The Circumference from the Area of a Circle calculator computes the circumference of a circle based on the circle's area (A).
INSTRUCTIONS: Choose your preferred area units and enter the following:
- A - the Area of the circle
Circumference: The calculator returns the circumference (C) in meters. However, this can be automatically converted to other length units via the pull-down menu.
The Math
The formula for the circumference of a circle from the area is as follows:
`c = 2π·sqrt(A/π)`
where:
- c is the circumference of the circle
- A is the area of the circle.
A circle is the set of all points equal in distance from a center point. This formula uses a form of the equation for the area of a circle to compute the circumference.
- Area: A = π • r2 .
- Therefore we know that `r = sqrt(A/pi)`.
- We also know that circumference of a circle is a function of the radius (C = 2 • π • r),
- therefore: `c = 2 * pi * sqrt(A/pi)`
Uses
If you know the area you wish to enclose, in a circular fence for example, this formula will tell you the circumference of the circle which is the length of the fence.
Circle Calculators
- Circle Area - Computes the area of a circle given the radius (A = π r2).
- Area of Circle Arc Segment f(r,θ) - Computes the area of an arc segment of a circle given the radius (r) and angle (θ)
- Area of Circle Arc Segment Area f(r,h) - Computes the area of an arc segment of a circle given radius (r) and the depth (h) into the circle.
- Area of Circle Sector f(r,Θ) - Computes the area of a sector (pie slice) of a circle given the radius (r) and angle (Θ).
- Angle of Circle Sector f(r,h) - Computes the angle in a circle from the radius and depth of the chord.
- Area of Circle Annulus - Computes the area of an annulus (ring) given the inner radius (r) and outer radius (R).
- Radius of Circle from Center and a Point - Computes the radius of a circle given the center point (h,k) and any other point (x,y) on the circle.
- Circumference of Circle - Computes the circumference of a circle given the radius (C = 2 π r).
- Circle Arc Length - Computes the length of an arc length on a circle given the radius (r) and angle (Θ)
- Circle within a Triangle - Computes the radius of a circle inscribed within a triangle given the length of the three sides (a,b,c) of the triangle.
- Circle around a Triangle - Computes the radius of a circle that circumscribes a triangle given the length of the three sides (a,b,c) of the triangle.
- Circle Diameter from Area - Computes the radius and diameter of a circle from the area.
- Circle Radius from Circumference - Computes the radius of a circle given the circumference.
- Circle Circumference from Area - Computes the circumference of a circle given the area.
- Circle Radius from Area - Computes the radius of a circle given the area.
- Chord Length: Computes the length of a chord in a circle from the radius and height.
- Circle Radius from Chord - Computes the radius of a circle based on the length of a chord and the chord's center height.
- Equation of Circle from Center and Point Coordinates - Develops the general equation of a circle based on the coordinates of the center (h,k) and any point on the circle (x,y).
- Circle with same Perimeter as an Ellipse - Computes the radius of the circle with the same perimeter of an ellipse defined by the semi-major and semi-minor axes.
- Rectangles to Cover a Circle - Computes the number of rectangles needed to minimally cover a circle based on the circle's diameter and the length and width of the rectangles.