# Req: Calculating Preferred Values ("E" Series")

#### D4Ve

Jan 7, 2011
3
Hi folks

I'm a newbie to the forum, so be nice to me

I was trying to write some Python script to calculate resistor values, and wanted to automatically generate lists of the preferred ranges of resistor values (E6, E12, E24 etc.).

From what I've been able to find by reading & Googling, the "E series" are logarithmic series / geometric series in which each decade is divided into E values, and the value of its n-th member may be calculated using the formula:

10^(n/E)

So for the E12 series, this should give values (with rounding & to 2 sig figures) of:
10,12,15,18,22,26,32,38,46,56,68,83

However, the E12 series for resistors actually goes:
10,12,15,18,22,27,33,39,47,56,68,82

What is the reason for the discrepancy?
Is it a quirk of history, or do I need to check my sums?

Many thanks in anticipation

Dave
(Swansea,UK)

#### Resqueline

Jul 31, 2009
2,848
Hi Dave, welcome to the forums!

I've noticed that discrepancy myself, and I have no other explanation for it other than a quirk of history, but it would be interesting to know the reason behind those #'s.

Take the awg tables for instance. It's based on some quirky logic/math/reasoning from the 1800's but how sensible/practical is it in everyday use nowadays?

#### D4Ve

Jan 7, 2011
3
Thanks for the quick reply Resqueline.

I've been doing some more research...

The formula that I quoted only seems to be a rough guide.
The reasons behind the commercially used number series are unclear, and there doesn't seem to be a simple formula or algorithm linking all of the elements in the series which will facilitate their generation by a computer program.

Dave

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,505
The issue gets even more odd when you look at E24, E48, E96, E192, etc. You might expect that each one would slot in values in the gaps left by the previous series, but that doesn't happen.

See here. And as you pointed out, the differences are much greater with some values as others.

I think the issue is that E3 and E6 came first and values were just slotted in for E12 and E24, but the errors became too high to do that with E48, and above so the values were recalculated. (That's my guess anyway)

#### D4Ve

Jan 7, 2011
3
Thanks Steve

I found an interesting article on Wikipedia:
http://en.wikipedia.org/wiki/Preferred_number

Sadly no answer to my question in this article, but it was interesting to discover that preferred values don't just apply to electronic components. Lots of everyday items (from the coins in my pocket to wine bottles, pen nibs and camera settings) are also based on geometric series, usually with a common factor of 2 or a root of 2.
However, as with the E series, they don't always follow the calculated values either!

Best wishes

Dave

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,505
Yes, I am also familiar with f-stops on cameras where the the number refers to the ratio between the focal length and the apparent aperture. The numbers used are not the closest to the ones you would calculate, however the *actual* values the represent are!

In that case the numbers can't change because people know what they are(!) but the camera equipment would not function correctly if they were the actual sequence used (ignoring the fact that unless you set the aperture manually, the camera is typically free to use whatever aperture it wants to between the stops.

Of some geeky interest is that there were 2 series in use before they were standardised. I have never researched what happened with resistors prior to the E3 series.

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