Circumference and Area of a Circle Calculator
Calculate circle circumference, area, radius, and diameter with step-by-step solutions
Circle Calculator
Distance from center to edge
Distance across circle through center
Perimeter around the circle
Space inside the circle
Circle Measurements
Step-by-Step Solution
Example Calculation
Problem
Find the circumference and area of a circle with an 8 cm radius.
Solution
Given: Radius (r) = 8 cm
Formula for circumference: c = 2πr
Calculate: c = 2 × π × 8 = 16π ≈ 50.265 cm
Formula for area: A = πr²
Calculate: A = π × 8² = 64π ≈ 201.06 cm²
Circle Formulas
Circumference
Area
Radius
About π (Pi)
Understanding Circle Measurements
Circle Properties
A circle is a perfectly round shape where every point on the edge is exactly the same distance from the center. This distance is called the radius, and it's fundamental to calculating all other circle measurements.
Key Relationships
- •Diameter = 2 × Radius: The diameter is always twice the radius
- •Circumference ∝ Radius: Circumference increases proportionally with radius
- •Area ∝ Radius²: Area increases with the square of the radius
- •c = 2√(πA): Circumference and area are related through this formula
Common Applications
- •Architecture: Designing circular buildings, domes, and arches
- •Engineering: Calculating pipe capacities and wheel dimensions
- •Agriculture: Determining irrigation coverage areas
- •Manufacturing: Designing circular parts and components
Fun Fact: If you could wrap a string around the Earth's equator and then add just 1 meter to its length, the string would stand about 16 cm (6 inches) off the ground all the way around!
Quarter Circle Calculations
Quarter Circle Area
The area of a quarter circle is simply one-fourth of the full circle area:
Quarter Circle Perimeter
The perimeter includes the arc plus two radii: