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Circle Calculator

Calculate circle area, circumference, and diameter

Area

314.16 sq ft

Circumference

62.83 ft

Diameter

20.00 ft

Units

Area

314.16

sq ft

Circumference

62.83

ft

Diameter

20.00

ft

Circle Diagram

r = 10.0ft
d = 20.0ftC = 62.83ft

Area

314.16

sq ft

Circumf.

62.83

ft

Diameter

20.00

ft

Formulas Used

Circle Area

Area = π × r²

The area enclosed by a circle, calculated as pi times the radius squared.

Where:

r= Radius of the circle
π= Pi, approximately 3.14159

Circle Circumference

Circumference = 2 × π × r

The perimeter (distance around) the circle.

Where:

r= Radius of the circle
π= Pi, approximately 3.14159

Diameter

Diameter = 2 × r

The diameter is twice the radius, passing through the center of the circle.

Where:

r= Radius of the circle

Example Calculations

1Circle with Radius 10

Inputs

Radius10

Result

Area314.16
Circumference62.83
Diameter20.00

Area = π × 10² = π × 100 = 314.16. Circumference = 2 × π × 10 = 62.83. Diameter = 2 × 10 = 20.00.

2Circle with Radius 7

Inputs

Radius7

Result

Area153.94
Circumference43.98
Diameter14.00

Area = π × 7² = π × 49 = 153.94. Circumference = 2 × π × 7 = 43.98. Diameter = 2 × 7 = 14.00.

Frequently Asked Questions

Q

How do you calculate the area of a circle?

Area of a circle = π × r², where r is the radius. For example, a circle with radius 5 has area = π × 5² = 78.54 square units. Alternatively, area = π × (d/2)² where d is the diameter.

  • Radius 1 → area = 3.14 sq units; radius 10 → area = 314.16 sq units
  • Doubling the radius quadruples the area (area grows with r²)
  • To find area from diameter: Area = π × (d/2)² = πd²/4
  • A 10-ft diameter circular patio has an area of 78.54 sq ft
  • For real-world projects, add 5–10% extra material to account for cuts and waste
Q

How do you calculate the circumference of a circle?

Circumference = 2 × π × r, where r is the radius. For a circle with radius 10, circumference = 2 × π × 10 = 62.83 units. Alternatively, circumference = π × d where d is the diameter.

  • Radius 5 → circumference = 31.42 units; radius 10 → 62.83 units
  • Circumference scales linearly with radius (double radius = double circumference)
  • To find circumference from diameter: C = π × d (simpler formula)
  • A 12-ft diameter round pool has a circumference of 37.7 ft for edging material
Q

What is the relationship between radius and diameter?

Diameter = 2 × radius. The diameter is twice the radius. If radius is 5, diameter is 10. The radius is half the diameter.

  • Diameter = 2 × radius; Radius = diameter / 2
  • A 24-inch pizza has a radius of 12 inches
  • When measuring round objects, measure the diameter across the widest point
  • For pipes and tubes, inner diameter (ID) and outer diameter (OD) differ by 2 × wall thickness
Q

What is the value of π (pi)?

π (pi) is approximately 3.14159, but is often rounded to 3.14 for calculations. It represents the ratio of a circle's circumference to its diameter. For precise calculations, use π = 3.14159265359.

  • π = 3.14159265358979... (irrational number, never terminates)
  • Using 3.14 vs 3.14159 causes less than 0.006% error in most calculations
  • For quick mental math, 22/7 (3.1429) is a handy approximation
  • π was calculated to over 100 trillion digits as of 2024

Understanding Circle Calculations

A circle is defined by its radius (distance from center to edge). All circle measurements can be calculated from the radius.

The area of a circle is π times the radius squared. The circumference is 2π times the radius.

The diameter is always twice the radius, and the circumference equals π times the diameter.

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Last Updated: Mar 26, 2026

This calculator is provided for informational and educational purposes only. Results are estimates and should not be considered professional financial, medical, legal, or other advice. Always consult a qualified professional before making important decisions. UseCalcPro is not responsible for any actions taken based on calculator results.

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