Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

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Circles within a Rectangle

The maximum number of circles possible within a rectangle - ex. numbers of pipes or wires in a conduit

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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.

w - rectangle width (in, mm, m)

h - rectangle height (in, mm, m)

d - circle diameter (in, mm, m)

s - space between circles - and between circles and rectangle walls (in, mm, m)


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Rectangular Pattern

 

Triangular Pattern

 

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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Unit Converters

Temperature

oC
oF


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Length

m
km
in
ft
yards
miles
naut miles


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Area

m2
km2
in2
ft2
miles2
acres


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Volume

m3
liters
in3
ft3
us gal


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Weight

kgf
N
lbf


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Velocity

m/s
km/h
ft/min
ft/s
mph
knots


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Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O


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Flow

m3/s
m3/h
US gpm
cfm


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