Circle Calculator: area, circumference and diameter

The circle is one of the most fundamental geometric shapes. This calculator computes the area, circumference (perimeter) and diameter from the circle's radius.

Circle formulas

For a circle with radius r:

• Area: A = π × r²
• Circumference: C = 2 × π × r
• Diameter: d = 2 × r

The number π (pi ≈ 3.14159) is the ratio of circumference to diameter of any circle, a universal constant.

Example 1: circle with integer radius

Problem: A circle has radius r = 10 cm.

1. Area:
   • A = π × 10² = π × 100 ≈ 314.16 cm².
2. Circumference:
   • C = 2 × π × 10 ≈ 62.83 cm.
3. Diameter:
   • d = 2 × 10 = 20 cm.

Answer: A ≈ 314.16 cm², C ≈ 62.83 cm, d = 20 cm.

Example 2: circle with decimal radius

Problem: A circle has radius r = 3.5 m.

1. Area:
   • A = π × 3.5² = π × 12.25 ≈ 38.48 m².
2. Circumference:
   • C = 2 × π × 3.5 ≈ 21.99 m.
3. Diameter:
   • d = 2 × 3.5 = 7 m.

Answer: A ≈ 38.48 m², C ≈ 21.99 m, d = 7 m.

Common uses of the circle calculator

• Computing areas of circular plots, gardens and plazas.
• Determining lengths of circular edges, frames and rings.
• Estimating materials for circular floors, rugs and coverings.
• Solving geometry problems in mathematics and physics.
• Designing mechanical parts like gears, wheels and pulleys.
• Calculating cross-sectional areas of pipes and cables.

Common mistakes when working with circles

• Using the diameter instead of the radius in formulas without dividing by 2.
• Confusing area (πr²) with circumference (2πr).
• Using a rough approximation of π (like 3.14) when precision is needed.
• Forgetting to square the radius when calculating area.

Pro tip

If you know the diameter instead of the radius, the formulas can be rewritten: A = π × (d/2)² = π × d²/4 and C = π × d. This avoids the intermediate step of computing the radius.