Immersed Weight Calculator - Apparent Weight in Fluids

An immersed weight calculator finds the apparent weight of an object once it is fully or partially submerged in a fluid. Pick a fluid, enter the object's mass and volume, and the calculator subtracts the buoyant force from the dry weight so you can read the net downward force in newtons, the verdict on whether the object will sink or float, and a parallel buoyant-force value for a hand check. The same calculator rearranges the formula when you need to solve for mass, displaced volume, fluid density, or local gravity from a known immersed weight.

• • Physics homework and labs: Check Archimedes-principle problems for steel blocks, wooden blocks, glass marbles, and submerged pendulums without re-deriving the algebra.
• • Scuba, free-diving, and snorkeling checks: Estimate the apparent weight of a diver, lead belt, or dive cylinder to plan weighting, or judge when a small object will hover in the water column.
• • Boat, pontoon, and float design: Back-solve the volume that a hull or float must displace to support a known load in fresh or salt water.

Buoyancy is what makes ships float, divers bob, and hot-air balloons rise. The immersed weight is the same physical force your bathroom scale would read if you stood on it underwater - usually much less than your dry weight, and sometimes negative, which means the buoyant force is bigger than the weight and the object needs to be tied down to stay submerged.

When the dry mass and the volume are not directly given, the same calculator is the right companion to a quick density calculator so you can convert a stated material density into the volume the immersed-weight formula needs.

The calculator evaluates Archimedes' principle in its SI form and rearranges it for the variable you selected in the Solve For menu. Standard gravity g is fixed at 9.80665 m/s^2 with an editable field for planetary comparisons.

• m: Mass of the object in kilograms (kg).
• rho: Mass density of the surrounding fluid in kilograms per cubic metre (kg/m^3).
• V: Volume of the submerged part of the object in cubic metres (m^3).
• g: Local gravitational acceleration in metres per second squared (m/s^2). Default 9.80665 m/s^2 is the NIST standard value.
• W_immersed: Resulting apparent weight in newtons (N). Positive = sinks, negative = floats (net upward force).

All five Solve For choices use the same physical relationship; the calculator simply inverts the equation for the variable you need. The dry weight, buoyant force, and net force verdict are reported in parallel so the result can be cross-checked by hand against rho * V * g and m * g.

According to Wikipedia (Buoyancy), the buoyant force on a body immersed in a fluid is equal to the weight of the fluid the body displaces and is given by B = rho * V * g, so the immersed weight is the dry weight minus that buoyant force.

If the object volume is given in cubic centimetres, litres, or gallons, the same fluid inputs can be passed through a quick volume calculator to convert the number to cubic metres before the immersed weight formula is evaluated.

Four ideas behind the immersed weight calculator that are worth understanding before you trust the numbers.

These four ideas show up in every buoyancy problem and in fluid-flow problems (Bernoulli's equation) and in straight-line motion problems, so the rest of the physics calculators on this site pick up the same vocabulary in a different form.

These four ideas show up in every buoyancy problem and are the same vocabulary the buoyancy calculator uses to solve for the buoyant force, displaced volume, or fluid density directly.

Use the immersed weight calculator in five steps.

1. 1 Pick the unknown: Open the Solve For menu and choose Immersed weight, Object mass, Object volume, Fluid density, or Gravity. The default Immersed weight is the most common case.
2. 2 Choose a fluid preset or Custom: Pick any preset to load a reference density, or pick Custom and enter your own density in the rho field.
3. 3 Enter the remaining inputs: Fill in the other fields needed for the chosen Solve For target. For Immersed weight you need mass, volume, and gravity.
4. 4 Optionally override gravity: The Gravity field defaults to 9.80665 m/s^2. Type 1.62 for the Moon, 3.71 for Mars, or 24.79 for Jupiter.
5. 5 Read the solved value and the secondary outputs: The Solved Variable panel shows the value of whichever variable you picked, while Dry Weight, Buoyant Force, and Net Force Direction give an independent cross-check.

A 5 kg piece of foam has a dry weight of about 49 N on Earth. Pick Fresh water, set Solve For to Object volume, enter 0 for the immersed weight, and the calculator returns about 0.005 m^3, which is roughly the 5 litre volume you would expect for a foam cube of density 1000 kg/m^3 that floats at the surface.

For a quick sanity check that the buoyant force the calculator reports matches a direct solve, the buoyant force calculator gives the same B = rho * V * g number from the same inputs without going through the dry weight first.

Practical reasons to use this immersed weight calculator instead of doing the algebra by hand.

• • One tool for five unknowns: Switch the Solve For menu to rearrange the same equation for immersed weight, object mass, displaced volume, fluid density, or local gravity.
• • Fourteen fluid presets save lookups: The preset list covers fresh water, sea water, mercury, gasoline, vegetable oil, baby oil, ethanol, corn syrup, milk, dish soap, rubbing alcohol, maple syrup, and honey.
• • Auditable secondary outputs: Dry weight, buoyant force, and net force verdict are reported in parallel with the primary answer for a one-line hand check against rho * V * g and m * g.
• • Sink or float verdict in plain words: The Net Force Direction row labels the result Sinks, Floats, or Neutral so you can read the answer without translating the sign of the newton value yourself.
• • Standard gravity with planetary override: The gravity field defaults to 9.80665 m/s^2 and accepts lower values for the Moon, Mars, or any other surface.

When the immersed weight turns into a moving-fluid or a fall-rate problem, the next stage of the calculation is one click away through the related calculators on this site.

When the immersed weight turns into a moving-fluid or a fall-rate problem, the same time and acceleration values feed the kinematics motion calculator so the next stage of the calculation is one click away.

What changes the answer the immersed weight calculator returns, and what it cannot capture.

• • The calculator assumes a single uniform fluid density and does not model a stratified ocean with a sharp halocline or thermocline.
• • Archimedes' principle applies to a static or quasi-static fluid. For a fast-moving object the calculator does not include added-mass or drag effects.
• • The fluid preset densities are reference values for typical conditions. Real fluids shift by 1 to 5 percent with temperature and pressure changes.

When the immersed weight is then used to estimate the work needed to lift the object out of the fluid, the resulting force times distance can be passed straight into a work and energy solver for a joules result.

For spring-scale problems, the same volume and dry-mass inputs are reused and only the Solve For menu is changed.

According to Engineering Toolbox, fresh water reaches its highest density of 1000 kg/m^3 at 4 deg C, with sea water denser still and mercury roughly 13.5 times denser than fresh water, which is why the same object can sink in one fluid and float in another.

According to NIST Special Publication 330, the conventional standard value of Earth-surface gravitational acceleration adopted for calculations is 9.80665 m/s^2, which is the default used here.

When the immersed weight is then used to estimate the work needed to lift the object out of the fluid, the resulting force times distance can be passed straight into the work energy power calculator for a joules result.