Circle Calculator
Calculate circle area, circumference, diameter, and radius from any known measurement. Includes sector area, arc length, circle SVG diagram, standard and general equation forms, and tangent line calculations.
Quick Calculator Get a fast estimate
units
Area
78.539816 sq units
Circumference
31.415927 units
Radius
5.000000 units
Diameter
10.000000 units
Area in π
25.0000π sq units
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How to Use the Circle Calculator
Select your known measurement (radius, diameter, circumference, or area) and enter the value. All other measurements are calculated instantly using π = 3.14159265...
The Extended Calculator adds sector area, arc length, and a circle SVG diagram. The Professional Calculator converts between standard and general equation forms and calculates tangent line lengths.
Need more detail?
Extended Calculator More options, charts, and scenario comparison
units
Circle Area
78.5398 sq units
Circumference
31.4159 units
Diameter
10 units
Area in π
25π
Circ in π
10π
Circle Formulas
Area: A = πr²
Circumference: C = 2πr = πd
Diameter: d = 2r
Sector area: A = (θ/360°) × πr²
Arc length: L = (θ/360°) × 2πr = rθ (θ in radians)
Standard equation: (x−h)² + (y−k)² = r²
General equation: x² + y² + Dx + Ey + F = 0
Circle Measurement Conversions
| Known | Radius | Area | Circumference |
|---|---|---|---|
| Radius r | r | πr² | 2πr |
| Diameter d | d/2 | πd²/4 | πd |
| Area A | √(A/π) | A | 2√(πA) |
| Circumference C | C/(2π) | C²/(4π) | C |
Need full precision?
Professional Calculator Complete parameters, sensitivity analysis, and detailed breakdown
Circle: centre (h, k), radius r
Standard Form
(x − 3)² + (y − 4)² = 25
General Form
x² + y² -6x -8y + 0 = 0
Centre
(3, 4)
Radius
5
Area
78.5398 sq units
Circumference
31.4159 units
D = −2h
-6
E = −2k
-8
F = h²+k²−r²
0
Frequently Asked Questions
Area = πr². If you know the diameter, r = d/2 so Area = π(d/2)² = πd²/4. Example: diameter 10 → r=5 → Area = π×25 ≈ 78.54.
Circumference = 2πr = πd. The number π ≈ 3.14159. For a circle with diameter 1 metre, the circumference is exactly π metres ≈ 3.14159 metres.
Sector area = (θ/360°) × πr². A sector is a "pie slice" portion of a circle. A 180° sector is a semicircle with area πr²/2.
Arc length L = (θ/360°)×2πr. In radians: L = rθ. Example: 90° arc (π/2 radians) with r=10 → L = 10×(π/2) ≈ 15.71 units.
(x−h)²+(y−k)²=r² where (h,k) is the centre. Example: centre (3,4), radius 5 → (x−3)²+(y−4)²=25. In general form: x²+y²−6x−8y=0.