Air at sea level | 1.225 | 0.0765 |
| Common dock float size | Approx. buoyancy (lb) | Typical use |
|---|---|---|
| 12 × 24 × 36 in | 325 | Light walkways |
| 12 × 36 × 48 in | 645 | Residential dock |
| 16 × 36 × 48 in | 860 | Heavier residential |
| 20 × 48 × 96 in | 2300 | Boat lifts, commercial |
Worked Examples
Example 1: Buoyant force on a sealed barrel. A 55-gallon drum is fully submerged in fresh water. Volume = 55 gal = 0.2082 m³. ρ = 1000 kg/m³. g = 9.80665 m/s².
B = 1000 × 0.2082 × 9.80665 = 2042 N, or about 459 lbf. The drum must weigh more than 459 lb to stay sunk.
Example 2: Will a block of oak float in water? Mass = 5 kg, volume = 7 L = 0.007 m³. Object density = 5 / 0.007 = 714 kg/m³. Fluid density = 1000 kg/m³. f_submerged = 0.714, so the block floats with about 71% of its volume below the surface.
Example 3: Floats for a 6 ft by 20 ft dock. Area = 120 ft². Using 28 lb/ft², required buoyancy = 3360 lb. With 645 lb floats, N = ceil(3360 / 645) = 6 floats. Supplied buoyancy = 3870 lb, reserve = 510 lb (about 15%).
FAQ
What weight do I need for an object to sink? The object plus any added ballast must weigh more than the buoyant force B = ρ × V × g, where V is the volume of the object underwater. Run the buoyant force tab to get that number, then make sure your total weight exceeds it.
Why does the sink-or-float tab show a percent submerged over 100%? That means the object is denser than the fluid and cannot float. The result is capped at 100% in the display and labeled "Sinks."
Should I use 28 lb/ft² or a higher number for my dock? 28 lb/ft² covers a basic treated frame with 5/4 decking and a small reserve for foot traffic. Composite decking, heavier framing, railings, roofs, or boat lifts push that number up. Use the dropdown presets or enter your engineered load.
Does salt water change the answer much? Seawater is about 2.5% denser than fresh water, so buoyant force and float capacity rise by roughly 2.5% in salt. For dock sizing this is small but meaningful at the margin.
Why is gravity an input? So the buoyant force tab works on other planets, in centrifuges, or with non-standard g values used in physics problems. Leave it at 9.80665 m/s² for normal Earth conditions.
