Circle Calculator
Calculate area, circumference, radius and diameter of a circle. Step-by-step explanation, free and no registration required.
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.
Does the calculator show the working steps?
Yes. In addition to the final result the calculator displays the intermediate steps so you can follow the solution — ideal for school, university or homework.
Guide
Quick Answer
The circle calculator computes circumference, area, diameter and radius of a circle from one known value.
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: Umfang = 2 x 3,14159 x 5 = 31,42 cm. Fläche = 3,14159 x 25 = 78,54 cm2. Durchmesser = 10 cm.
Sources · E-E-A-T
Official sources
Calculations are based on applicable German laws and official data:
Full methodology at Methodology.
Mathematics
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