Diameter Calculator

Diameter
10
Circle Calculator
Radius
5
Circumference
31.415927
Area
78.539816
Central angle
90
Central angle in degrees
90 deg
Central angle in radians
1.570796 rad
Arc length
7.853982
Chord length
7.071068
Sector area
19.634954
Sector perimeter
17.853982
Circular segment area
7.134954
Sagitta (segment height)
1.464466
Distance from centre to the chord
3.535534
Side of the largest inscribed square
7.071068
Worked out from Weisstein, Eric W. "Circle", "Circular Sector" and "Circular Segment", MathWorld and 2 other sources.

How this is worked out

7 steps
  1. Asked for the diameter: d = 2 r = 10.
  2. Radius from the known circumference: r = 5.
  3. Circumference C = 2*pi*r = 31.41592653589793; area A = pi*r^2 = 78.53981633974483.
  4. Central angle = 90 deg = 1.5707963267948966 rad.
  5. Arc s = r*theta = 5 * 1.5707963267948966 = 7.853981633974483.
  6. Chord = 2 r sin(theta/2) = 7.071067811865475; sector area = r^2*theta/2 = 19.634954084936208.
  7. Segment area = r^2 (theta - sin theta)/2 = 7.134954084936207; sagitta = r(1 - cos(theta/2)) = 1.4644660940672622.

Results are general information, not financial, tax, legal, medical or engineering advice.