Example 1
- r = 2
- α = 90°
1.141593 · chord 2.828427 · sagitta 0.585786
How much is the circle segment at r = 2 and 90°? The angle is in degrees.
Circle segment calculator
Enter a radius and an angle in degrees. The calculator finds the segment between the chord and the arc: area, chord length, and sagitta. At r = 2 and 90° the area is 1.141593, the chord is 2.828427, and the sagitta is 0.585786.
The angle is in degrees. This is not a sector. Sector area from the same angle is on the neighboring page.
Results
Enter data and click Calculate.
How it works
A circle segment is the region between a chord and an arc. From the same radius and angle the calculator reports the area, the chord, the sagitta, and the arc. The angle is in degrees, so 90 means 90°.
The area is r²/2 × (α·π/180 − sin(α·π/180)). The chord is 2r sin(α·π/360). The sagitta is r(1 − cos(α·π/360)). The arc is r × α·π/180.
At r = 2 and 90° the area is 1.141593, the chord is 2.828427, the sagitta is 0.585786, and the arc is 3.141593.
At r = 1 and 180° the area is 1.570796, the chord is 2, and the sagitta is 1. At r = 2 and 60° the area is 0.362344, the chord is 2, and the sagitta is 0.267949.
This is not a sector. Sector area from the same angle is on the neighboring page. The area of the whole circle from the radius alone is next door.
The numbers do not depend on the header unit switch. With radius 2 and 90° the area stays 1.141593. The labels follow the length unit in the header.
Formula
A = r²/2 × (α·π/180 − sin(α·π/180)). Chord c = 2r sin(α·π/360). Sagitta h = r(1 − cos(α·π/360)). Arc L = r × α·π/180. α in degrees.
90° and r = 2 give area 1.141593
The same inputs also give chord 2.828427 and sagitta 0.585786.
- segment
- The region between a chord and an arc. This is not a sector.
- chord
- The straight line that cuts the disk. At r = 2 and 90° it is 2.828427.
- sagitta
- The height from the midpoint of the chord to the arc. At r = 2 and 90° it is 0.585786.
- degrees
- The unit of the angle. 90 means 90°.
How to use
- Enter the radius, for example 2, and the angle in degrees, for example 90.
- Click Calculate. The area is 1.141593, the chord is 2.828427, and the sagitta is 0.585786.
- At r = 1 and 180° the area is 1.570796, the chord is 2, and the sagitta is 1.
- The angle is in degrees. 90 means 90°, not 90 radians.
- Sector area from the same angle is on the neighboring page.
Examples
Example 2
- r = 1
- α = 180°
1.570796 · chord 2 · sagitta 1
How much is the circle segment at r = 1 and 180°? A semicircle minus the triangle on the diameter.
Example 3
- r = 2
- α = 60°
0.362344 · chord 2 · sagitta 0.267949
How much is the circle segment at r = 2 and 60°? A common school angle.
Related calculators
Common questions
What is the circle segment at r = 2 and 90°?
The area is 1.141593. The chord is 2.828427. The sagitta is 0.585786. The arc is 3.141593.
Does the calculator also give the chord and the sagitta?
Yes. From the same radius and angle it reports the area, the chord, the sagitta, and the arc.
What does the area of a segment of a circle mean?
The region between a chord and an arc. This is not a sector. A sector has two radii.
Is the angle in radians?
No. The angle is entered in degrees. 90 means 90°.
What about r = 1 and 180°?
1.570796. That is π/2, a semicircle minus the triangle on the diameter.
What about r = 2 and 60°?
0.362344. 60° as in a school problem.
How is a segment different from a sector?
A sector has two radii and an arc. A segment is cut by a chord. That page also uses degrees.
Does 0° give zero?
Yes. At 0° the result is zero.
Where is the area of the whole circle?
On the circle area page. No angle there.
Does a comma in 90.5 work?
Yes. 90.5 and 90,5 are the same angle.
What if I type 1 as I used to in radians?
The calculator uses 1°, not 1 rad. At 60° and r = 2 the result is 0.362344.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.