Spike's Calculators

Circular Segment

Calculate the area and perimeter of a circular segment. This calculator uses feet and or inches for measurements.

Chord = a straight line connecting two points on the circumference of a circle.
Arc = the section of the circle's circumference from where the two points of a chord intersect the circle's circumference.

Circular Segment = the area between the chord and the arc.

Note:
the segment height has to be smaller or equal to the the radius of the circle it is part off.

Circular Segment Area and Perimeter

Length of Chord ft in n
d
Segment Height ft in n
d
Decimal Precision

Results:

Angle °
Area of the Segment
Decimal Square Feet ft²
Square Feet ft² in²
Decimal Square Inches in²
Square Inches in²
Square Metres
Perimeter of the Segment
Decimal Feet ft
Feet ft in
Decimal Inches in
Inches in
Metres m
Arc Length
Decimal Feet ft
Feet ft in
Decimal Inches in
Inches in
Metres m

Calculation

1. the chord length in feet and or inches
2. the height of the segment in feet and or inches
3. decimal precision, the number of digits after the decimal point

Results

1. the length of the radius in decimal feet
2. the angle a in degrees
3. the area of the circular segment in decimal square feet
4. area in square feet and inches
5. the area in decimal square inches
6. the area in square inches
7. the area in square metres
8. the perimeter (circumference) of the circular segment in decimal feet
9. the perimeter in lineal feet and inches
10. the perimeter in decimal inches
11. the perimeter in inches
12. the perimeter in metres
13. the arc length in decimal feet
14. the arc length in lineal feet and inches
15. the arc length in decimal inches
16. the arc length in inches
17. the arc length in metres

Formula
r = h/2+c²/(h*8)
a =  cos ((2r² - c²) / 2r² )
arc = a(π/180)r
A = r * arc / 2 - s * ( r - h ) / 2
P = arc+ c
h is the segment height
c is the chord length
a is the angle in degrees
arc is the length of the arc
π = 3.14159265358979
A is the area of the segment
P = the circumference of the segment

Conversions
one square foot ( ft²) = 144 square inches (in²)
one square inch (in²) = 0.00694444444444443 square feet (ft²)
one square foot ( ft²) = 0.09290304 square metres (m²)
square inch (in²) = 0.00064516 square metres (m²)