Circle Area Calculator
Enter the radius or diameter of a circle and get the exact and decimal area, plus full step-by-step work.
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Solution
How to Find the Area of a Circle
The area of a circle is the amount of space enclosed within it. The formula uses pi ($\pi \approx 3.14159$) and the radius ($r$) — the distance from the center to the edge:
$$A = \pi r^2$$If you know the diameter instead, divide by 2 first to get the radius: $r = d \div 2$.
Step-by-Step: Finding Area from Radius
Find the area of a circle with radius $r = 7$.
Step 1 — Write the formula:
$$A = \pi r^2$$Step 2 — Substitute the radius:
$$A = \pi \times 7^2$$Step 3 — Square the radius:
$$A = \pi \times 49$$Step 4 — Multiply by $\pi$:
$$A = 49\pi \approx 153.9380\ \text{square units}$$Step-by-Step: Finding Area from Diameter
Find the area of a circle with diameter $d = 12$.
Step 1 — Find the radius:
$$r = \frac{d}{2} = \frac{12}{2} = 6$$Step 2 — Apply the area formula:
$$A = \pi \times 6^2 = 36\pi \approx 113.0973\ \text{square units}$$Common Circle Area Values
| Radius | $r^2$ | Exact Area | Decimal Area |
|---|---|---|---|
| 1 | 1 | $\pi$ | 3.1416 |
| 2 | 4 | $4\pi$ | 12.5664 |
| 3 | 9 | $9\pi$ | 28.2743 |
| 5 | 25 | $25\pi$ | 78.5398 |
| 10 | 100 | $100\pi$ | 314.1593 |
Frequently Asked Questions
What units is the area in?
Area is in square units. If you enter the radius in centimeters, the area is in cm². If you enter feet, the answer is in ft².
What is the difference between radius and diameter?
The radius goes from the center to the edge. The diameter goes all the way across through the center. Diameter = 2 × radius.
Why is the formula $\pi r^2$?
Pi ($\pi$) is the ratio of a circle's circumference to its diameter. Through integral calculus — or geometric proof by slicing the circle into thin sectors — it can be shown that the enclosed area always equals $\pi r^2$.
