With this calculator you can calculate the area, circumference, radius and diameter of a circle. You can select how many decimal places the results should be rounded to and the calculation is always continued with the rounded results.
Contents
Formulas
| Diameter | d = 2 ∙ r | ||
| Area |
A = π ∙ r²
A =
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| Circumference |
C = 2 ∙ π ∙ r
C = π ∙ d
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Radius and diameter
The center of a circle is the point inside the circle that is equidistant from any point on the circle.
The radius of a circle is the distance between the center and any point on the circle.
The diameter is the distance from any point p1 on the circle and the point p2 on the circle farthest from p1. If you connect p1 and p2 with a line, then this line always passes through the center.
The diameter is always twice the radius. If r is the radius and d is the diameter, then:
Area of a circle
The area of a circle can be calculated using either the radius or the diameter. If A is the area, d is the diameter, and r is the radius, then the following applies:
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| 4 |
Example 1:
A circle has a radius of 3 cm. The area is to be calculated:
| A | = | π∙r² |
| = | π∙(3 cm)² | |
| = | π∙9 cm² | |
| ≈ | 28.274334 cm² |
Example 2:
A circle has a diameter of 4 cm. The area is to be calculated:
| A | = |
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| = | 4 cm²∙π | |||
| ≈ | 12.56637 cm² |
If the area is known and the radius or diameter is to be calculated, then the corresponding formula can be resolved to r or d respectively.
| A |
| π |
| 4∙A |
| π |
Example:
The area of the circle is 4 cm². The radius r and the diameter d are to be calculated.
| r | = |
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| = |
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| ≈ | 1.128379 cm |
| d | = |
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| = |
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| = |
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| ≈ | 2.256758 cm |
Note: d could also have been calculated by multiplying r by 2.
Circumference of a circle
The circumference of a circle can be calculated using the radius or the diameter. For the calculation of the circumference with the radius the following formula is used:
And for the calculation with the help of the diameter:
Example with radius:
A circle has a radius of 2 cm. The circumference is to be calculated.
| C | = | 2∙π∙r |
| = | 2∙π∙2 cm | |
| = | π∙4 cm | |
| ≈ | 12.56637 cm |
Example with diameter:
A circle has a diameter of 2 cm. The circumference is to be calculated.
| C | = | π∙d |
| = | π∙2 cm | |
| ≈ | 6.28319 cm |
If the circumference is known and the radius or diameter is to be calculated, then the corresponding formula must be resolved to r or d.
| C |
| 2∙π |
| C |
| π |
Example:
The circumference C of the circle is 6 cm. The radius r and the diameter d are to be calculated.
| r | = |
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| = |
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| = |
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| ≈ | 0.95493 cm |
| d | = |
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| = |
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| ≈ | 1.90986 cm |
Note: d could also have been calculated by multiplying r by 2.