Circles within a Rectangle  Calculator
Calculate the maximum number of circles within a rectangle  can be used to calculate the numbers of pipes or wires in a conduit or similar.
The calculator below estimates the maximum number of circles that may fit within a rectangle. The calculator can be used to calculate
 the number of pipes  or wires  that fits within a conduit or similar applications
Input the rectangle inside dimensions  height and width and the circles outside diameters.
Default values are for 0.5 inch circles inside a 10 inch x 10 inch square. The calculator is generic and any kind of units can be used  as long as the same units are used for all values.
Rectangular Pattern
Rectangular Pattern  Circle Coordinates
Copy and paste the circle center coordinates to your application. x = 0 and y = 0 is top left corner of rectangle.
x y
Tip!  the values can be adapted and modified in excel or in a text editor for use in a CNC Gcode generator or similar.
Triangular Pattern
Triangular Pattern  Circle Coordinates
Copy and paste the circle center coordinates to your application. x = 0 and y = 0 is top left corner of rectangle.
x y
Be aware!  The algorithm is quite simple  switching rectangle width and height may influence the number calculated. Switching the input values above changes the layout and gives
Note!  with some combinations of rectangular shapes and circle sizes  one or two more circles  or even more  may be added with a modified layout of the circles. In the default triangular example above  two more circles can be added in between if the left and right bottom circles are moved to the left and right border. The algorithm used for the calculation is quite simple and may underestimate the number of circles in some cases.
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