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.
Related Topics

Electrical
Electrical engineering with units, amps and electrical wiring. Wire gauges, electrical formulas, motors and more. 
Mathematics
Mathematical rules and laws  numbers, areas, volumes, exponents, trigonometric functions and more.
Related Documents

Area of Intersecting Circles
Calculate area of intersecting circles 
Area Survey App
Online app that can be used to make an exact plot of a surveyed area  like a room, a property or any 2D shape. 
Area Units Converter
Convert between units of area. 
Circles  Circumferences and Areas
Circumferences and areas of circles with diameters in inches. 
Circles Outside a Circle
Calculate the numbers of circles on the outside of an inner circle  like the geometry of rollers on a shaft. 
Discrete Data Sets and their Mean, Median and Mode Values
Calculate the arithmetic mean, median and modal values from discrete data sets. 
Elementary Curves
Ellipse, circle, hyperbola, parabola, parallel, intersecting and coincident lines. 
Elementary Surfaces
Ellipsoid, sphere, hyperboloid, cone and more. 
Equal Areas  Circles vs. Squares
Radius and side lengths of equal areas, circles and squares. 
Length of a Spiral
Calculate the length of a spiral or the length of material contained in a roll. 
Smaller Circles within a Large Circle  Calculator
Calculate the number of small circles that fits into an outer larger circle  ex. how many pipes or wires fits into a larger pipe or conduit. 
Smaller Rectangles within a Larger Rectangle
The maximum number of smaller rectangles  or squares  within a larger rectangle (or square). 
Solving Equations of the First Degree with One Unknown
Equations with one unknown. 
Solving First Degree Equations with Two Unknowns
Online calculator and solbing procedure for two equations with two unknowns. 
Solving Quadratic Equation with One Unknown
How to solve a quadratic equation. 
Squaring with Diagonal Measurements
A rectangle is square if the lengths of both diagonals are equal.