Circle Area Calculator

Calculate area, circumference, and diameter of a circle

Radius (r)

How to Use This Circle Area Calculator

Enter the radius of the circle

The radius is the distance from the center to any point on the edge. Enter any positive number in your preferred unit (inches, cm, meters, etc.).

Click Calculate

The calculator instantly computes the area using the formula A = pi r squared, plus the circumference and diameter.

Review all circle measurements

Results show area in square units, circumference (perimeter), and diameter. All values update automatically when you change the radius.

Circle Measurements Reference Table

Radius	Diameter	Circumference	Area
1	2	6.283	3.142
2	4	12.566	12.566
3	6	18.850	28.274
4	8	25.133	50.265
5	10	31.416	78.540
10	20	62.832	314.159
20	40	125.664	1256.637

Note: Values are shown to 3 decimal places. Units depend on your input (if radius is in cm, area is in cm squared).

Circle Formulas and Concepts

Area Formula: A = pi r squared

The area of a circle equals pi times the radius squared. Pi (approximately 3.14159) is the ratio of circumference to diameter for any circle. This formula has been known since ancient times. Archimedes proved it by approximating circles with polygons.

Circumference Formula: C = 2 pi r

The circumference (perimeter) of a circle equals 2 times pi times the radius. Since diameter equals 2r, you can also write this as C = pi d. The circumference is always a bit more than 3 times the diameter.

Diameter and Radius Relationship

The diameter is always twice the radius. The radius extends from center to edge. The diameter spans edge to edge through the center. All radii of a circle have equal length. All diameters of a circle have equal length.

Real-World Applications

Construction and landscaping

Calculate materials for circular patios, round foundations, or circular gardens. Find how much edging material you need (circumference) and how much surface area to cover.

Manufacturing and engineering

Determine material requirements for circular parts, calculate cross-sectional areas of pipes and wires, or find the surface area of cylindrical objects.

Education and homework

Students learning geometry can verify their calculations and understand the relationships between radius, diameter, circumference, and area.

Frequently Asked Questions

What is pi and why is it used?

Pi is a mathematical constant approximately equal to 3.14159. It represents the ratio of any circle's circumference to its diameter. Pi is irrational, meaning its decimal representation never ends or repeats. It appears in formulas for circles, spheres, waves, and many areas of mathematics and physics.

How do I find the radius if I know the area?

Rearrange the area formula: r = square root of (A / pi). For example, if area is 78.54 square units, divide by pi to get 25, then take the square root to find radius equals 5 units.

What's the difference between circumference and perimeter?

Perimeter is the general term for the distance around any shape. Circumference specifically refers to the perimeter of a circle. For polygons, we say perimeter. For circles, we say circumference.

Can I use diameter instead of radius?

Yes. Since diameter equals 2 times radius, you can use A = pi times (d/2) squared, which simplifies to A = (pi times d squared) / 4. Many people find it easier to measure diameter directly.

Why does area use square units?

Area measures two-dimensional space. When you multiply radius by radius (r squared), you're multiplying length times length, which gives square units. If radius is in meters, area is in square meters.

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