Our Circle Calculator allows you to quickly and easily calculate the essential parameters of a circle. Simply enter a value, and the calculator will automatically determine the radius, diameter, circumference, and area of the circle. This tool is especially useful for mathematical computations, design projects, or when you need precise measurements for crafting and construction.
Circle Calculator
Please fill in one field, and the rest will be calculated automatically:
Calculating the Area of a Circle
The area of a circle represents the total surface enclosed by the circle. There are different formulas for calculating the area, depending on whether the radius, circumference, or diameter of the circle is known.
| Known Value | Formula |
|---|---|
| Radius (r) | \(A = \pi \times r^2\) |
| Circumference (C) | \(A = \frac{C^2}{4 \times \pi}\) |
| Diameter (d) | \(A = \frac{\pi \times d^2}{4}\) |
Here, A denotes the area, r is the radius, C is the circumference, and d is the diameter of the circle. The constant \(\pi\) (Pi) is approximately 3.14159.
Example: If the radius of a circle is 5 cm, the area can be calculated as follows:
\(A = \pi \times (5)^2 = \pi \times 25 \approx 78.54 \, \text{cm}^2\)Calculating the Radius of a Circle
The radius of a circle is the distance from the center of the circle to any point on its perimeter. Depending on whether the area, circumference, or diameter is known, different formulas can be used to calculate the radius.
| Known Value | Formula |
|---|---|
| Area (A) | \(r = \sqrt{\frac{A}{\pi}}\) |
| Circumference (C) | \(r = \frac{C}{2 \times \pi}\) |
| Diameter (d) | \(r = \frac{d}{2}\) |
In these formulas, r represents the radius, A is the area, C is the circumference, and d is the diameter. The constant \(\pi\) (Pi) is approximately 3.14159.
Example: If the area of a circle is 78.54 cm², the radius is calculated as follows:
\(r = \sqrt{\frac{78.54}{\pi}} \approx 5 \, \text{cm}\)Calculating the Diameter of a Circle
The diameter of a circle is the straight line passing through the center of the circle, connecting two points on its boundary. Depending on whether the radius, circumference, or area is known, the diameter can be calculated using different formulas.
| Known Value | Formula |
|---|---|
| Radius (r) | \(d = 2 \times r\) |
| Circumference (C) | \(d = \frac{C}{\pi}\) |
| Area (A) | \(d = 2 \times \sqrt{\frac{A}{\pi}}\) |
Here, d denotes the diameter, r is the radius, C is the circumference, and A is the area of the circle. The constant \(\pi\) (Pi) is approximately 3.14159.
Example: If the radius of a circle is 7 cm, the diameter can be calculated as:
\(d = 2 \times 7 = 14 \, \text{cm}\)Calculating the Circumference of a Circle
The circumference of a circle is the total length of its boundary. There are various ways to calculate the circumference, depending on whether the radius, diameter, or area is known. The following formulas demonstrate how to compute the circumference:
| Known Value | Formula |
|---|---|
| Radius (r) | \(C = 2 \times \pi \times r\) |
| Diameter (d) | \(C = \pi \times d\) |
| Area (A) | \(C = 2 \times \pi \times \sqrt{\frac{A}{\pi}}\) |
In these formulas, C represents the circumference, r is the radius, d is the diameter, and A is the area of the circle. The constant \(\pi\) (Pi) is approximately 3.14159.
Example: If the diameter of a circle is 10 cm, the circumference is calculated as follows:
\(C = \pi \times 10 \approx 31.42 \, \text{cm}\)More Math-Tools: