Circle Calculator
Calculate radius, diameter, circumference, and area from any single known circle parameter.
Radius
5
Diameter
10
Circumference
31.415927
Area
78.539816
Circumference = 2πr | Area = πr²
How to Use the Circle Calculator
- Select your known circle dimension: Radius (r), Diameter (d), Circumference (c), or Area (a).
- Enter the numerical value into the input box.
- The calculator automatically solves and displays the remaining three circle properties.
Formulas & Principles
Diameter: d = 2r
Circumference: C = 2πr = πd
Area: A = πr² = π(d/2)²
Radius from Area: r = √(A / π)
Radius from Circumference: r = C / (2π)
Frequently Asked Questions
What value of Pi (π) is used in calculations?
This calculator uses high-precision JavaScript Math.PI (approximately 3.141592653589793) for accurate scientific results.
How do I find the diameter if I only know the circumference?
Divide the circumference by Pi (d = C / π). For example, a circumference of 31.42 units yields a diameter of approximately 10 units.
How does doubling the radius affect the circle area?
Because area is proportional to the square of the radius (r²), doubling the radius increases the surface area by a factor of 4 (2² = 4).
Why this calculator matters
This calculator helps solve mathematical problems faster and with fewer manual arithmetic mistakes. It is useful for studying, research verification, technical engineering checks, and everyday problem-solving.
When to use it
Use it when you need a fast answer, a cross-check for manual calculations, or a clear step-by-step verification of your result.
Quick tips
Double-check your inputs, keep units consistent across all fields, and verify boundary conditions.
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