Area of a circle
The area of a circle is a fundamental concept in geometry that helps us measure the space enclosed by a circular shape. From designing pizza slices to calculating the size of a park fountain, understanding how to find the area of a circle is essential in everyday life and engineering. Jump to the questions
Practise now
Calculate the area using the pi button on your calculator or alternatively use 3.142. Round to 1 decimal place.
Topic guide
What this worksheet practises
This worksheet helps you practise calculating the area of a circle. The area is the amount of two-dimensional space inside the boundary of the circle. You will need to use the value of pi (π) and the radius of the circle to solve these problems.
Key method
The formula for the area of a circle is:
Area = π × r²
Where 'r' is the radius of the circle. The radius is the distance from the centre of the circle to its edge.
If you are given the diameter (the distance straight across the circle, passing through the centre), you must halve it to find the radius before using the formula.
Worked example
Calculate the area of a circle with a radius of 6cm. Give your answer to 1 decimal place.
Step 1: Write down the formula.
Area = π × r²
Step 2: Substitute the radius into the formula.
Area = π × 6²
Area = π × 36
Step 3: Calculate the result using your calculator.
Area = 113.0973355...
Step 4: Round to 1 decimal place.
Area = 113.1 cm²
Common mistakes to avoid
A frequent error is multiplying the radius by 2 instead of squaring it. Remember that r² means r × r, not r × 2. For example, if the radius is 4, r² is 4 × 4 = 16, not 4 × 2 = 8.
Things to remember
Always check whether the question gives you the radius or the diameter. If you are given the diameter, your very first step must be to divide it by 2.