The formula for circle area is πr², where r is the radius

To find the area of a circle, multiply pi (π, approximately 3.14159) by the radius squared. The radius is the distance from the center of the circle to its edge. If you know the radius, you can calculate the area in seconds using a calculator or by hand.

The formula works the same way whether you are working with a circle drawn on paper, a circular room you need to carpet, or a circular garden you plan to fence. Once you have the radius measurement, the math is straightforward.

Key Takeaways

  • The area formula is π times the radius squared (πr²), where the radius is half the diameter.
  • You must square the radius before multiplying by pi — squaring means multiplying the number by itself.
  • If you only know the diameter, divide it by 2 to get the radius, then use the formula.
  • A scientific calculator or spreadsheet will give you a more precise answer than rounding pi to 3.14.

Finding the radius from the diameter

If you have the diameter of the circle instead of the radius, divide the diameter by 2. The diameter is the distance across the circle through its center, so the radius is always half that distance.

For example, if a circle has a diameter of 10 inches, the radius is 5 inches. Once you have the radius, you can move forward with the area formula.

Squaring the radius

Before you multiply by pi, you must square the radius. Squaring means multiplying the number by itself. If the radius is 5, then 5 squared (written as 5²) equals 5 × 5, which is 25.

This step is straightforward to skip or do wrong, so double-check it. Write out the multiplication if you are doing it by hand: radius × radius. A calculator will have a button labeled x² or ^ that does this for you.

Multiplying by pi

Once you have the radius squared, multiply that result by pi. Pi is an irrational number that starts 3.14159265... and never repeats. For most everyday purposes, using 3.14159 or even 3.14 is close enough.

If you are using a calculator, look for a π button — it will give you a more precise value than typing 3.14 by hand. Spreadsheet programs like Excel or Google Sheets also have a PI() function that returns the full precision value the program can handle.

Working through a complete example

Suppose you have a circular table with a radius of 2 feet and you want to know its area. Start by squaring the radius: 2 × 2 = 4. Then multiply by pi: 4 × 3.14159 = 12.566 square feet.

If you round pi to 3.14, you get 4 × 3.14 = 12.56 square feet. The difference is small, but using more decimal places in pi gives you a more accurate answer. For a larger circle, the difference becomes more noticeable.

Using a spreadsheet or calculator

Open your calculator or spreadsheet and enter the formula directly. In a spreadsheet, type =PI()*A1^2, where A1 is the cell containing your radius. The ^ symbol means "to the power of," so ^2 means squared.

On a basic calculator, enter the radius, press the x² button, then multiply by pi. On a scientific calculator, you can often type the whole formula at once. Either way, the result is the area in square units (square feet, square inches, square meters, depending on what unit you measured the radius in).

Converting between radius and diameter in your calculation

Sometimes a problem gives you the diameter but asks for area. Rather than writing down the radius separately, you can put the conversion into the formula itself. The formula becomes π(d/2)², where d is the diameter.

For a circle with diameter 10 inches, this becomes π(10/2)² = π(5)² = π × 25 = 78.54 square inches. This approach saves a step and reduces the chance of writing down the wrong number.

Frequently Asked Questions

What if I only know the circumference?

The circumference formula is 2πr, so you can rearrange it to find the radius: r = circumference ÷ (2π). Once you have the radius, use the area formula πr² as normal. For a circle with circumference 31.4 inches, the radius is 31.4 ÷ (2 × 3.14159) = 5 inches, and the area is π × 5² = 78.54 square inches.

Do I need to use 3.14159 or can I round pi to 3.14?

Rounding to 3.14 works for rough estimates and everyday situations. For homework, tests, or work that requires precision, use more decimal places or the π button on your calculator. The difference grows with larger circles — for a radius of 100, using 3.14 versus 3.14159 changes your answer by about 15 square units.

What units should my answer be in?

The area is always in square units. If you measure the radius in inches, the area is in square inches. If the radius is in meters, the area is in square meters. Always include the unit in your final answer so someone reading it knows what the number means.

Can I use this formula for a semicircle or partial circle?

Yes. For a semicircle, calculate the full area using πr² and divide by 2. For a quarter circle, divide by 4. For any wedge-shaped slice, divide the full area by the number of equal slices, or multiply by the fraction of the circle the slice represents.