Example 1
- α = 90°
- r = 2
3.141593
What is the sector area at 90° and r = 2? 3.141593. A quarter of 4π.
Circle sector area
Type an angle in degrees and a radius. Sector area is a fraction of the disk: (α/360)×πr². 90° and r = 2 give 3.141593. 180° and r = 1 give 1.570796. 360° and r = 1 give 3.141593.
The angle is in degrees. 90° and r = 2 give a quarter of a disk of r = 2, 3.141593. A full 360° at r = 1 is the whole circle area, 3.141593.
Results
Enter data and click Calculate.
How it works
Sector area is a pizza slice of the circle. The calculator computes (α/360)×π×r×r. With 90° and r = 2 you have a quarter of 4π, which is π. The result is 3.141593.
The fields are angle α in degrees and radius r. 180° and r = 1 give half of π, 1.570796. 360° and r = 1 close the whole disk: 3.141593. That is the same πr² as on the circle area card, only here the angle may be tighter.
0° leaves zero. 720° at r = 1 gives two disks, 6.283185. A minus angle gives a minus area.
Arc length takes the same angle and r, but computes the edge. Segment area is another figure. That page also uses degrees. Circle area from r alone is on the neighbouring page.
The header units switch does not multiply anything. 90 and 2 stay 3.141593 whatever the label says.
90° and r = 2 give 3.141593. 180° and r = 1 give 1.570796. 360° and r = 1 give 3.141593.
Formula
P = (α/360) × πr²
How to use
- Type the angle in degrees, for example 90, and the radius, for example 2.
- Click Calculate. Sector area comes out 3.141593.
- 180° and r = 1 give 1.570796. 360° and r = 1 give 3.141593.
- The angle is in degrees. 90 means a quarter disk, not 90 radians.
- Arc length from the same angle lives on the neighbouring card.
90° and r = 2 give 3.141593
Sector area is (α/360)×πr². 90° and r = 2 give 3.141593. 180° and r = 1 give 1.570796. 360° and r = 1 give 3.141593.
- sector
- A fraction of the disk. 90° and r = 2 give 3.141593. 360° closes 3.141593 at r = 1.
- angle
- The first field, in degrees. 180° with r = 1 gives 1.570796.
- radius
- The second field. At r = 2 a quarter disk is 3.141593. At r = 1 the whole disk is 3.141593.
Examples
Example 2
- α = 180°
- r = 1
1.570796
What is the sector area at 180° and r = 1? 1.570796. Half of π.
Example 3
- α = 360°
- r = 1
3.141593
What is the sector area at 360° and r = 1? 3.141593. The whole disk, π.
Related calculators
Common questions
What is the sector area at 90° and r = 2?
3.141593. A quarter of π×4, which is π.
What does sector area mean?
A fraction of the disk. The angle over 360 times πr². 180° is half.
What about 180° and r = 1?
1.570796. Half of π.
What about 360° and r = 1?
3.141593. The whole circle area, πr².
Is the angle in radians?
No. The field takes degrees. 90 means 90°.
Does 0° give zero?
Yes. Zero degrees, zero sector.
How is this different from arc length?
Here the area. There the edge length from 2πr.
How is a sector different from a segment?
A sector is a pizza slice. A segment is cut by a chord. That page also uses degrees.
Where is the area of the whole circle?
On the circle area card. No angle there.
Does a comma in 90.5 work?
Yes. 90.5 and 90,5 are the same angle.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.