Material Calculator - Calculate Displacement
Calculator for the displaced volume of a floating body (e.g. a ship) and how many percent of the body are above and below the surface. Please enter the density of the floating body or its mass and volume. The approximate density of water is given with 1000 kg/m³, here can be entered a different value for the density at a specific temperature or for a different medium. The density of the floating body must be lower than the density of the medium, otherwise, the body will sink completely.
This calculator is based on Archimedes' principle, which states that the upward buoyant force is equal to the weight of the medium that the body displaces. For a body B, floating in a medium M, applies: VB * ρB = VM * ρM
Below the surface is ρB / ρM * 100%
If the mass is in kilograms (kg), the unit for the volume is cubic meters (m³). If the mass is in grams (g), the unit for the volume is liters (l).
Example: seawater has a density of approximately ρM=1030 kg/m³. An iceberg with a density of ρB=918 kg/m³ is about 11% above the surface.
Archimedes' principle was discovered around the middle of the third century BCE by Archimedes of Syracuse and named after him. Archimedes was commissioned by a king to determine whether his crown was made of pure gold as ordered, or whether cheaper and lighter materials had been mixed in. Of course, the crown should not be destroyed in the process. The idea of how to do this came to Archimedes when he got out of a bathtub. If he puts the crown in a container of water, he can measure how much the water level rises, i.e. how much water is displaced by it. This allows the volume of the crown to be determined. The mass is easy to measure with a balance scale anyway, and the density is derived from both values. If this density matches that of gold, then the crown is made of solid gold. However, Archimedes determined a lower density, which revealed a fraud.