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How ArcMap calculates proportional symbol s...   Tim Haverland Feb 20, 2007
Re: How ArcMap calculates proportional symb...   Garrett Davis Mar 08, 2007
Re: How ArcMap calculates proportional symb...   Tim Haverland Mar 08, 2007
Re: How ArcMap calculates proportional symb...   Tim Haverland Mar 12, 2007
Re: How ArcMap calculates proportional symb...   Ted Mellnik Feb 06, 2008
Re: How ArcMap calculates proportional symb...   vincent leroux Jul 16, 2009
Re: How ArcMap calculates proportional symb...   Dan Eck Aug 08, 2009
Re: How ArcMap calculates proportional symb...   Dan Eck Sep 25, 2009
Re: How ArcMap calculates proportional symb...   Dan Eck Sep 25, 2009
Re: How ArcMap calculates proportional symb...   Barbara Schneider Oct 15, 2009
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Subject How ArcMap calculates proportional symbol sizes 
Author Tim Haverland 
Date Feb 20, 2007 
Message Ever wonder how ArcMap calculates proportional symbol sizes? The key is that the area of the symbols is proportional to the data values; i.e., the size in points is proportional to the square root of the data values (see below for the special case of Flannery Appearance Compensation).

Here ya go! No more trial and error!

Normal case:
Pj = (Valj/ValMin)^0.5 * Pmin

Flannery Appearance Compensation case:
Pj = 1.0083 * (Valj/ValMin)^0.5716 * Pmin

Where:
Pj = point size of the j'th feature
Valj = value of the j'th feature
ValMin = minimum value
Pmin = minimum point size
^0.5 is to the power of 0.5 (square root)
^0.5716 is to the power of 0.5716

Based on these equations, you can also determine the minimum point size needed to standardize the symbol sizes for two layers that have different minimums for the symbolized field:

Normal case:

PminB = (VminB/VminA)^0.5 * PminA

Flannery Appearance Compensation case:

PminB = 1.0083 * (VminB/VminA)^0.5716 * PminA

Where:
PminB = minimum point size for layer B
VminB = minimum data value for layer B
VminA = minimum data value for layer A
PminA = minimum point size for layer A

For example, given layer A has a minimum pt size of 2 and a minimum value of 10; if layer B has a minimum value of 20 then the minimum point size for layer B should be:

Normal case: (20/10)^0.5 * 2 = 2.83
Flannery: 1.0083 * (20/10)^0.5716 * 2 = 3.0

With these minimum point sizes the values in layer A will be symbolized in the same proportion as those in layer B.

Hope this helps someone!

Tim
NOAA Fisheries
Silver Spring, MD

References:

Flannery J (1971). “The Relative Effectiveness of Some Common Graduated Point Symbols in the Presentation of Quantitative Data.” Canadian Cartographer, 8(2), 96–109.

Tanimura S (2006). “Proportional Symbol Mapping in R.” Journal of Statistical Software, 15(5), 1-5. http://www.jstatsoft.org/v15/i05/v15i05.pdf 
   
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Subject Re: How ArcMap calculates proportional symbol sizes 
Author Garrett Davis 
Date Mar 08, 2007 
Message Hi,

Thanks, I need this formula for what Im doing.
How are the proportional bar charts calculated? . How could I apply this methodology to the Proportional Bar Charts symbology?You can only choose the maxiumum size for the bar representing the largest data value.

Thanks,

Garrett
UNC Chapel Hill Environmental Finance Center 
   
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Subject Re: How ArcMap calculates proportional symbol sizes 
Author Tim Haverland 
Date Mar 08, 2007 
Message For circles, the size in points is proportional to the square root of the data value. For bars the length of the bar in points should be directly proportional to the data value.

So the eqs would be:

Pj = (Valj/ValMax) * Pmax

and

PmaxB = (VmaxB/VmaxA) * PmaxA

Works on paper ... check it out with ArcGIS and let me know what you find out.

Tim
 
   
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Subject Re: How ArcMap calculates proportional symbol sizes 
Author Tim Haverland 
Date Mar 12, 2007 
Message I checked the formulas and they work with ArcMap. One note: to get the bar chart symbols to match perfectly between two layers, you'll also have to standardize the symbols' width and depth in both layers (rt.click on layer>Properties>Symbology tab>Properties... button). 
   
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Subject Re: How ArcMap calculates proportional symbol sizes 
Author Ted Mellnik 
Date Feb 06, 2008 
Message Does min mean non-zero min?
--
Ted Mellnik
tmellnik@charlotteobserver.com 
   
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Subject Re: How ArcMap calculates proportional symbol sizes 
Author vincent leroux 
Date Jul 16, 2009 
Message Hi guys,

I've tested the formula given by Tim (thanks for it !) and I've noticed that it can't be used to create manually a legend in the layout view...

Although the result of the formula are right when you check it with point of a certain size within the map, it doesn't work in the layout view...

Say if I want to manually create a legend, I use the formula to find the size I should use for a given value. When it's done and I'm dragging the result over the data frame view to check if the size a correct, they are not !!

There is therefore a major problem here... 
   
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Subject Re: How ArcMap calculates proportional symbol sizes 
Author Dan Eck 
Date Aug 08, 2009 
Message Okay,

Before I read your post, I modified my data so that each field had the same min(0) and max (75000) values. When I plot the data, however, the circles for my second data set is smaller than my other two data sets. I started with an intial layer and copied it to create two additional layers and then changed which field plotted in the two new layers. For some reason the circles for the second set of data has a smaller circle for the same max value (75000) than the other two data sets / layers. 
   
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Subject Re: How ArcMap calculates proportional symbol sizes 
Author Dan Eck 
Date Sep 25, 2009 
Message What does ArcMap do when the minimum value is zero? If the min value is zero, the ratio goes to infinity. 
   
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Subject Re: How ArcMap calculates proportional symbol sizes 
Author Dan Eck 
Date Sep 25, 2009 
Message Looks like ArcGIS must use the minimum value > 0 in the equation. Since I am bringing my data in via Excel, I'm able to add a dummy record that is the minimum value > 0 for all the data layers being plotted.

It would be nice if in the proportional dialog box ArcGIS allow the usere to input a minimum value to define the proportional symbol size rather than having to manipulate the input data. 
   
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Subject Re: How ArcMap calculates proportional symbol sizes 
Author Barbara Schneider 
Date Oct 15, 2009 
Message Hi Tim,

this is exactly what I was looking for! I implemented it and it works great.

Thanks,
Barbara
ESRI Switzerland