How to Use Circle & Sector Calculator
- Enter Any One Measurement: Enter the Radius, Diameter, Circumference, or Area.
- Click Calculate: Instantly find all corresponding circle dimensions and arc lengths.
Explanation & How It Works
A circle is a geometric figure made up of points on a plane equidistant from a center point. The constant Pi is defined as the ratio between a circle's circumference and its diameter (π ≈ 3.14159265).
Calculation Formula & Rules
Diameter = 2 × r
Circumference = 2 × π × r = π × d
Area = π × r²
Arc Length = 2 × π × r × (θ / 360)
Example Calculation
Example: A circular garden has a diameter of 10 meters.
- Radius:
r = 10 / 2 = 5 meters. - Circumference (fence length):
2 × 3.14159 × 5 = 31.42 meters. - Area (grass coverage):
3.14159 × 5² = 78.54 m².
History of Pi (π)
The value of Pi is irrational; hence, its decimal places neither terminate nor repeat themselves. The value of Pi was approximated as 3.125 by the ancient Babylonians and 3.16 by the Egyptians. In modern days, supercomputers have computed Pi to over 100 trillion decimal digits.
Frequently Asked Questions
What is the relationship between diameter and circumference?
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The circumference is always approximately 3.14159 (pi) times longer than the diameter.