Circle Calculator
Please provide any value below to calculate the remaining values of a circle.
Definition of a Circle
A circle is a simple closed shape. It is the set of all points in a plane that are at a given distance from a given point, the center; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any point of the circle and the center is called the radius.
Parts of a Circle
- Center (or origin): The point from which all points on the circle are equidistant.
- Radius: The distance from the center to any point on the circle.
- Diameter: A line segment that passes through the center and has both endpoints on the circle. It is twice the length of the radius.
- Circumference: The perimeter or boundary of the circle.
- Arc: A portion of the circumference of a circle.
- • Major arc: An arc that is greater than a semicircle.
- • Minor arc: An arc that is less than a semicircle.
- Chord: A line segment whose endpoints both lie on the circle.
- Secant: A line that intersects the circle at exactly two points.
- Tangent: A line that touches the circle at exactly one point.
- Sector: A region bounded by two radii and an arc.
- • Major sector: A sector that is greater than a semicircle.
- • Minor sector: A sector that is less than a semicircle.
The Constant π
The ratio of a circle's circumference to its diameter, denoted by the Greek letter π (pi), is a mathematical constant approximately equal to 3.14159. The number π appears in many formulas across mathematics and physics. It is an irrational number, meaning it cannot be expressed exactly as a ratio of two integers, although fractions such as 22/7 are commonly used to approximate it.
The number π is also a transcendental number, meaning it is not the root of any non-zero polynomial equation with rational coefficients. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge.
The ancient problem of "squaring the circle" involved constructing a square with the same area as a given circle using only a finite number of steps with compass and straightedge. In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that π is a transcendental number. That is, π is not the root of any polynomial with rational coefficients. It had been known for decades that the construction would be impossible if π were transcendental, but π was not proven transcendental until 1882. Approximate constructions with any given non-perfect accuracy exist, and many such constructions have been found.
Circle Formulas
where:
- R: Radius
- D: Diameter
- C: Circumference
- A: Area
- π: 3.14159...