Circle Segment Calculator

A circular segment is the piece of a circle you get when you slice it with a straight line, leaving the curved cap between the chord and the arc. It is a shape that turns up in a surprising number of real problems: the cross-section of liquid in a horizontal cylindrical tank, an arched window or doorway, a curved retaining wall, a bridge arch, a part-filled pipe, or any design that uses a circular arc. This calculator works out the four measurements people most often need from just the radius and the central angle: the area of the segment, the length of the chord that cuts it off, the length of the arc above it, and the height, also called the sagitta, which is the depth from the chord up to the top of the arc. Those last two are especially handy in practice. The arc length tells you how much edging or material follows the curve, while the height is exactly what you measure as the depth of fluid in a round tank lying on its side, which makes this tool useful for working out tank contents. Enter the radius and the angle in degrees and every result updates instantly, so you can size an arch to fit an opening, or find the angle that gives a particular fill depth by adjusting the inputs. It saves you from the awkward trigonometry of converting to radians and combining sines and cosines, which is easy to slip up on by hand. The exact formulas, the conversion from degrees to radians, and a clear worked example are set out below so you can follow the method and trust the numbers.

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