Circle Area Calculator
Area and circumference of a circle from its radius.
Input sheet
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Pizzas, pipes, garden ponds, and round tabletops all come down to the area and circumference of a circle, both of which follow directly from the radius.
How it works
Area is pi × radius²; circumference is 2 × pi × radius.
Area grows with the square of the radius, so doubling the radius quadruples the area — a 16-inch pizza has four times the food of an 8-inch one, not twice. Circumference, by contrast, grows in direct proportion to the radius.
Both formulas use pi (π ≈ 3.14159), the constant ratio of any circle's circumference to its diameter.
Area = π × radius²; circumference = 2 × π × radius
Worked examples
A circle with a radius of 5. → ≈ 78.54 square units
π × 5² = π × 25 ≈ 78.54; circumference is 2 × π × 5 ≈ 31.42.
A 14-inch-diameter pizza (radius 7). → ≈ 153.94 square inches
π × 7² = π × 49 ≈ 153.94 square inches of pizza.
Tips & gotchas
- If you have the diameter instead of the radius, halve it first — the radius is half the diameter.
- Because area scales with the square of the radius, comparing round items by diameter is misleading; compare by area.
- For a quick estimate, area ≈ 3.14 × radius²; use the full π for precision work.
FAQ
What is the difference between radius and diameter?
The radius runs from the center to the edge; the diameter runs all the way across through the center and equals twice the radius.
Why does doubling the radius quadruple the area?
Area depends on radius squared. Doubling the radius multiplies the area by 2², which is 4.
What value of pi does this use?
It uses the full-precision constant π ≈ 3.14159265, so results are exact to the displayed decimals.
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