The Circle Surface Area Calculator calculates the area inside a circle using the formula A = πr². You can start from the radius, the diameter (A = πd² ÷ 4) or the circumference (A = C² ÷ 4π).
Circle Surface Area Calculator
Area of a circle (often searched as "surface area of a circle") from radius, diameter or circumference.
Strictly speaking a circle is flat, so it has an area rather than a surface area — but the calculation people mean by “surface area of a circle” is exactly this. Enter one measurement below to calculate the area and circumference.
Formula
A = πr²
Equivalent forms:
- From diameter: A = πd² ÷ 4
- From circumference: A = C² ÷ (4π)
- Circumference: C = 2πr = πd
Where:
- A = area of the circle
- r = radius (center to edge)
- d = diameter (edge to edge through the center) = 2r
- C = circumference (distance around the circle)
- π ≈ 3.14159
How the Calculation Works
Step 1: Get the radius. If you entered the diameter, it is divided by 2; if you entered the circumference, r = C ÷ 2π.
Step 2: Square the radius (r × r).
Step 3: Multiply by π. The result is the area in square units.
Variables Explained
| Variable | Meaning | Unit |
|---|---|---|
| r | Radius | mm, cm, m, in, ft |
| d | Diameter | mm, cm, m, in, ft |
| C | Circumference | mm, cm, m, in, ft |
| A | Area | mm², cm², m², in², ft² |
Example Calculation
From the radius
Given: radius = 5 cm
Calculation: A = 3.14159 × 5² = 3.14159 × 25
Result: A ≈ 78.54 cm² (circumference ≈ 31.42 cm)
From the circumference
Given: circumference = 50 in
Calculation: A = 50² ÷ (4 × 3.14159) = 2,500 ÷ 12.566
Result: A ≈ 198.94 in²
Common Area Conversion Table
| Unit | Equivalent |
|---|---|
| 1 cm² | 100 mm² |
| 1 m² | 10,000 cm² |
| 1 ft² | 144 in² |
| 1 m² | 10.7639 ft² |
Shape Properties
Of all shapes with the same perimeter, a circle encloses the greatest area. The area grows with the square of the radius: doubling the radius makes the area four times larger.
Circle vs sphere vs disc
- Circle: a flat shape; area = πr².
- Sphere (ball): a 3D shape; surface area = 4πr² — exactly four times the area of a circle with the same radius.
- Disc with thickness: a short cylinder; total surface area = 2πr² + 2πrh.
Dimensions Explained
Which measurement is easiest?
For a round table or pipe end, measuring straight across (the diameter) is usually easiest. For a tree trunk or column, wrap a tape around it to get the circumference and use that mode.
Frequently Asked Questions
What is the surface area of a circle?
It is the area enclosed by the circle, A = πr². A circle with a 5 cm radius has an area of about 78.54 cm².
How do you find the area of a circle with the diameter?
Use A = πd² ÷ 4, or halve the diameter to get the radius and use πr². A 10 cm diameter gives about 78.54 cm².
How do you find the area of a circle from the circumference?
Use A = C² ÷ (4π). This skips the step of finding the radius first.
Does a circle have a surface area?
A circle is two-dimensional, so it has an area, not a surface area. “Surface area” applies to 3D solids such as spheres and cylinders.
What is the difference between area and circumference?
Area (square units) is the space inside the circle. Circumference (linear units) is the distance around its edge.
What is the surface area of a sphere compared with a circle?
A sphere’s surface area is 4πr², four times the area of a circle with the same radius.