Circle Calculator
Calculate the area, circumference, diameter, and arc length of a circle from radius, diameter, or circumference.
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How to use this calculator
All circle measurements derive from the radius using π ≈ 3.14159265.
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Select which measurement you already know (radius, diameter, circumference, or area).
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Enter its value.
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All other circle measurements are calculated automatically.
Frequently asked questions
What is π (pi)?
Pi (π) is the ratio of any circle's circumference to its diameter. It is approximately 3.14159265... and is irrational (never-ending, non-repeating decimal). It appears not just in circles but throughout mathematics, physics, and engineering.
What is the difference between circumference and perimeter?
Circumference specifically refers to the perimeter of a circle (or ellipse). Perimeter is the general term for the total boundary length of any 2D shape. Circumference = 2πr.
How do I find the area of a semicircle?
Area of semicircle = πr² / 2. Perimeter of semicircle = πr + 2r (the curved arc plus the diameter). This comes up in architecture (arched doorways, tunnels) and physics (cross-sections of pipes).
How is circle area used in real life?
Pizza size (πr² determines how much pizza you get — a 16-inch pizza has 4× the area of an 8-inch), land surveying, pipe cross-sections (flow rate ∝ r²), wheel rotation, and any cylindrical container volume (V = πr²h).
Circle calculations with π
Why area grows as r² but circumference grows as r
Doubling the radius quadruples the area but only doubles the circumference. A pizza with 14-inch diameter has 3.06× more area than a 8-inch pizza — not 1.75× as the diameter ratio suggests. Always compare pizza sizes by area, not diameter.
Arc length and sector area
For a sector with central angle θ (in degrees): Arc length = 2πr × θ/360; Sector area = πr² × θ/360. A 90° sector (quarter circle) has area = πr²/4 and arc length = πr/2. These formulas appear in engineering, robotics (rotation arcs), and clock face design.
Circles in coordinate geometry
The equation of a circle with center (h, k) and radius r is (x−h)² + (y−k)² = r². A circle centered at the origin: x² + y² = r². These forms are used in GPS, radar systems, and collision detection in games.
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