Circle Calculator
Enter the radius, diameter, circumference or area of a circle and get the other three values, together with the formulas used for them.
Result
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Formulas
Diameter: d = 2 * r
Circumference: U = 2 * Pi * r = Pi * d
Area: A = Pi * r²
Note: These calculations are for informational purposes only and do not replace professional tax or financial advice. All information without guarantee.
FAQ
Frequently Asked Questions
How do I calculate the area of a circle?
Area equals pi times radius squared (A = pi times r squared). With a radius of 5 cm, the area is approximately 78.54 square centimeters.
How do I calculate the circumference of a circle?
Circumference equals 2 times pi times radius (or pi times diameter). With a diameter of 10 cm, the circumference is approximately 31.42 cm.
Can I calculate the circle from the circumference or the area?
Yes. Choose at the top which value you know – radius, diameter, circumference or area – and the calculator works out all the others. From the circumference the radius is r = circumference / (2 × π), from the area r = √(A / π). Example: a tree circumference of 150 cm measured with a tape corresponds to a diameter of 47.75 cm and a cross-sectional area of about 1,790.49 cm².
Guide
What is the Circle Calculator?
The circle calculator computes circumference, area, diameter and radius of a circle from one known value.
How does the Circle Calculator work?
Enter the radius, diameter, circumference or area. The calculator computes all other values: circumference = 2 * pi * r, area = pi * r squared. Additionally, circular segment and sector are calculated.
Key Data and Facts
Circumference = 2 * pi * r = pi * d. Area = pi * r squared. Pi approx. 3.14159. Sector area = (angle / 360) * pi * r squared.
Step-by-Step Guide
How to calculate circle dimensions step by step: 1. Enter one known dimension: radius (r), diameter (d = 2r), circumference (U) or area (A). 2. Calculate all dimensions: circumference = 2 x pi x r = pi x d. Area = pi x r². Diameter = 2 x r. Radius = d / 2. 3. From circumference to radius: r = U / (2 x pi). 4. From area to radius: r = sqrt(A / pi). 5. Calculate a circular sector (pie slice): arc length = (angle / 360) x 2 x pi x r. Sector area = (angle / 360) x pi x r². 6. Calculate an annulus (ring): area = pi x (R² - r²), where R is the outer radius and r is the inner radius. 7. Pi ≈ 3.14159265. For rough estimates, pi ≈ 3.14 is sufficient. Tip: the circumference of a circle grows linearly with the radius, while the area grows quadratically – doubling the radius means four times the area.
Calculation Example
Radius 5 cm: circumference = 2 x 3.14159 x 5 = 31.42 cm. Area = 3.14159 x 25 = 78.54 cm2. Diameter = 10 cm.
Sources
Official sources
Calculations are based on applicable German laws and official data:
Full methodology at Methodology.
Reviewed by Konstantin Iakovlev · Last updated:
Mathematics
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