Circle Calculator
Enter any one circle value — radius, diameter, circumference, or area — and instantly get all other properties. Includes sector, arc, chord, inscribed shapes, and a live SVG diagram.
5 cm
RADIUS
78.54 cm²
AREA
31.416 cm
CIRCUMFERENCE
| Solve Any Circle
⚠ Enter any ONE value below — radius, diameter, circumference, or area. Leave the others blank; all will be calculated automatically.
Circle Diagram
5 cm
RADIUS R
10 cm
DIAMETER D
31.4159 cm
CIRCUMFERENCE C
78.5398 cm²
AREA A
📐 All Circle Properties
5 cm
RADIUS R
10 cm
DIAMETER D
31.4159 cm
CIRCUMFERENCE C
78.5398 cm²
AREA A
39.2699 cm²
SEMI-CIRCLE AREA
15.708 cm
SEMI-CIRCLE ARC
100 cm²
D² (DIAMETER SQ.)
25 cm²
R² (RADIUS SQ.)
3.1416
C / D = π
3.1416
A / R² = π
7.0711 cm
INSCRIBED SQ. SIDE
50 cm²
INSCRIBED SQ. AREA
8.6603 cm
INSCRIBED △ SIDE
32.476 cm²
INSCRIBED △ AREA
📝 Step-by-Step Derivations
Start: known radius
r = 5 cm
Diameter
d = 2r = 2×5 = 10 cm
Circumference
C = 2πr = 2×π×5 = 31.4159 cm
Area
A = πr² = π×5² = 78.5398 cm²
Back-verification
r = C/(2π) = 31.4159/(2π) = 5 ✓
🍕 Sector & Arc Properties (θ = 90°)
90°
ANGLE θ
1.5708 rad
RADIANS
7.854 cm
ARC LENGTH
19.635 cm²
SECTOR AREA
7.0711 cm
CHORD LENGTH
7.135 cm²
SEGMENT AREA
1.4645 cm
SAGITTA (HEIGHT)
25%
% OF CIRCLE
π (Pi) — The Heart of Every Circle
Every circle calculation uses π ≈ 3.14159265358979… — a transcendental number with infinite, non-repeating decimals. It is the ratio of any circle's circumference to its diameter: C/D = π, always, no matter how big or small the circle is.
π = 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510
58209 74944 59230 78164 06286 20899 86280 34825 34211 70679
82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 …
C/D = π
Circumference ÷ Diameter
A/R² = π
Area ÷ Radius²
π = 4(1-1/3+1/5-1/7…)
Leibniz series
355/113 ≈ π
Accurate to 6 decimal places
Circle Formulas & Properties
A circle is the set of all points equidistant from a center point — that distance is the radius, r. All four fundamental circle measurements — radius, diameter, circumference, and area — can be derived from any single one of them, because they’re all tied together through the constant π. Know any ONE value and this calculator reconstructs the rest instantly, along with sector, arc, and inscribed-shape properties for the same circle.
All Circle Formulas
From radius r: Diameter d = 2r · Circumference C = 2πr · Area A = πr²From diameter d: r = d/2, then use the radius formulas aboveFrom circumference C: r = C/(2π), A = C²/(4π)From area A: r = √(A/π), then use the radius formulas aboveSector (angle θ in degrees): Arc length L = (θ/360) × 2πr · Sector area A_s = (θ/360) × πr²Chord length c = 2r·sin(θ/2) · Inscribed square side s = r√2 · Inscribed equilateral △ side s = r√3Why this matters: because every property is derivable from any other, you never need to know a circle’s radius directly to work with it. A tape measure around a pipe gives circumference; a caliper across it gives diameter; a flow-area calculation needs area — this calculator converts freely between all of them so you only ever need to measure whichever one is easiest to reach.
— FAQ