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Properties of a Circular segment

This tool calculates the basic geometric properties of a circular segment. Enter below the circle radius R and either one of: central angle φ or height h or distance d. Note, that the angle φ can be greater than 180° which represents a segment bigger than the semicircle. In that case distance d is negative and height h is bigger than R. The calculated results will have the same units as your input. Please use consistent units for any input.

R =
φ =		deg rad
...or
h =
...or
d =
Geometric properties:
φ (rad) =
h =
d =
Area =
Perimeter =
Arc length =
Chord length =
dc =

Definitions

Geometry

For a circular segment the definitions shown in the following figure are used:

For a circular segment with radius R and central angle φ, the chord length L_AB and its distance d from centre, can be found from the right triangle that occupies half of the region defined by the central angle (see next figure):

The height h of the circular segment h and its arc length L are found easily:

The area A and the perimeter P of a circular segment, can be found with these formulas:

where L the arc length and L_AB the chord length.

The centroid (center of gravity) of the circular segment is located along the bisector of the central angle φ, and at a distances from the chord equal to:

where d the distance of the chord from the centre.