Rectangles to Cover a Circle

The Rectangles to Cover a Circle calculator computes the number of rectangles needed to cover a circle based on the diameter of the circle and the length and width of the rectangles.

INSTRUCTIONS: Choose units and enter the following:

• (D) Diameter of Circle
• (L) Length of Rectangle
• (W) Width of Rectangle

Rectangles to Cover a Circle (nR): The results the following:

• (n) Number of rows of rectangles
• (nRec) Total Number of Rectangles using partial rectangle on the end (trimmings)
• (TL) Total Length of trimmed rectangles
• (xTrim) Total Number of Rectangles if only whole rectangles can be used.
• (Rn) Length of individual rows of rectangles.

Note: the length value above is returned in meters.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The Rectangles to Cover a Circle algorithm steps down a circle and computes the number of rows based on the width and then the ideal length of each row to cover the circle fully.  This algorithm provides BOTH the number of rectangles need:

1. assuming the reuse of trimmed rectangle pieces and,
2. assuming trimmed pieces are discarded.

Circle Calculators

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• 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. 
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• 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.
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• Circle Radius from Chord - Computes the radius of a circle based on the length of a chord and the chord's center height.
• Circle Equation from Center and one Point - 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 Equation from Three Points: Develops the general equation of a circle that goes through three points that are not in a straight line.
• 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.
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