Calculate Liters in a Plate

Calculator how many liters fit in a (soup) plate of a certain size or how much is in the plate at a certain fill level.

Mathematically, a soup plate is approximately a spherical segment. The size of the plate is precisely determined by specifying the diameters at the bottom and top as well as the height, the volume is πh / 6 * ( 3/4 * D² + 3/4 * d² + h² ) with the height h, the lower diameter d and the upper diameter D. The lengths must be measured inside the plate if the plate wall has a notable thickness.


Example: a soup plate with a base diameter of 15 cm, an opening of 25 cm and a height of 5 cm has a maximum content of almost one and three quarters of a liter when it is filled to the brim.

Please enter both diameters and the height of the plate. The volume will be calculated.

Bottom diameter:cm
Mouth diameter:cm

If the diameter at the bottom is 0, then the plate is a bowl.


Half full plate

Example of a partially filled soup plate: the plate above is filled to half the height. It contains 0.67 liters, the filling width is 21.2 centimeters.

Please enter both diameters, the height and the filling level of the plate. Volume, fill width and filled fraction will be calculated.

Bottom diameter:cm
Mouth diameter:cm
Filling level:cm
Filling width:cm
Filled fraction:%

The filling width is the diameter of the plate at the fill level. The calculation is complicated. First the radius of the underlying sphere is calculated, then the missing length from the center of the bottom of the plate to the spherical shell. From this, the filling width can be determined using the formula for the circular layer, from which with the level height the new volume results.

Soup plate

This soup plate has an opening of 22 cm, a base diameter of 13 cm and a height of 4 cm, so it holds a bit more than 1 liter of water. If it is filled up to 3 cm, it contains 0.7 liters of water and is 66.5% full.

Here you can convert metric volume units into customary and imperial units.

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