Circular segment (arch)
Area and perimeter, with the formula worked through and a drawing to scale.
Result
- Area
- 7.135 sq ft
- = 7.135 sq ft · 0.662859 m²
- Perimeter
- 14.925 ft
- = 14.925 ft · 4.5492 m
- Chord (span)
- 7.0711 ft
- Rise (height of the arch)
- 1.4645 ft
- Arc length
- 7.854 ft
The working
Area: A = ½ r² (θ − sin θ), θ in radians
Perimeter: P = r θ + 2 r sin(θ/2)
θ = 90° = 1.5708 radians A = ½ × 5² × (1.5708 − sin θ) = 7.135 P = arc + chord = 7.854 + 7.0711 = 14.925
Values in feet; areas in sq ft.
About the circular segment (arch)
The part of a circle cut off by a straight line — the shape of an arched door head above the springing line.
Every formula on this site is explained step by step in Learn: area and perimeter.
Other shapes
Square Rectangle Parallelogram Rhombus Trapezoid (trapezium) Kite Triangle — three sides Triangle — base and height Right triangle Isosceles triangle Equilateral triangle Triangle — two sides and the angle between Circle Semicircle Quarter circle Sector (pie slice) Ring (annulus) Ellipse (oval) Regular polygon (pentagon, hexagon, octagon…) L-shape Any polygon — by corner points