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.  

1. Area:  A = π • r² .  
2. Therefore we know that `r =  sqrt(A/pi)`.  
3. We also know that circumference of a circle is a function of the radius (C = 2 • π • r), 
4. 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.

Related Calculators:

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• Area of Annulus- This computes the area of an annulus (ring) given the inner radius (r) and outer radius (R).
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• Arc Lengths - This computes the length of a cord segment (arc length) on a circle given the radius (r) and angle (Θ)
• Circle within a Triangle -  This 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 - This computes the radius of a circle that circumscribes a triangle given the length of the three sides (a,b,c) of the triangle.
• Radius from Circumference - This computes the radius of a circle given the circumference.
• Circumference from Area - This computes the circumference of a circle given the area.
• Radius from Area - This computes the radius of a circle given the area.
• Radius from Cord-  This computes the radius of a circle based on the length of a cord and the cord's center height.