Immersed Weight Calculator
Enter your object's weight and volume, choose a fluid, and this calculator instantly returns the immersed weight (the apparent weight underwater) and the buoyant force lifting the object. It covers 12 preset fluids from gasoline to mercury, supports a custom fluid density, and shows a full step-by-step breakdown of the Archimedes principle math. Switch between metric (kg, m^3) and imperial (lb, ft^3) units at the top.
What is immersed weight?
Immersed weight (sometimes called apparent weight or submerged weight) is how heavy an object feels when it is fully or partially submerged in a fluid. It is always less than the dry weight because the fluid pushes back with an upward buoyant force. If the buoyant force exceeds the object's weight, the immersed weight becomes negative, which means the object floats. The concept is central to naval architecture, hydrostatics, fluid-density measurement, and many everyday experiments.
Archimedes' principle and the formula
Archimedes of Syracuse discovered around 250 BC that a submerged object displaces a volume of fluid equal to its own submerged volume, and the fluid exerts an upward force exactly equal to the weight of that displaced fluid. In modern notation: Buoyant force = fluid density x submerged volume Immersed weight = object weight (in air) - buoyant force Where both the object weight and the buoyant force are expressed in the same units (kg or lb in the weight convention used here, or equivalently newtons when using SI force units). A fully submerged object displaces its entire volume; a partially submerged object displaces only the fraction that is below the surface.
Floats vs. sinks: the density rule
An object floats when its average density is lower than the fluid density, and sinks when it is higher. At equal densities the object is neutrally buoyant, hovering motionless at any depth. Submarines and fish use this by adjusting their effective volume (ballast tanks or swim bladders) to change their average density relative to water. This calculator shows the density ratio automatically: if the object density is below the fluid density, the immersed weight will be zero or negative, confirming flotation.
Practical uses of immersed weight calculations
Naval architects use immersed weight to determine how much cargo a vessel can carry before it sits too deep in the water. Gemologists use it to identify minerals by comparing dry weight with submerged weight to find specific gravity. Laboratory scientists use it when calibrating scales and measuring the density of irregular objects that cannot be measured geometrically. Divers and the sport of underwater weigh-in (underwater weighing for body composition) both rely on the same principle. Even the hydrometer, a simple instrument for measuring wine or battery acid concentration, is just a calibrated float whose immersed depth encodes the fluid density.
Common fluid densities
| Fluid | Density (kg/m³) | Density (lb/ft³) | Notes |
|---|---|---|---|
| Gasoline | 700 | 43.7 | Varies with blend and temperature |
| Rubbing alcohol | 786 | 49.1 | 70% isopropanol solution |
| Baby oil | 830 | 51.8 | Mineral oil based |
| Vegetable oil | 920 | 57.4 | Average cooking oil |
| Fresh water | 1000 | 62.4 | Pure water at 4 degrees C |
| Sea water | 1025 | 64 | Average ocean salinity ~3.5% |
| Milk | 1030 | 64.3 | Whole milk (3.5% fat) |
| Dish soap | 1060 | 66.2 | Typical liquid detergent |
| Maple syrup | 1320 | 82.4 | Grade A dark amber |
| Corn syrup | 1380 | 86.2 | Light corn syrup |
| Honey | 1420 | 88.7 | Average floral honey |
| Mercury | 13600 | 849 | Liquid metal at room temperature |
Reference densities used in the preset fluid list. Values at approximately 20 degrees C.
Frequently asked questions
Why does an object weigh less underwater?
Water (or any fluid) exerts pressure on all sides of a submerged object. Because pressure increases with depth, the pressure on the bottom face of the object is greater than on the top face. This net upward pressure difference produces the buoyant force, which is exactly equal to the weight of the fluid displaced. That upward force partially cancels the downward pull of gravity, so the object appears lighter.
What does a negative immersed weight mean?
A negative immersed weight means the buoyant force exceeds the object's dry weight. In practice, the object floats: you would need to push it down to keep it submerged. The magnitude of the negative value tells you how much downward force (ballast) you would need to add to hold it fully under. For example, an immersed weight of -0.5 kg means you need to attach at least 0.5 kg of ballast.
Does the shape of the object affect the result?
Shape does not matter - only the total submerged volume does. A solid steel cube and a hollow steel ball of identical volume displace exactly the same amount of fluid and therefore experience the same buoyant force. Shape affects drag and how the object moves through the fluid, but not the static buoyant force.
How do I use this calculator for a floating object?
Set the submerged fraction to reflect how much of the object is below the surface. A raft floating half-submerged would use 0.5. Alternatively, enter the full volume and reduce the fraction until the immersed weight reaches zero - that is the equilibrium draft. If your object floats completely (density well below the fluid), you can use ballast to keep it submerged: add extra weight until the combined dry weight exceeds the buoyant force for the combined volume.
What units does this calculator use?
In metric mode the calculator works in kilograms (weight) and cubic metres (volume), reporting buoyancy also in kilograms (weight-equivalent, not newtons). To convert to newtons, multiply by 9.80665. In imperial mode it uses pounds and cubic feet. Fluid densities are shown in kg/m^3 for metric and lb/ft^3 for imperial.