Geometry Circle 360 Degrees Calculator

This calculator helps you calculate various properties of a circle when the angle is 360 degrees. Whether you need to find the circumference, area, or sector area, this tool provides quick and accurate results with clear explanations.

What is Circle Geometry?

Circle geometry is a branch of mathematics that deals with the properties and relationships of circles. A circle is a set of all points in a plane that are at a given distance (radius) from a given point (center). When the angle is 360 degrees, the circle is complete, and you can calculate its full circumference and area.

Key Terms

Radius (r): The distance from the center to any point on the circle.

Diameter (d): The distance across the circle through the center (d = 2r).

Circumference (C): The perimeter of the circle.

Area (A): The space enclosed by the circle.

Key Formulas

Here are the essential formulas for circle geometry when the angle is 360 degrees:

Circumference

C = 2πr

Where:

C = Circumference
π (pi) ≈ 3.14159
r = Radius

Area

A = πr²

Where:

A = Area
π (pi) ≈ 3.14159
r = Radius

Sector Area

A_sector = (θ/360) × πr²

Where:

A_sector = Sector Area
θ = Central angle in degrees (360 for full circle)
π (pi) ≈ 3.14159
r = Radius

How to Use This Calculator

Using this calculator is simple. Follow these steps:

Enter the radius of the circle in the input field.
Select the units (centimeters, meters, inches, etc.).
Click the "Calculate" button to see the results.
Review the calculated values for circumference, area, and sector area.
Use the "Reset" button to clear the inputs and start over.

Note

All calculations are based on the assumption that the angle is 360 degrees, which means the sector area is equal to the full area of the circle.

Examples

Let's look at a few examples to see how the calculator works.

Example 1: Small Circle

If the radius is 5 cm:

Circumference: 2 × π × 5 ≈ 31.42 cm
Area: π × 5² ≈ 78.54 cm²
Sector Area (360°): π × 5² ≈ 78.54 cm²

Example 2: Medium Circle

If the radius is 10 meters:

Circumference: 2 × π × 10 ≈ 62.83 meters
Area: π × 10² ≈ 314.16 meters²
Sector Area (360°): π × 10² ≈ 314.16 meters²

Example 3: Large Circle

If the radius is 100 inches:

Circumference: 2 × π × 100 ≈ 628.32 inches
Area: π × 100² ≈ 31415.93 inches²
Sector Area (360°): π × 100² ≈ 31415.93 inches²

FAQ

What is the difference between circumference and area?

Circumference is the distance around the circle, while area is the space enclosed by the circle. They are calculated using different formulas and have different units.

Can I calculate the radius from the circumference?

Yes, you can rearrange the circumference formula to solve for radius: r = C / (2π).

What is the sector area when the angle is 360 degrees?

The sector area is equal to the full area of the circle when the angle is 360 degrees.

How accurate are the calculations?

The calculations use π (pi) with a precision of 15 decimal places to ensure accuracy.