Calculate Liters in a Bowl

Calculator how many liters fit in a round bowl of a certain size.

Mathematically, a bowl is a spherical cap, a cut-off part of a sphere. The size of the bowl is precisely determined by specifying the inner width (diameter) and height. The height may not exceed half the diameter. If the height is exactly half the diameter, then the bowl is a hemisphere.

Most bowls are flattened at the bottom to keep them from wobbling. If the flat is only on the outside, then the following calculation applies. However, if the flattening is on the inside and not straight, like at the plate, then the value calculated here is too low, and an exact calculation would then be much more complicated.

Bowl 30 cm diameter, 10 cm height

Example: a bowl with a diameter of 30 cm and a height of 10 cm has a volume of a bir more than 4 liters.

Please enter the diameter and height of the bowl, the volume and diameter of the underlying sphere will be calculated. If the bowl is only partially filled, enter the filling width for the diameter and the filling height for the height.

Sphere diameter:cm

The formulas are:
Height in cm: h
Bowl radius in cm: a = diameter / 2
Sphere radius in cm: r = ( a² / h + h ) / 2
Volume in liters = h² * π / 3 * ( 3 * r - h ) / 1000

Wooden bowl

This wooden bowl has an inner diameter of 17 cm and an inner height of 5 cm, so it holds a bit more than 0.6 liters. The bowl is flat on the outside of the bottom so that it stands stable.

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

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