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Convert visual mags/arcsecond² to cd/m²
0.00 mag/arcsec²=1.080×105 cd/m²
=1.080×108 mcd/m²
=1.080×1011 µcd/m² ( 108000000000.00 µcd/m² )

Using the formula:
[value in cd/m2] = 10.8×104 × 10(-0.4*[value in mag/arcsec2])

OpenOffice formula: =108000*POWER(10;(-0.4*mags))
MS-Excel formula: =108000*POWER(10,(-0.4*mags))
  Where mags is the cellname that contains the mag/arcsec2 reading.


Convert cd/m² to visual mags/arcsecond²

Using the formula:
[value in mag/arcsec2] = Log10([value in cd/m2]/108000)/-0.4

OpenOffice formula: =(LOG(cdm2/108000))/-0.4))
  Where cdm2 is the cellname that contains the cd/m2 reading.

 
This formula was derived from conversations on the Yahoo-groups darksky-list
Topic: [DSLF]  Conversion from mg/arcsec^2 to cd/m^2
Date range: Fri, 1 Jul 2005 17:36:41 +0900 to Fri, 15 Jul 2005 08:17:52 -0400
 PDF summary of conversation.

Percentages to mpsas to percentages
 


The direction of darkening/lightening is included the calculation. For example:
  an increase of 0.5mpsas is 36.90% darker.
   a decrease of 0.5mpsas is 58% brighter.

You can use the following formulas:

Percent to mpsas:
 mpsas =-2.5*LOG(1 + pct)
Ex. for darkening of 36.9%:
 mpsas = -2.5*log(1 - 0.369)
       = .5 mpsas

mpsas to percent:
10^(mpsas/-2.5)-1
(Open office formula)  POWER(10,(mpsas/-2.5))-1
Ex. for darkening of 0.5mpsas:
  pct = 10^(0.5/-2.5)-1
      = 10^(-0.2)-1
      = 0.631 -1
      = -36.9%