Compute area, circumference and diameter of any circle.
Enter any one value — radius, diameter, circumference, or area — and the rest are calculated automatically.
Radius
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Diameter
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Circumference
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Area
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Using π = 3.14159265359
The Circle Calculator computes all four circle properties — radius, diameter, circumference, and area — from any single input. Enter a value in any field and the calculator instantly fills in the other three. This bidirectional computation makes it useful for any circle problem, whether you are given the radius and need the area, or given the circumference and need the diameter.
d = 2r (diameter is twice the radius)
C = 2πr = πd
A = πr² = π × (d/2)²
Find area from radius: r = 5. A = π × 5² = 25π ≈ 78.54.
Find circumference from diameter: d = 10. C = π × 10 ≈ 31.42.
Find radius from area: A = 153.94. r = √(153.94 ÷ π) = √49 = 7.
Find diameter from circumference: C = 62.83. d = 62.83 ÷ π ≈ 20.
π is one of the most famous constants in mathematics. Defined as the ratio of a circle\'s circumference to its diameter, π ≈ 3.14159265359... It is an irrational number, meaning its decimal expansion never terminates and never repeats. It is also transcendental, meaning it is not the root of any polynomial with rational coefficients — a fact proven in 1882 that also proves the impossibility of "squaring the circle" with compass and straightedge.
Throughout history, mathematicians have computed π to ever-greater precision. Archimedes estimated it as 22/7 ≈ 3.1429 using inscribed and circumscribed polygons. Chinese mathematician Zu Chongzhi computed it as 355/113 ≈ 3.1415929 in the 5th century, accurate to 7 digits — a record that stood for 800 years. Today, π has been computed to over 100 trillion digits using supercomputers, though only about 39 digits are needed to calculate the circumference of the observable universe to within the width of a hydrogen atom.
Circles are everywhere in engineering, physics, and design. Wheels, gears, pipes, wires, and lenses all rely on circular geometry. The cross-sectional area of a pipe determines its flow rate (πr²); the circumference of a wheel determines how far it travels per revolution (2πr); the area of a circular lens determines how much light it collects. Even fields like economics borrow circular concepts: the "unit circle" in complex analysis underpins much of signal processing and quantum mechanics.
In education, the circle is where students first meet π and where the relationship between algebra and geometry becomes vivid. The formula A = πr² is one of the first non-trivial formulas involving π that students learn, and it sets the stage for the integral calculus derivation of the same formula (integrating thin concentric rings from 0 to r). Mastering circle calculations is therefore both practically useful and mathematically foundational.
Area = π × r², where r is the radius. Equivalently, Area = π × (d/2)² where d is diameter.
Circumference = 2 × π × r = π × d. It is the perimeter of the circle.
π ≈ 3.14159265359. It is an irrational number (never terminates or repeats). For most calculations, 3.1416 or 22/7 is accurate enough.
Diameter = 2 × radius. The radius is the distance from center to edge; the diameter is the full width across the circle passing through the center.
r = √(Area ÷ π). For example, if area = 78.54, then r = √(78.54/π) = √25 = 5.
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