Circle Calculator
Calculate circle properties including radius, diameter, circumference, area, arc length, and sector area. Enter any value and get all other measurements.
A = πr² | C = 2πrCircle Properties
Area
78.5398 cm²
Circle Input
Circle Properties
Radius (r)
5.0000 cm
Half the diameter
Diameter (d)
10.0000 cm
d = 2r
Circumference (C)
31.4159 cm
C = 2πr ≈ 6.283r
Area (A)
78.5398 cm²
A = πr² ≈ 3.14r²
Arc & Sector
Arc Length
7.8540 cm
(25.0% of circumference)
Sector Area
19.6350 cm²
(25.0% of total area)
Quick Reference
| Angle | Fraction | Arc Length | Sector Area |
|---|---|---|---|
| 30° | 1/12 | 2.618 cm | 6.545 cm² |
| 45° | 1/8 | 3.927 cm | 9.817 cm² |
| 60° | 1/6 | 5.236 cm | 13.090 cm² |
| 90° | 1/4 | 7.854 cm | 19.635 cm² |
| 120° | 1/3 | 10.472 cm | 26.180 cm² |
| 180° | 1/2 | 15.708 cm | 39.270 cm² |
| 270° | 3/4 | 23.562 cm | 58.905 cm² |
| 360° | 1 (full) | 31.416 cm | 78.540 cm² |
Circle Formulas
Basic Formulas
- Diameter: d = 2r
- Circumference: C = 2πr = πd
- Area: A = πr²
Derived Values
- r from C: r = C / (2π)
- r from A: r = √(A / π)
- Arc: L = (θ/360) × 2πr
- Sector: S = (θ/360) × πr²
π (Pi) ≈ 3.14159265358979... is the ratio of a circle's circumference to its diameter.
Circle Properties
Area
78.5398 cm²
?How to Calculate Circle Properties
Circle formulas: Circumference = 2 x pi x radius = pi x diameter. Area = pi x radius squared. Diameter = 2 x radius. From any measurement, you can calculate all others. Pi (approximately 3.14159) is the ratio of circumference to diameter for all circles.
What is a Circle?
A circle is a perfectly round shape where every point on its edge is the same distance (radius) from the center. Key measurements include radius (center to edge), diameter (edge to edge through center), circumference (perimeter), and area (space enclosed). All these measurements are mathematically related through the constant pi.
Key Facts About Circles
- Circumference = 2 x pi x r = pi x d (approximately 3.14159 x diameter)
- Area = pi x r squared (where r is the radius)
- Diameter = 2 x radius; radius = diameter / 2
- Pi (3.14159...) is the ratio of circumference to diameter
- From any circle measurement, all others can be calculated
- Area of a circle is about 78.5% of the area of its bounding square
- A semicircle has half the area and half the circumference of a full circle (plus diameter)
- Arc length = (angle/360) x circumference for a sector
Quick Answer
Circle formulas: Circumference = 2 x pi x radius = pi x diameter. Area = pi x radius squared. Diameter = 2 x radius. From any measurement, you can calculate all others. Pi (approximately 3.14159) is the ratio of circumference to diameter for all circles.
Frequently Asked Questions
The circumference (C) of a circle is calculated using C = 2πr or C = πd, where r is the radius and d is the diameter. This represents the total distance around the circle.
The area (A) of a circle is calculated using A = πr², where r is the radius. This represents the total space enclosed by the circle.
The diameter is exactly twice the radius (d = 2r), or equivalently, the radius is half the diameter (r = d/2). The diameter passes through the center of the circle.
Pi (π) is a mathematical constant approximately equal to 3.14159... It represents the ratio of a circle's circumference to its diameter. Pi is an irrational number, meaning its decimal representation never ends or repeats.
Arc length is the distance along a portion of a circle's circumference. It's calculated as (θ/360°) × 2πr, where θ is the central angle in degrees. A 90° arc is one-quarter of the circumference.
A sector is a "pie slice" shape of a circle, bounded by two radii and an arc. Its area is calculated as (θ/360°) × πr², where θ is the central angle in degrees.
Last updated: 2025-01-15
Circle Properties
Area
78.5398 cm²