Math
Square pyramid
Find volume, slant height and surface area of a right square pyramid.
Calculators / Math / Circular segment area
Circular segment area calculator
Calculate the area between a chord and its circle arc.
On this page
Segment area7.13units²
Arc length7.85units
Chord length7.07units
Calculator controls
How to calculate
Calculate the area between a chord and its circle arc.
Segment area = r^2*(a*pi/180-sin(a*pi/180))/2 units²; Arc length = r*a*pi/180 units; Chord length = 2*r*sin(a*pi/360) units
Worked example
Circle radius: 5; Central angle (degrees): 90.
Segment area: 7.13 units²; Arc length: 7.85 units; Chord length: 7.07 units.
Assumptions and limits
Angles above 180 degrees describe the major segment. At 0 or 360 degrees the chord is degenerate. Use a single length unit.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Calculate the area between a chord and its circle arc.
When this tool is useful
Segment area = r^2*(a*pi/180-sin(a*pi/180))/2 units²; Arc length = r*a*pi/180 units; Chord length = 2*r*sin(a*pi/360) units
Understanding your inputs
| Input | What to enter |
|---|---|
| Circle radius | Enter a number of at least 1e-12 and no more than 1000000000000. |
| Central angle (degrees) | Enter a number of at least 0 and no more than 360. |
Frequently asked questions
What assumptions does this calculation use?
Angles above 180 degrees describe the major segment. At 0 or 360 degrees the chord is degenerate. Use a single length unit.
How is the result calculated?
Segment area = r^2*(a*pi/180-sin(a*pi/180))/2 units²; Arc length = r*a*pi/180 units; Chord length = 2*r*sin(a*pi/360) units