Circle Calculator

Calculate radius, diameter, circumference, and area of a circle. Enter any value and get all properties instantly with formulas and visual representations.

What do you know?

Enter Circle Radius

Radius (r)
5.0000
Diameter (d)
10.0000
Circumference (C)
31.4200
Area (A)
78.5400

Formulas Used

• Diameter: d = 2r = 10.0000
• Circumference: C = 2πr = πd = 31.4200
• Area: A = πr² = 78.5400
Where π (pi) ≈ 3.14159265359

Properties Comparison

Area Visualization

About Circles

A circle is a perfectly round 2D shape where every point on its edge is equidistant from the center. This distance is called the radius. Circles are fundamental in geometry, appearing everywhere in nature, engineering, and mathematics.

Key Circle Properties

  • Radius (r): Distance from center to edge
  • Diameter (d): Distance across circle through center = 2r
  • Circumference (C): Distance around the circle = 2πr or πd
  • Area (A): Space inside the circle = πr²
  • Pi (π): Mathematical constant ≈ 3.14159 (ratio of circumference to diameter)

Real-World Applications

  • Wheel and tire design (automotive engineering)
  • Circular gardens and landscaping
  • Pizza sizes and food portions
  • Pipe and tube calculations (plumbing, construction)
  • Planetary orbits and astronomy
  • Lens design and optics

Frequently Asked Questions

How do I find the area of a circle?

The area of a circle is calculated using the formula A = πr², where r is the radius. For example, if the radius is 5 units, the area is π × 5² = 3.14159 × 25 ≈ 78.54 square units.

What's the formula for circumference of a circle?

Circumference = 2πr or πd, where r is the radius and d is the diameter. Since diameter is twice the radius (d = 2r), both formulas give the same result. For a circle with radius 5, C = 2 × π × 5 ≈ 31.42 units.

How do I calculate the radius if I know the area?

To find radius from area, use the formula r = √(A/π). For example, if the area is 78.54, then r = √(78.54/3.14159) = √25 = 5 units. Our calculator does this automatically when you select "Area" mode.

What is pi (π) and why is it important for circles?

Pi (π) is a mathematical constant approximately equal to 3.14159. It represents the ratio of a circle's circumference to its diameter. This ratio is the same for every circle, regardless of size, making π essential for all circle calculations.

How do I convert diameter to radius?

The radius is always half the diameter. Simply divide the diameter by 2. For example, if the diameter is 10 units, the radius is 10 ÷ 2 = 5 units. Conversely, diameter = 2 × radius.

Can I use this calculator for circles in different units?

Yes! The calculator works with any unit of measurement (inches, feet, meters, centimeters, etc.). Just ensure you're consistent. If you enter radius in meters, all results will be in meters (circumference) and square meters (area).

What's the difference between circumference and perimeter?

Circumference and perimeter mean the same thing - the distance around a shape. "Circumference" is specifically used for circles and curves, while "perimeter" is more general and applies to any closed shape (squares, triangles, etc.).

How accurate are the calculations?

Our calculator uses JavaScript's built-in Math.PI constant (accurate to 15 decimal places) and displays results to 4 decimal places. This is more than sufficient for virtually all practical applications, from homework to professional engineering calculations.

What Our Users Say

★★★★★

“Perfect for my geometry homework! The ability to enter any property and get all the others is super helpful. The formulas shown make it easy to check my work.”

Emily S.
High School Student
★★★★★

“As a landscape designer, I use this daily to calculate circular garden beds and fountains. The visual charts help me explain dimensions to clients clearly.”

Marcus T.
Landscape Designer
★★★★★

“Simple, fast, and accurate. I teach middle school math and recommend this to all my students for circle problems. The export feature is great for record keeping!”

Ms. Rodriguez
Math Teacher