Article
Area of a circle
Circle area is the disk, not the rim. You type the radius and compute πr².
The circle area calculator does this. Circumference is on the circumference page.
The idea in brief
Radius is the line from the center to the rim. Area is the surface of the disk. Circumference is the length of that rim, on a different card.
Diameter is twice the radius. If you type the diameter into the radius field, the result is four times too large.
On this page: π (pi) is a constant of about 3.14. r is the radius, the distance from the center to the rim. A is area, the surface of the disk. r² means radius times radius. The formula A = πr² is pi times the radius squared.
When this helps
| Situation | What the card shows |
|---|---|
| The problem gives the radius and you need the area. | The card computes area as π times the radius squared. |
| The problem gives the diameter, not the radius. | Divide the diameter by two first, then use the same πr². |
| You need the area of the disk, not the length of the rim. | Circumference is a separate page with 2πr. This card stays on area. |
The formula
A = π r². At r = 3 you get about 28.27. At r = 10 it is about 314.16. If someone gave a diameter, divide by two first. Typing 10 instead of 5 for a diameter of 10 overstates area by four, because r is squared.
This is not circumference 2πr and not the surface of a sphere. Circumference is a separate card. Sphere volume is too. The area card stays on one number: how much room the disk takes on the plane.
A worked example
Radius 3
A = π × 3 × 3 ≈ 28.27. At r = 10 you get ≈ 314.16. The result unit follows the label: cm² or in². The typed 3 does not convert when you flip the header.
Typical numbers from the card
| Inputs | Result |
|---|---|
| The radius is 3. | The area is about 28.27. |
| The radius is 10. | The area is about 314.16. |
| The diameter is 10, so the radius is 5. | The area is about 78.54. |
Typical mistakes
| Mistake | What goes wrong | How to avoid it |
|---|---|---|
| You type the diameter into the radius field. | The area comes out four times too large, because the radius is squared. | For a diameter of 10, type radius 5. |
| You compute circumference instead of area. | That is a different formula. Circumference is on the 2πr page. | Count circumference on the circle-circumference page. |
| You replace π with 22/7 even though the card uses ordinary π. | The rounding will differ from the card. | Leave ordinary π from the calculator, unless the problem asks for 22/7. |
Before you compute area
- You type the radius, not the diameter and not the circumference.
- If you know the diameter, divide it by two first.
- The result unit is the radius unit squared, for example cm².
- This is not sphere surface area and not volume.
Frequently asked questions
What is the area at r = 3?
About 28.27. π × 9.
And at r = 10?
About 314.16. π × 100.
What if I know the diameter?
Divide by two, then use πr². Diameter 10 means r = 5, area about 78.54.
Is this circumference?
No. Circumference is 2πr, a different card.
Which π does the card use?
Ordinary engine π, not the 22/7 fraction, unless you approximate on paper yourself.
Do units change?
Area comes in the radius unit squared. r in cm gives cm².