Circle
Arc, segment, sector
Torus
Circle
▲
* Input a value in any field
Radius (R)
Diameter (D)
Circumference (P)
Area (A)
Arc, Segment, Sector Calculator
▲
* Input 2 values in any unmarked fields
Radius (r)
Central angle (θ)
Arc length (L)
Sector area
Sector circumference
Segment area
Segment circumference
Triangle base (c)
Segment height (h)
Triangle height (t)
Input limit:
Input limit:
Torus
▲
* Input 2 values in any unmarked field
Outer radius (R)
Inner radius (r)
Ring radius (a)
Mean radius (c)
Torus volume (V)
Torus surface Area (S)
Input limit:
S = 4π
2
a c = π
2
(R + r)(R − r) = π
2
(R
2
− r
2
)
R = c + a r = c − a
Example 1 - segment area
▲
Find the expression for the area of a segment defined by the radius r and the segment height h.
The area of a sector whose angle equals to θ is:
(θ in radians)
The area of the triangle formed by the two radii and
the cord c is:
The value of t is:
t = r - h
The value of c using the Pythagoras theorem is:
θ is:
Now the area of the segment is:
And after substituting the value of θ we get the final value:
Notice that when r = h
(
segment is half circle
)
A
segment
= r
2
cos
-1
0 =
r
2
π / 2 this is half circle area.