Calculate the Volume of a Box with Rounded Corners

Calculator of how many milliliters, centiliters, deciliters or liters fit in a rectangular container with rounded corners.

The base of this box is rectangular or square with rounded corners formed by a circle. Mathematically, this is a general cylinder with a rounded rectangle as its base. The diameter of the circle (twice the radius) is measured across a corner where a straight side meets the curve of the circle.

Example: a square round corner box has a side length and width of 8 cm and a height of 10 cm. The diameter of the circle at the corners is 2.5 cm (2 x 1.25). Then 42.5 centiliters fit in there.

Please state length and width (if the base is a square, one value is sufficient), height (or fill level) and circle diameter. The content in milliliters (ml), centiliters (cl), deciliters (dl) and in liters (l) will be calculated.

This jar for spices is 5.5 cm long and 5.5 cm wide, 7.5 cm high and has a circle diameter of 1.5 cm. It has a capacity of 136 milliliters.

Rounding corners on rectangular and cuboid shapes is a very common practice. For larger objects, such as furniture, this can reduce the risk of injury if you bump into them. Often, however, it is just a question of design; round shapes are more pleasing, they look more natural and are sometimes easier to grip.

The rounding here is limited to two dimensions: length and width. Towards the height, however, the edges are straight. Shapes in which all corners and edges are rounded would be much more complicated to calculate and they are not particularly common for containers. Things with a round bottom, for example, tip over easily.