Calculate a Circle Sector

Calculator for the circumference and size of a pie slice of a circle, with different units. A circle sector or circular sector is a not completely drawn through circle. Such a field as cultivated area is often found in agriculture, where center pivot irrigation faces an obstacle, can't rotate full and has to go back.
Please enter circle radius and pie angle and choose the units. Arc length, circumference and area will be calculated. For the units, the metric units as well as inches, feet, yards, miles and acres can be selected.

Radius:		cmdmmkminftydmi
Angle:		°rad*π
Arc length:		cmdmmkminftydmi
Circumference:		cmdmmkminftydmi
Area:		cm²dm²m²km²ahasq insq ftsq ydacsq mi

Units of measurement: cm=centimeter, dm=decimeter, m=meter, km=kilometer, in=inch, ft=foot, yd=yard, mi=mile, ²,sq=square, a=are, ha=hectare, ac=acre

Angle: °=degrees, rad=radian, *π=multiples of pi

Formulas:

Radius r, angle α
Arc length l = 2rπ * α/360°
Circumference u = l+2r
Area A = r²π * α/360°

A pie or circle sector shaped field.

Example: with a radius of 50 meters and an angle of 240 degrees, which roughly corresponds to the angle in the image above, the length of the arc would be just over 209 meters. The combination of the arc length and the two straight lines would of course be exactly 100 meters longer (plus twice the radius) at just over 309 meters. The area covered would be just over half a hectare.

The pivot irrigation system was invented in Iowa in 1914 and is also often used in the USA. But there are also huge fields in the Egyptian desert, for example, which are automatically irrigated in this way. The individual fields there have radii of over 400 meters. With a radius of 400 meters, just over 50 hectares can be irrigated in a full circle. The pivot irrigation method is labor-saving and effective, but it is often very detrimental to the groundwater.

Last updated on 06/27/2025. Author: Jürgen Kummer

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