Buoyancy Calculator
Archimedes, priced live: the upward push equals the weight of whatever fluid the volume displaces — how many kilos your hull, your diver or your drum gets for free.
Buoyancy Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Static fluid — no currents, waves or viscosity
- Uniform density fluid; compressible-depth effects ignored
In short: An object displacing 0.03 m³ (30 L) of fresh water earns F_b = ρ·g·V = 294.199500 N of upward push — enough to carry 30.000000 kg of weight (the displaced water's own mass, exactly). In seawater at about 1,025 the same hull carries 30.750000 kg — salt floats boats a little higher, and the card shows the percentage a swimmer feels moving from pool to sea. The identity is worth saying out loud: the support in newtons, divided by g, IS the displaced mass in kilograms. Archimedes' insight needs no formula beyond a weighing — this page prices it, and the buoyant force never depends on what floats there, only on what got pushed aside.
Formula
F_b = ρ_fluid·g·V · carries m = ρ_fluid·V · floats iff ρ_object < ρ_fluid
Archimedes' principle: the fluid pushes up with the WEIGHT of whatever was displaced — the push depends on the fluid and the displaced volume, and not at all on what is doing the displacing. Whether the thing floats is a separate comparison: object density against fluid density. Density (page 619) measures the crowdings; this page prices the support.
Worked Example
- Enter the displaced volume — for a floating hull, the submerged part only.
- Pick the fluid; read the upward push in newtons.
- Read the carry card: the mass this buoyancy would hold up.
- Switch to seawater to see why ships ride higher in the ocean than the canal.
Defaults: 294.199500 N, carrying 30.000000 kg in fresh water; 30.750000 kg in seawater. A 0.5 m³ barrel displaces 490.332500 N of support — half a tonne of help.
Strengths & Limits Of This Model
Where this engine is strong
- Carry card in kilograms — the hull-loading number
- Fresh vs salt comparison priced from your volume
Where it stops
- No hull geometry — you supply the displacement
- No wave or dynamic lift
Practical Use Cases
Boating
load a hull to its line, honestly
Diving
weight belts against salt and fresh
Teaching
the bathtub insight, with digits
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Buoyancy Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Whose density is in the formula?
The FLUID's — that surprises everyone once. The push equals the weight of the displaced liquid, so what matters is what got pushed aside and what it weighed. The object's own density enters only the separate question of whether it sinks deep enough to matter.
Why do ships float if steel sinks?
Because the SHIP is mostly air: its average density — steel plus all that empty hull — sits below water's, so it displaces enough water to hold itself before the deck goes under. The float test is averages, not materials; the bar floats when the cathedral of air around it counts too.
Why does the sea hold you up better than the pool?
Salt dissolves more crowd into the water: about 1,025 vs 1,000, so the same body displaces 2.5% more weight and rides that much higher. The card prices your switch — swimmers feel it as free lift, cargo plans feel it as the Plimsoll line.
Does the buoyant force depend on depth?
Only through the fluid's density — deeper water is negligibly denser, so for practical depths the push is constant once fully submerged. What grows with depth is PRESSURE, a different ledger; the net upward push cares only about the gradient, not the squeeze.
What does the carry card actually price?
The most weight this displacement could hold at the surface: ρ·V — exactly the mass of fluid pushed aside. A 30 L displacement carries 30 kg of fresh water's worth; load past it and the volume that must submerge does not exist. It is the Plimsoll line, computed.
Why 'weight of the displaced fluid' and not 'volume'?
Because the fluid's WEIGHT is what the pressure difference integrates to: deeper face pushed up harder than the shallow face pushed down, and the difference equals exactly the column's weight. Volume alone would price nothing — mercury and air share volumes, never bills.
Does this work on the Moon?
The push scales with g: weaker gravity, weaker buoyancy — but also lighter cargo, and the carry card in KILOGRAMS stays the displaced volume's fluid mass regardless. The g chip lets you watch newtons move while kilograms hold still, which is the mass/weight lesson wearing flippers.
Where does the displaced volume come from in practice?
For floaters, the waterline: submerged geometry only. For sinkers, all of it. For the in-between — a diver with a vest — the diver adjusts volume (air in the vest) until support meets weight, which is why buoyancy control is the first skill and the last mastered.