Circle, Sector & Annulus Geometry Calculator
Compute radius, circumference & area, solve arc lengths, chords & circular segments, and model ring annulus cross-sections
Distance from center to perimeter
Enclosed Surface Area & Boundary
78.540 cm²
Exact: 25π cm²
Circumference: 31.416 cm (10π cm)
Circle Radius (r)
5.000 cm
Diameter: 10.000 cm
Linear Circumference (2πr)
31.416 cm
Exact: 10.000π cm
Inscribed Square (Side s)
7.071 cm
Area: 50.000 cm² (r√2)
Circumscribed Square (Side 2r)
10.000 cm
Area: 100.000 cm² (4r²)
Circle radius dimension
0° to 360° subtended arc span
Circular Arc Length & Sector Area
s = 8.378 units • 33.510 units²
Central Angle: 60.00° (1.0472 rad • π/3)
Straight Chord Length (L)
8.000 units
L = 2r · sin(θ / 2)
Circular Segment Area
5.802 units²
Sector Area – Triangle Area
Sagitta / Arch Height (h)
1.072 units
h = r – r · cos(θ / 2)
Apothem / Triangle Base Height
6.928 units
d = r · cos(θ / 2)
External boundary radius
Internal bore radius (r < R)
Cylindrical Extrusion (Optional Pipe Volume)
Axial length of hollow pipe
Annulus Cross-Sectional Surface Area
160.221 units²
Exact: 51.000π units²
Wall Thickness: 3.000 units • Mean Radius: 8.500 units
Wall Radial Thickness (w)
3.000 units
w = R – r
Hollow Solid Material Volume
8,011.06 units³
V = A_annulus · L
Internal Bore Flow Area
153.938 units²
π · r² internal lumen area
Longest Chord Tangent to Inner (L_t)
14.283 units
L_t = 2√(R² – r²) • Area = π(L_t/2)²