One of the most used geometry tools for students and professionals. Calculate circle area, circumference, diameter, and sector area from any input — radius, diameter, circumference, or area. Uses A = πr² with a full step-by-step breakdown in any unit.
✓Formula verified against NIST pi constant and Khan Academy geometry curriculum — April 2026
Choose what measurement you already know
cm
Enter a positive value.
Distance from center to edge of circle
deg
Enter central angle to compute sector area and arc length
Area
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📋 Full Circle Properties
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Sources & Methodology
✓Circle area formulas verified against NIST mathematical constants (pi = 3.14159265358979) and Khan Academy geometry curriculum aligned with Common Core State Standards.
Pi value: 3.14159265358979323846. Used throughout for area, circumference, sector, and arc length calculations in this calculator
Methodology: Radius from input: r (direct), d/2 (diameter), C/(2pi) (circumference), sqrt(A/pi) (area). Then: Area = pi x r^2. Circumference = 2 x pi x r. Diameter = 2r. Semicircle area = pi x r^2 / 2. If angle entered: Sector area = (angle/360) x pi x r^2. Arc length = (angle/360) x 2 x pi x r. Pi = 3.14159265358979.
⏱ Last reviewed: April 2026
How to Calculate the Area of a Circle
The area of a circle is one of the most fundamental formulas in geometry and mathematics. This circle area calculator is an essential tools resource for students, engineers, architects, and anyone working with circular geometry. Whether you know the radius, diameter, circumference, or even the area itself, this calculator can solve for all other circle properties in one click.
All Circle Area Formulas
A = π × r² (from radius)
Example: r = 5 cm → A = π × 25 = 78.5398 cm²
A = π × d² / 4 (from diameter)
Example: d = 10 cm → A = π × 100 / 4 = 78.5398 cm²
A = C² / (4π) (from circumference)
Example: C = 31.416 cm → A = 987.0 / 12.566 = 78.5398 cm²
Circle Properties Reference Table
Radius (r)
Diameter (d)
Circumference (C)
Area (A)
1
2
6.2832
3.1416
2
4
12.5664
12.5664
5
10
31.4159
78.5398
7
14
43.9823
153.9380
10
20
62.8318
314.1593
15
30
94.2478
706.8583
20
40
125.6637
1,256.6371
Sector Area and Arc Length
A sector is a "pie slice" of a circle defined by a central angle. Sector area = (angle / 360) x π x r². Arc length (the curved edge) = (angle / 360) x 2 x π x r. For a quarter circle (90 degrees) with r = 5: Sector area = 0.25 x π x 25 = 19.635 square units. Arc length = 0.25 x 2 x π x 5 = 7.854 units.
Why Doubling Radius Quadruples Area
Because area scales with r², doubling the radius multiplies area by 4. A circle with r = 10 has exactly 4 times the area of a circle with r = 5. This non-linear relationship has practical implications — a 16-inch pizza has 2.56 times the area of a 10-inch pizza (not 1.6 times), making larger sizes dramatically better value per square inch.
💡 Pro Tip: To find the radius when you only know the area: r = sqrt(A / π). Example: A = 314.16 sq cm → r = sqrt(314.16 / 3.14159) = sqrt(100) = 10 cm. This is the reverse of the standard formula and is useful in engineering when you need to size a circular cross-section for a target area.
Frequently Asked Questions
A = pi x r^2, where r is radius and pi = 3.14159. Also: A = pi x d^2 / 4 (from diameter), or A = C^2 / (4 x pi) from circumference. Example: r = 5: A = pi x 25 = 78.54 square units.
A = pi x (d/2)^2 = pi x d^2 / 4. Example: d = 10: A = pi x 100 / 4 = pi x 25 = 78.54 square units. Halve the diameter to get the radius, then apply A = pi x r^2.
A = C^2 / (4 x pi). Example: C = 31.416: A = 987.0 / 12.566 = 78.54 sq units. Or find radius: r = C / (2 x pi), then A = pi x r^2.
A = pi x 5^2 = 78.5398 square units. Circumference = 31.416 units. Diameter = 10 units.
A = pi x 10^2 = 314.159 square units. Circumference = 62.832 units. Diameter = 20 units.
Semicircle area = pi x r^2 / 2. Perimeter = pi x r + 2r. Example: r = 5: Area = pi x 25 / 2 = 39.27 sq units. Perimeter = 5 x (pi + 2) = 25.71 units.
r = sqrt(A / pi). Example: A = 78.54: r = sqrt(78.54 / pi) = sqrt(25) = 5 units. Diameter = 2r = 10. Circumference = 2 x pi x 5 = 31.42 units.
Area (A = pi x r^2) measures the space inside the circle in square units. Circumference (C = 2 x pi x r) measures the distance around the circle in linear units. For r = 5: area = 78.54 sq units, circumference = 31.42 units.
Sector area = (angle / 360) x pi x r^2. Arc length = (angle / 360) x 2 x pi x r. Example: r = 5, angle = 90: Sector area = 19.63 sq units. Arc length = 7.85 units.
Integrating concentric rings at each radius x (each with area 2 x pi x x x dx) from 0 to r gives A = pi x r^2. Visually, a circle can be cut into thin slices rearranged into a rectangle of width pi x r and height r, giving area pi x r^2.
Area uses square units matching the input: cm^2, m^2, in^2, ft^2, etc. If radius is in cm, area is in cm^2. Circumference uses the same linear unit as radius.
Pi = circumference / diameter = 3.14159265358979. It is irrational with infinite non-repeating decimals. Use 3.14159 or your calculator's built-in pi for accuracy. For rough estimates, 22/7 = 3.14286 is a common approximation.
Radius = 20/2 = 10. A = pi x 10^2 = 314.159 square units. Circumference = 2 x pi x 10 = 62.832 units.