Area of Circle Calculator
Use this free area of circle calculator to find the area of any circle from whichever measurement you have: the radius, the diameter, or the circumference. Type a number and the area updates instantly, along with the matching diameter and circumference for reference — and the full A = πr² formula is shown so you can see exactly how the answer was found.
Enter your numbers
Pick what you know about the circle — the calculator converts it to a radius automatically. Results update as you type.
Your results
| Radius (r) | — |
|---|---|
| Diameter (d) | — |
| Circumference (C) | — |
| Formula used | — |
Area is shown to 2 decimal places; reference values to 4. All are exact mathematical results, not estimates.
How to use this calculator
Start by choosing which measurement you already have: the radius (center to edge), the diameter (all the way across), or the circumference (the distance around). The input box updates to match your choice. Then just type the number — the area appears immediately, and you never need to press Calculate, though the button is there if you prefer.
Because the result panel also shows the matching radius, diameter, and circumference, the tool doubles as a quick converter between circle measurements. Try a radius of 5 and you'll see an area of 78.54; switch to diameter mode and enter 10, and you get the same answer, because a diameter of 10 means a radius of 5.
Everything recalculates the moment you type, so you can explore: double the radius and watch the area quadruple, or work backward from a circumference you measured with a tape measure. If your input isn't a positive number, you'll see a plain-language message explaining the problem instead of a wrong answer.
How it works
The area of a circle is A = πr², where r is the radius and π (pi) is about 3.14159. You square the radius — multiply it by itself — and then multiply by pi. That is the whole formula; everything else the calculator does is just converting your input into a radius first.
When you enter a diameter, the calculator uses r = d ÷ 2: the radius is exactly half the diameter. A diameter of 10 gives r = 5, so A = π × 5² = π × 25 ≈ 78.54 square units.
When you enter a circumference, the calculator first solves C = 2πr for the radius, giving r = C ÷ (2π), and then applies A = πr². This is the same as the shortcut A = C² ÷ (4π). A circumference of 31.42 gives r ≈ 5, so the area is again about 78.54 square units.
Assumptions: your measurement is positive and all lengths are in the same unit. The area is in square units of that unit (cm², in², ft², …), while diameter and circumference are in the original unit. These are exact mathematical results, not estimates.
Frequently asked questions
What is the formula for the area of a circle?
The area of a circle is A = πr², where r is the radius. Square the radius — multiply it by itself — and then multiply by pi (about 3.14159). This one formula handles every circle, no matter how big or small.
How do I find the area of a circle if I only know the diameter?
Divide the diameter by 2 to get the radius, then use A = πr². For example, a diameter of 10 gives a radius of 5, so the area is π × 25 ≈ 78.54 square units. This calculator does that conversion for you when you pick the diameter mode.
How do I find the area of a circle from the circumference?
First find the radius with r = C ÷ (2π), then apply A = πr² — or use the shortcut A = C² ÷ (4π) directly. For example, a circumference of 31.42 gives an area of about 78.54 square units. Choose the circumference mode above and the calculator handles the steps.
What is the area of a circle with radius 5?
A = π × 5² = 25π ≈ 78.54 square units. A circle with diameter 10 has exactly the same area, because its radius is 10 ÷ 2 = 5.
What units should I use for circle measurements?
Any unit works — inches, centimeters, feet, meters — as long as you use the same unit for every input. The diameter and circumference come out in that unit, and the area comes out in square units of it, such as in² or cm².