Circle Calculator
Solve a circle from radius, diameter, circumference or area — any one gives the rest.
Inputs
Radius (r)
5.000000
Diameter (d)
10.000000
Circumference (C)
31.415927
Area (A)
78.539816
Step by step
Radius
r = 5
= 5
Diameter
d = 2r = 2 × 5
= 10
Circumference
C = 2πr = 2 × π × 5
= 31.41592654
Area
A = πr² = π × 5²
= 78.53981634
How it works
A circle is completely defined by a single measurement: its radius. Every other property follows directly from r. The diameter is twice the radius. The circumference (perimeter) is 2πr ≈ 6.28318·r. The area enclosed is πr² ≈ 3.14159·r². π (pi) is an irrational constant approximately equal to 3.14159265.
Formulas
Diameter
d = 2r
- r
- Radius
- d
- Diameter
Circumference
C = 2πr = πd
- C
- Circumference
- r
- Radius
Area
A = πr²
- A
- Area
- r
- Radius
Frequently Asked Questions
What is π (pi) and why does it appear in circle formulas?
π is the ratio of a circle's circumference to its diameter — it's approximately 3.14159265. It appears in every circle formula because it's the fundamental constant connecting a circle's linear dimensions (radius) to its rotational measures (arc length, area).
How do you find the circumference from the area?
First find the radius from the area: r = √(A/π). Then compute C = 2πr. For example, if A = 100, then r = √(100/π) ≈ 5.642, and C = 2π × 5.642 ≈ 35.45.
What is the difference between circumference and perimeter?
They mean the same thing: the total length of the boundary. 'Perimeter' is the general term for polygons; 'circumference' is specifically used for circles and curved shapes.