Circle Calculator

How to Calculate Circle Properties

Understanding and calculating the properties of a circle is fundamental in geometry. Here's a comprehensive guide on how to calculate the radius, diameter, area, and circumference of a circle:

Circle Formulas

The key formulas for circle calculations are:

• Diameter (d) = 2 × radius (r)
• Area (A) = π × r²
• Circumference (C) = 2 × π × r

Where π (pi) is approximately 3.14159.

Calculation Steps

1. Identify the given value (radius, diameter, area, or circumference).
2. Use the appropriate formula to calculate the unknown properties.
3. If needed, use algebra to rearrange formulas to solve for a specific variable.

Example Calculation

Let's calculate all properties of a circle with a radius of 5 units:

1. Given: Radius (r) = 5 units
2. Diameter: d = 2r = 2 × 5 = 10 units
3. Area: A = πr² = π × 5² ≈ 78.54 square units
4. Circumference: C = 2πr = 2 × π × 5 ≈ 31.42 units

Visual Representation

This diagram illustrates a circle with radius 5 units, showing its key properties: radius (r), diameter (d), circumference (C), and area (A). The radius is shown in orange, diameter in green, and the circle's outline in blue.