# What is the reason that the value "47" is so popular in electrical engineering?

We often see component values of 4.7K Ohm, 470uF, or 0.47uH. For example, digikey has millions of 4.7uF ceramic capacitors, and not a single 4.8uF or 4.6uF and only 1 listed for 4.5uF (specialty product).

What's so special about the value 4.7 that sets so far apart from say 4.6 or 4.8 or even 4.4 since in the 3.. series we usually 3.3,33, etc. How did these numbers come to be so entrenched? Perhaps a historical reason?

• @MichaelKjörling: that's funny, when I saw the title of this question I immediately thought of the ST:VOY episode where Neelix overhears and uses "Engineering authorization Omega-4-7" - never realized the use of 47 was so deliberate. Commented May 4, 2013 at 5:09
• The number 47 comes up in almost every episode of TNG and Voyager. I'm not quite geeky enough to know the backstory on that, but maybe it's related to this question. Commented Aug 1, 2014 at 4:40
• @KevinKrumwiede this seems to be an explanation, although I don't think it's the EE answer Commented Sep 15, 2014 at 0:29
• – user107801
Commented Jul 1, 2016 at 19:33
• Is it something like 1:2:2:5 Ratio used in weight-box and the antique "Resistance-Box" ? (read telephonecollecting.org/resistance.html A typical box may contain coils with the following numbers of ohms: 1, 2, 2, 5, 10, 20, 20, 50, 100, 200, 200, 500, up to 10,000 in some boxes")
– user107801
Commented Jul 1, 2016 at 19:45

Due to resistor colour-coding bands on leaded components two-significant digits were preferred and I reckon this graph speaks for itself: -

These are the 13 resistors that span 10 to 100 in the old 10% series and they are 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82, 100. I've plotted the resistor number (1 to 13) against the log of resistance. This, plus the desire for two-significant digits, looks like a good reason. I tried offsetting a few preferred values by +/-1 and the graph wasn't as straight.

There are 12 values from 10 to 82 hence E12 series. There are 24 values in the E24 range.

EDIT - the magic number for the E12 series is the 12th root of ten. This equals approximately 1.21152766 and is the theoretical ratio the next highest resistor value has to be compared to the current value i.e. 10K becomes 12.115k etc.

For the E24 series, the magic number is the 24th root of ten (not suprisingly)

It's interesting to note that a slightly better straight line is got with several values in the range reduced. Here are the theoretical values to three significant digits: -

10.1, 12.1, 14.7, 17.8, 21.5, 26.1, 31.6, 38.3, 46.4, 56.2, 68.1 and 82.5

Clearly 27 ought to be 26, 33 ought to be 32, 39 ought to be 38 and 47 ought to be 46. Maybe 82 should be 83 as well. Here's the graph of traditional E12 series (blue) versus exact (green): -

So maybe the popularity of 47 is based on some poor maths?

• The value "33" seems a bit curious, since sqrt(10) is 3.1622. If in addition to the "smooth" series there were also values which were nominally centered on "2.000" and "5.000", then it would make sense to have a value which was nominally centered on "3.000" and "3.333" [so as to allow some nice whole-number ratios of nominal values], but the series doesn't seem to allow any nice whole-number ratios. Commented May 3, 2013 at 15:23
• It's not about integers at all. The same sequence going from 1 to 10 instead of from 10 to 100 will have fractional digits. The issue is trying to stay to two significant figures, not integers. Commented May 3, 2013 at 19:33
• @supercat FWIW, it was E6 that was used in the first place; IMO the (still arguably most common) values 10 15 22 33 were chosen for simplicity. Although 10^1/6 = 1.47..., taking those exact values gave us 10/15 = 22/33 = 2/3; 33/100 = 1/3 (great when simple R ratios are needed); because all of those values were significantly rounded up (with 33 rounded almost 5%), it follows that also 46 should be moved up a bit to compensate for this, at the same time giving a value that's a bit nearer to 50. Further (E12, E24 etc.) numbers were used to match the spaces that were already there.
– user20088
Commented Oct 20, 2016 at 14:08
• The selected 47 and 33 quite possibly are preferred over the calculated 46 and 32, because to get the venerable "50" you could use 47 + 3.3 = 50.3 (.6%), whereas 46 + 3.2 = 49.2 (1.6%) Commented Jun 25, 2020 at 20:45
• jonk explains why 47 instead of 46 here. Commented Apr 18, 2021 at 2:22

Have you ever noticed the dials on a scope are always 1-2-5-10-20-50-...? This has a simple and similar reason, although the values on the dials are a bit more rounded for convenience.

