⭕ Circle Calculator

Calculate all circle measurements

Distance from center to edge

Circle Formulas

Radius (r)

r = d / 2
r = C / (2π)
r = √(A / π)

Diameter (d)

d = 2r
d = C / π
d = 2√(A / π)

Circumference (C)

C = 2πr
C = πd
C = 2√(πA)

Area (A)

A = πr²
A = π(d/2)²
A = C² / (4π)

Quick Reference

Radius = 1
Diameter: 2
Circumference: 6.28
Area: 3.14
Radius = 5
Diameter: 10
Circumference: 31.42
Area: 78.54
Radius = 10
Diameter: 20
Circumference: 62.83
Area: 314.16
Radius = 15
Diameter: 30
Circumference: 94.25
Area: 706.86
Radius = 20
Diameter: 40
Circumference: 125.66
Area: 1256.64
Radius = 25
Diameter: 50
Circumference: 157.08
Area: 1963.5

What is Pi (π)?

π ≈ 3.14159265358979...

An irrational number that never ends or repeats

Pi (π) is the ratio of a circle's circumference to its diameter. This ratio is constant for all circles, regardless of size.

Why is π important?

  • Appears in all circle calculations
  • Used in trigonometry, physics, and engineering
  • One of the most important constants in mathematics
  • Celebrated on Pi Day (March 14 = 3/14)

Common Approximations

22/7 ≈ 3.142857 (simple fraction approximation)
3.14 (common in everyday calculations)
3.14159 (accurate to 5 decimal places)

Real-World Applications

🏗️ Construction

  • • Calculate circular pool dimensions
  • • Design round patios and decks
  • • Determine circular driveway size
  • • Plan circular garden beds

🍕 Everyday Use

  • • Pizza size comparisons
  • • Circular table seating
  • • Wheel and tire measurements
  • • Round cake/pie servings

🔧 Engineering

  • • Gear and pulley design
  • • Pipe diameter calculations
  • • Circular motion physics
  • • Wheel circumference for distance

🎨 Design

  • • Logo and graphic design
  • • Circular patterns and mandalas
  • • Round window dimensions
  • • Circular art layouts

Circle Parts

Radius (r):Distance from center to any point on the circle
Diameter (d):Distance across circle through center (longest chord)
Circumference (C):Distance around the circle (perimeter)
Area (A):Amount of space inside the circle
Chord:Line segment connecting two points on circle
Arc:Part of the circumference
Sector:Pie-slice shaped region (two radii + arc)
Tangent:Line that touches circle at exactly one point

How to Use This Calculator

1

Enter Your Values

Input the required values in the calculator fields above. Make sure all inputs are valid numbers.

2

Click Calculate

Press the "Calculate" button to perform the calculation and see your results.

3

Review Results

Review the calculated results displayed below. Use these values for your needs.

About Circle Calculator

The Circle Calculator is a useful tool for calculating circle values. This calculator helps you quickly and accurately determine the results you need for your calculations.

When to Use This Calculator

  • Quick Calculations: Get instant results without manual computation
  • Accuracy: Ensure precise calculations every time
  • Planning: Use for project planning and estimation
  • Verification: Double-check your manual calculations

Why Use Our Calculator?

  • Instant Results: Get accurate calculations immediately
  • Easy to Use: Simple interface for all skill levels
  • 100% Free: No registration or payment required
  • Mobile Friendly: Works on all devices
  • Accurate: Precise mathematical calculations

Tips for Best Results

  • Double-Check Inputs: Verify all values before calculating
  • Use Valid Numbers: Ensure inputs are valid numbers
  • Review Results: Check results for reasonableness
  • Clear and Retry: Clear inputs if you need to recalculate
Frequently Asked Questions

How do I measure the radius of a circle?

Find the center point and measure to any point on the edge. If you can only measure diameter (across), divide by 2 to get radius.

What if I only know the area?

Use r = √(A / π) to find radius. For example, if area = 78.54, then r = √(78.54 / 3.14159) = √25 = 5.

Why is the area formula πr² and not 2πr?

2πr gives circumference (1D perimeter). πr² gives area (2D space inside). The squared term accounts for two dimensions.

How accurate should I make my calculations?

For everyday use, π = 3.14 is fine. For construction, use 3.14159. For engineering/science, use your calculator's π button (many more digits).

Can I calculate part of a circle?

Yes! For a sector (pie slice): multiply circle area by (angle/360°). For arc length: multiply circumference by (angle/360°).