Calculate Liters in a Measuring Cup

Calculator how many liters are in a measuring cup with an elliptical base of a certain size and fill level.

In simplified mathematical terms, a measuring cup is an truncated elliptic cone. The base at the bottom is approximately an ellipse, the opening is a larger ellipse with the same ratio of diameters. This also applies to every straight cross-section. The lengths must be measured inside the measuring cup. The formula for the maximum content is π/2 * ( ab + cd ) * h, with height h, lower semi-axes a, b and upper semi-axes c, d. The long semi-axis at the level is calculated with a + ( c - a ) * i/h, with the fill level i. Short semi-axis analogous.

Measuring Cup sketch

Example: a measuring cup is 10 cm high. The diameters at the bottom are 8 and 7 cm, at the opening they are 9 and 7.875 cm. Completely filled (fill level 10 cm), almost half a liter fits into the measuring cup. If it is filled to 6 cm, then it holds 0.284 liters.

Please enter three diameters and the filling height. Fourth diameter and content will be calculated.

Large diameter bottom:cm
Small diameter bottom:cm
Large diameter top:cm
Small diameter top:cm
Fill level:cm

Filled measuring cup

This measuring cup has a height of 14.5 cm, the bottom diameters are 10.5 and 7.5 cm, the top diameters are 12.5 and 9.5 cm. So the ellipses above and below are not in the same proportion, and the bottom is not an exact ellipse. It holds exactly one liter at the upper filling line at a height of 13 cm, the content of the calculated measuring cup is 0.985 liters. When filled to 8.3 cm then it shows 600 ml (0.6 l) and calculates as 585 ml.
Considering that the lengths were determined by hand with the usual measurement errors and the cup is not a perfect elliptical truncated cone, the calculated values match the actual ones very well.

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

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