Immersed Weight Calculator

Immersed Weight Calculator — fast, accurate results online. Enter your values and get instant answers.

kg
kg/m³
kg/m³

Results

Calculated
Immersed (apparent) weight
—
In N; negative means the object would float
Buoyant force
—
In N, fully submerged
Weight in air
—
In N (m × 9.81)
Object volume
—
In litres (m ÷ density)

What immersed weight is and when to use this calculator

Immersed weight, also called apparent weight in a fluid, is what a scale would read if you suspended an object completely under water or another liquid. It is smaller than the object's weight in air because the fluid pushes upward on it with a buoyant force. This calculator takes the object's mass, its average density and the fluid's density, then reports the immersed weight, the buoyant force, the weight in air and the object's volume.

Engineers and students use it for problems about divers' equipment, submerged pipes and anchors, hydrostatic weighing to find density, and tanks that must support underwater loads. If the object is denser than the fluid the immersed weight is positive and it sinks. If it is less dense the result is negative, which the calculator marks as floating, and the size of that negative number is the downward force needed to hold it under. It assumes the object is fully submerged.

Formula and variables

Archimedes' principle says the buoyant force equals the weight of fluid displaced.

  • Volume: V = m / ρo, where m is mass in kg and ρo is object density in kg/m³.
  • Buoyant force: Fb = ρf × V × g, with ρf the fluid density and g = 9.81 m/s².
  • Weight in air: W = m × g.
  • Immersed weight: Wi = W − Fb = m g (1 − ρf / ρo).

The compact form shows why the density ratio is all that matters: the closer the fluid density is to the object's density, the closer the immersed weight is to zero.

Worked example: a 5 kg aluminium block in fresh water

Take m = 5 kg, ρo = 2700 kg/m³ (aluminium), ρf = 1000 kg/m³ (fresh water).

  • Volume: V = 5 / 2700 = 0.0018519 m³ = 1.852 L.
  • Buoyant force: 1000 × 0.0018519 × 9.81 = 18.17 N.
  • Weight in air: 5 × 9.81 = 49.05 N.
  • Immersed weight: 49.05 − 18.17 = 30.88 N, about 3.15 kgf.

Checking with the compact formula: 49.05 × (1 − 1000/2700) = 49.05 × 0.6296 = 30.88 N, which matches the calculator.

Common mistakes and how to interpret the result

  • Entering weight instead of mass. The mass field is in kilograms, not newtons or pounds.
  • Using the wrong fluid density. Sea water is about 1025 kg/m³, not 1000; salt water increases buoyancy slightly.
  • Using density of the material instead of the whole object. A hollow steel hull or an air-filled container has an average density far below that of solid steel.
  • Ignoring a negative result. A negative immersed weight means it floats; a fully submerged calculation is then only the force needed to hold it down, not its resting state.

Frequently Asked Questions

Why does an object weigh less in water?
Water pressure increases with depth, so the fluid pushes up on the bottom of the object harder than it pushes down on the top. The net upward force equals the weight of the displaced water.
Does shape or depth affect immersed weight?
Not for a fully submerged object in a fluid of uniform density. Only volume and the fluid density matter, so the result is the same at 1 m or 10 m.
What does a negative result mean?
The object is less dense than the fluid, so it would float if released. The magnitude is the extra downward force needed to keep it fully underwater.
Is g fixed at 9.81 m/s²?
Yes. That is a good approximation near Earth's surface; standard gravity is 9.80665 m/s², which changes the results by less than 0.1 percent.

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