Many phenomena are perceived as being logarithmic (the best known one being sound).

Look at this sequence:

\begin{array}{|c|c||c|} n & \log(n)\\ \hline 10&1.00\\ 22&1.34\\ 47&1.67\\ 100&2.00\\ 220&2.34\\ 470&2.67\\ 1000&3.00\\ \end{array}

See how nicely and evenly spaced they fit on every $\frac{1}{3}$ and $\frac{2}{3}$? You can't even see the line is slightly curved.

The practical use for this is when you want to do a quick log scale graph. Instead of trying to draw a log scale yourself you just draw a line with an evenly spaced grid like the image below and you are nearly spot-on. And the grid is nearly on octaves too, at least good enough for a quick pen and paper analysis of a circuit where things vary with 6dB/octave. With decades this number is actually closer to 20dB/decade than 18, but I'm talking orders of magnitude here. Both lines are pretty easy to draw.

The resistors/capacitors/inductors are pretty much similar. If you want an evenly divided range of resistors you can simply pick the 10-22-47 values.

See how handy these values are? They are easy to do calculations, evenly spaced and therefore commonly used. Remember that in 'the old days' computers and calculators weren't too common, so values were chosen to make things as easy as possible.

• @DanNeely I wish I had known that trick in physics class in school. Commented May 3, 2013 at 19:14
• same here. Aside from one teacher who could hand place 2-9 in approximately correct places all of mine only marked powers of 10 in handdrawn graphs. Commented May 3, 2013 at 19:19
• $\log(3) \approx 0.5$, half way between 1 and 10 (hence many analog multimeters use 1-3-10-30-...). So there is your easy to place 5th tick mark (1-2-3-5-10). Commented May 3, 2013 at 19:44
• ...and log(7) is ~ halfway between log(5) and log(10). Add a few small nudges left and right (or let us assume they were just hand drawing error), interpolate the last 3 values; and now I know how he managed to freehand a log scale. Thanks. Commented May 3, 2013 at 20:08

Uhm, there are lots of answers stating that power series are chosen for values, but there no answers WHY power series are chosen.

In first glance there's nothing suspicious with linear series. Let's choose simple series like 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 ohm for resistors. Ont bad. Now, expand series to 100 ohm: 11, 12... hundred of different values... thousand values for kiloohm and... million for megaohm range? Nobody will make them all. Ok. we can make them with different step for every decade: 1, 2, 3 ... 9, 10, 20, 30 ... 90, 100, 200. This seem more reasonable. Very old series had such values (capacitors were).

Let's look on a problem from another side. Fabrication process have tolerance, generally constant in units of nominal values. Say, 10 ohm resistor is actually somewhere between 9 and 11 ohm and 1000 ohm one is between 900 and 1100 (i took 10% tolerance for example). You see, there's no need to make 1001 ohm resistor, because such small difference does not make sence with such broad range.

So, it is reasonable to choose neighbour values such way, that tolerance margins will touch together: R[i]+tol% = R[i+1]-tol%. This leads us to solution to choose step proportional to nominal value (and near to twice the tolerance): say, after 100 should be 120 and after 200 should be 240, not 22. Lets build such series for example (given 5% tolerance, so every next value should be 10% greater):

             1,
1    × 1.1 = 1.1
1.1  × 1.1 = 1.21
1.21 × 1.1 ≈ 1.33
... 1.46
... 1.61
... 1.77
... 1.94
... 2.14
... 2.36


Look, we get power series very similar E24 series. Of course actual E24 is somethat aligned, first to have whole number of steps in a decade, and second to include most values already produced (thats why 3.0 and 3.3 there, not 3.2 not 3.1).

The standard 10% tolerance values for resistors (very old) are

10  12  15  18  22  27  33  39  47  56  68  82


So 47 was already a choice. 10, 22, and 33 are also popular.

The standard 5% values are:

10  11  12  13  15  16  18  20  22  24  27  30
33  36  39  43  47  51  56  62  68  75  82  91


This allows 47 as well.