Circle Calculator
Find a circle’s area, circumference, radius, and diameter from any one of those four. The formulas are A = πr² and C = 2πr, with π the same constant used on paper.
r = 5 · C = 31.4159265359
- Diameter is twice the radius: d = 2r = 2 × 5 = 10.
- Circumference C = 2πr = 2 × 3.14159265359 × 5 = 31.4159265359.
- Area A = πr² = 3.14159265359 × 5² = 78.5398163397.
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How to Use the Circle Calculator
Choose the one measurement you know — radius, diameter, circumference, or area — then Calculate. The other three are filled from A = πr² and C = 2πr (or C = πd).
- Select From radius, From diameter, From circumference, or From area.
- Enter a non-negative number. Zero is allowed and describes a point.
- Read the area (or the radius, when you started from area), plus diameter and circumference.
A triangle’s area belongs on the Triangle Area Calculator. Converting the square units after you have A belongs on the Area Converter. A slice of this circle — one arc and its sector — belongs on the Arc Length Calculator. A solid ball belongs on the Sphere Calculator (V = (4/3)πr³).
Area and Circumference
The radius is the distance from the center to any point on the circle. The diameter is a straight cut through the center, so it is exactly two radii. The circumference is the perimeter: wrap 2π radii around the rim, or π diameters.
Area is π times the square of the radius. That is not “π times r, then squared.” Square first: r², then multiply by π. Solving for r from a known area takes a square root: r = √(A / π). Solving from a known circumference is a division: r = C / (2π).
Circle Calculator Examples
Radius 5
d = 10. C = 10π ≈ 31.4159265359. A = 25π ≈ 78.5398163397.
Diameter 10
The same circle as radius 5. r = 10 / 2 = 5, then the same C and A.
The unit circle
r = 1, so C = 2π ≈ 6.28318530718 and A = π ≈ 3.14159265359. Trigonometry later uses this circle on the coordinate plane; here it is just the circle of radius 1.
Circumference 10π
r = 10π / (2π) = 5. Starting from C recovers the first example.
A point circle
r = 0 gives d = 0, C = 0, A = 0. Nothing is wrapped and nothing is enclosed.
A negative radius
A length cannot be negative. The calculator rejects −1 instead of quietly using |r|.
What π Is
π is the ratio of circumference to diameter for every circle: C / d = π. It is irrational, so 3.14 and 22/7 are classroom shortcuts, not the constant. This page uses the same π your calculator’s π key uses (about 3.141592653589793). A homework sheet that says “use 3.14” will differ in the last digits; that is the approximation, not an error in A = πr².
A fraction of this rim and disk belongs on the Arc Length Calculator (L = rθ, sector (1/2)r²θ). A sphere’s volume V = (4/3)πr³ and surface S = 4πr² belong on the Sphere Calculator.
Common Circle Mistakes
Using 3.14 and calling it exact
3.14 × 25 = 78.5, while π × 25 ≈ 78.5398. Fine for a one-decimal estimate; not the same as the π-key value.
Computing (πr)² instead of πr²
(π × 5)² ≈ 246.74, which is π²r², not the area. Square the radius, then multiply by π.
Using diameter in A = πr² without halving
A = πd² / 4. Plugging d = 10 into πr² as if r were 10 gives four times the area.
Confusing circumference with area
C is a length (units of r). A is square units. For r = 5 they are 31.4… and 78.5… — different numbers and different dimensions.
Converting m² to ft² on this page
The result is already in the square of your input unit. Use the Area Converter to change m² into ft² or acres.
Circle Calculator FAQs
What is the area of a circle?
A = πr². For radius 5, A = 25π ≈ 78.5398163397 square units.
What is the circumference of a circle?
C = 2πr, or C = πd. For radius 5, C = 10π ≈ 31.4159265359.
How do you find the radius from the area?
r = √(A / π). Divide the area by π, then take the square root.
Is π equal to 3.14 or 22/7?
Those are approximations. This page uses the full calculator constant ≈ 3.141592653589793.
Does this convert square units or find a triangle’s area?
No. Use the Area Converter for m² and ft², and the Triangle Area Calculator for ½bh, Heron, or SAS.
Are my numbers sent to a server?
No. The calculation runs locally in your browser.
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Reviewed by Prof. Dr. Khalil Mudassar (PhD) · Last updated: [mc_modified_date]
Sources
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Disclaimer
This calculator is intended for general educational and practical use. Review important results before relying on them in professional work.