How to find the area of a circle
The area of a circle is pi times the radius squared: A = π × r². The radius is the distance from the center to the edge. For a radius of 5, the area is π × 5² = π × 25 = about 78.54 square units.
To see where the formula comes from, slice the circle into thin wedges and rearrange them alternately point-up and point-down. The result approaches a rectangle of height r and width πr, and multiplying gives πr². The same radius gives you the distance around the edge through the circle circumference calculator.
How to use this calculator
Enter the radius. If you only know the diameter, halve it first (radius = diameter ÷ 2). The answer is in square units of whatever unit you used — square inches, cm², m², and so on.
The most frequent mistake is entering the diameter in the radius box, which makes the answer four times too large. A second is mixing units. Keep in mind that area units are squared, so 1 m² is 10,000 cm², not 100 cm². For a slice of the disc rather than the whole of it, the sector area calculator takes the radius and the central angle.
From diameter or circumference
If you have the diameter d, area = π × (d ÷ 2)². From the circumference C, the radius is C ÷ (2π), then apply the same formula. To find the diameter or circumference instead, use the circle diameter calculator.
These routes matter because circles are often measured indirectly — a pipe is easier to wrap a tape around than to measure across the centre.
Frequently asked questions
- What is the formula for the area of a circle?
- A = π × r², where r is the radius. Square the radius and multiply by pi (about 3.14159).
- How do I find the area from the diameter?
- Divide the diameter by 2 to get the radius, then use A = π × r². For a diameter of 10, radius is 5 and area is about 78.54.
- What is the area of a circle with radius 5?
- About 78.54 square units (π × 25).
- What units is the area in?
- Square units of whatever you measured the radius in — square inches, square cm, square metres, etc.
- What happens to the area if I double the radius?
- The area becomes four times larger, not twice as large. Because the radius is squared, area scales with the square of any length change — a radius of 10 gives about 314.16 square units, four times the 78.54 you get from a radius of 5.