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You can calculate the area of a circle using a simple formula. We’ll show you how to calculate the area of a circle using different formulas.
Formula for calculating the area of a circle
You can calculate the area of a circle using the formula A=π⋅r², where AA is the area, r is the radius, and π (pi) is approximately 3.14. Alternatively, you can also calculate the area using the diameter d: A=π⋅d2/4.
- If you only know the diameter of the circle, you can determine the radius by halving the diameter. Radius = diameter/2
- You can obtain an accurate result by entering the number pi on your calculator using the π symbol.
- The circumference of a circle can also be easily calculated using these values. The formula for this is: C = 2·π·r.
- Calculation examples: A circle with a radius of r=7 cm: A=π⋅(7 cm)²=π⋅49 cm²≈153.94 cm²
- A circle with a diameter d=20 cm: A=π⋅(20 cm)²/4=π⋅400 cm²/4=π⋅100 cm²≈314.16 cm²
- Online calculators and apps: There are numerous online calculators available for quick and accurate calculation of circle areas, for example at smart-rechner.de or via corresponding math apps. These tools also help with converting units and offer additional functions such as calculating circumference or radius.
Working with units
- From cm² to m²: divide by 10,000
- From mm² to cm²: divide by 100
- The correct unit is important so that the result can be interpreted and processed correctly.
Calculating a circular ring
A circular ring is created when you cut a smaller circle with radius r out of a larger circle with radius R. You can calculate the area of the circular ring as follows:
- ARing=π⋅(R²−r²)
- This is particularly useful if you want to calculate the area of a round frame or a ring, for example.
- With these formulas, examples, and notes on the unit, you are well equipped to correctly calculate the area of a circle in practice.
