Advertisement

Archimedes principle calculator

Compare true and apparent weight for an immersed object. Choose direct volume, object density, a liquid-level rise or a weighing measurement.

Calculator

Rounded textbook references. Custom density is used only for Custom; the reference is ignored when solving for density. Use measured data for other conditions.

Use the density at the measurement temperature. Water near 4 C is about 1000 kg/m3.

Apparent weight
78.4532
Apparent mass
8
True object mass
10
True object weight
98.0665
Displaced fluid volume
0.002
Object density if fully immersed
5,000
Fluid density
1,000
Displaced fluid mass
2
Buoyant force
19.6133

Advertisement

How this calculator works

Subtract buoyancy from true weight to obtain the signed support force needed to hold an immersed object at rest. A negative result means that a downward restraint is required. The density inferred for the object assumes complete immersion and no absorbed liquid or trapped bubbles. For a straight-sided vessel, surface area times liquid-level rise measures displaced volume. A scale calibrated in mass reports support force divided by the calibration gravity; this page uses the entered gravity for both.

Formula

B = rho_fluid g V; W = mg; apparent weight = W - B; apparent mass = m - rho_fluid V. Fully immersed object density = m/V. Displacement from liquid rise: V = A delta h.

Worked example

A 10 kg object displacing 0.002 m3 of water experiences 19.6133 N buoyancy at standard gravity. Its true weight is 98.0665 N and apparent weight is 78.4532 N, equivalent to an 8 kg reading.

Advertisement

Frequently asked questions

Can apparent weight be negative?

Yes. It represents a downward holding force when buoyancy exceeds the object weight, rather than a reading on an ordinary hanging scale.

Can I infer density from partial immersion?

The result m/V is the true average object density only when V is the entire object volume. Partly immersed displaced volume is smaller.

Do bubbles matter?

Attached bubbles and trapped air add displacement and can bias an immersion density measurement.

Sources

Advertisement