# Why do many capacitors and resistors have 47 as their two first digits?

I’ve been goofing around with circuits lately, and I noticed right away that many resistors were 470 kOhm, 4700 ohm or som other 4.7 x 10^x. Then I noticed capacitors were like this too (different units obviously.). Another set of common digits is 22. There must be some reason, historical or convenience, for this. Does anybody know?

Yes, the standard values for 10% tolerance resistors are:

100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820

Very roughly a logarithmic scale in ratios of 1.2.

This small number of values also made it easy to decipher the color code at one glance. After a while you’d see double orange, or brown black and know right away what it was.

If you were to have 12 increases between 100 and 1000, which were equally spaced (i.e., each value was the same percentage increase from the next), you’d have (to 6 significant figures):
100
121.153
146.780
177.828
215.443
261.016
316.228
383.119
464.159
562.341
681.292
825.404
1000
(and similar series between other consecutive powers of 10)

However, they are only given to 2 significant figures in the 10% series. I’m not sure why we have 470 rather than 460 in that series, but I suspect it’s connected with similar approximations in the 5% series, which has 24 steps between consecutive powers of 10.

Here is a good chart of the “E numbers” that the prior two posts talk about.

The idea is, for a given tolerance level, you want to pick a bunch of standard values that are roughly logarithmically-spaced apart.

You also want values that do not overlap a lot at the edges of their tolerance range. The example given on that site is that if you make 100Ω resistors with 10% tolerance, then a given resistor from the batch may have an actual resistance between 90Ω and 110Ω. So it doesn’t make any sense to also manufacture a 110Ω resistor. Likewise, a 115Ω resistor would also have an overlapping tolerance with the 100Ω model. So the next preferred number is 120Ω.

This series of preferred values for 10% tolerance resistors is known as the E12 series, because there are 12 values for each decade. The E12 numbers go:

100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820.

Then the next decade is 1000, 1200, 1500, 1800, and so on.

I don’t think they even make resistors that wonky anymore; even the cheap packs of 1/2 watt stuff you can get at Radio Shack have 5% tolerance now.

So the 5% preferred numbers (E24) just split the difference between the E12 numbers.

100, 110, 120, 130, 150, 160, 180, 200, etc.

So in all the E-number series, you’ll find 470, 4.7k, 47k, and so on. Now, why do those particular values seem to common in resistors? I don’t have a definite answer, but I’ve noticed it as well.

My guess is that they’re commonly used because they’re close to the middle of the decade and so are frequently chosen to make voltage dividers.

I love the series of preferred numbers. Unsurprisingly, things with the whiff of logarithms have always tickled me.

Perhaps best is the dirty little detail that in just one of the decades of the series, one of the numbers gets shifted slightly. I picture some consortium of companies coming up with this, and some of them are being good citizens but at least one of them is being crass and working to skew the whole system to fit some arbitrary historic choice their company already made. That is, one company already makes a 46k resistor (or something like that), and they had to besmirch the entire beautiful system with this stupid exception to suit the short term interests of this one company, whom the others must have just hated for it.

One detail: it’s common in transistor transistor logic to control an output with an NPN transistor whose emitter essentially grounds the output when in a conducting state. If the transistor is not in the conducting state the output goes up because it’s connected to the +5 rail through a pullup resistor. A 47k resistor works right for this situation. Since TTL outputs are common interface points between things designed at different times by different people, it has become a de facto expectation that that 47k resistor will be there. At least, this is my read. This is one reason 47 is so common in resistors.

All of the above plus you often didn’t care within 25% what the actual resistance and 470 ohm was the best estimate to half of 1000 ohm resistor. So you might have seen that some more than, say, 220 ohm.

I thought perhaps with capacitors it is a function of dielectric and size. Resistors had similar values to make the various RC equations work out.

There are only two digits in the resistor code. bands 1 and 2 The third band is the bultipler

red is 2 and thats true of the multiplier. 10 to the 2nd power or 1000

yellow is 4. multiplier 10 to the 4th

A very easy coding to learn. red,red,red was one of the most common resistors. 2.2K

The standard sizes were tied in to the voltage. There were standard power supply voltages. If you wanted to apply a bias to a tubes plate or grid the resistor size was pretty standard. Standard voltage means you need the same resistor to get the right voltage drop.

Here’s another place where something similar occurs. First, if you take every second value in the series you get the series 100, 150, 220, 330, 470, and 680, where each value is about 50% larger than the previous one. That’s the series used for 20% tolerance components. If you do that again, you are left with 100, 220 and 470 – and that might be part of the reason why values starting with 22 and 47 are relatively common.

But with steps as big as that, you might as well use just one significant figure and have a series like 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, etc. With many currencies, e.g., the Euro and Sterling, those are the values chosen for coins and notes. Those coins and notes are, of course, components used to create various specific values in the currency, and there’s a trade-off between the number of different coins and notes in the currency and the number of coins and notes needed to put together the various specific values. Fewer different coins and notes mean that you will need more coins and notes to create specific values, and this 1/2/5 series seems to be a good compromise.

Wonderful, I knew it had to be something like that.

No, there can be more bands. Here’s an online translator for 5 bands:
http://www.ankaudiokits.com/resistorcodes.html

AFAIK, resistor and capacitor values are determined mathematically and implemented from those numbers, as the above progressions show, and always have been. That is, there is not some “natural” size or coefficient that makes those values easier to manufacture. (Battery cells, OTOH, produce a specific voltage because of the nature of the materials, and cannot be arbitrarily changed, so the functional implementation is what drives the standard values.)

You can have four or five bands in higher precision units. Three unit bands plus a multiplier is quite common.

Well if you are going to have ± 10% parts, there is no point in having more values, is there ?
(using Ohms but could be uF etc)

With 10% parts,
100 Ohms covers 90 to 110.
120 Ohms covers 110 to 132
150 Ohms covers 135 to 165
180 Ohms covers 162 to 198
220 Ohms covers 198 to 242

See how the entire range is covered ? (almost, there’s rounding to the nearest 10 and hence gap.)

Or to put it another way, the capacitance of a capacitor is determined by its size and electrolyte material, but both of those are chosen in such a way as to make the specific capacitance that is desired.

Well… true, for low-precision through-hole resistors. *Precision *through-hole resistors, such as those made by Vishay, do not have color bands. They just print the value right on the package.

It’s also worth mentioning that the vast majority of resistors sold today do not have a color code on the package, being surface-mount and all.

FWIW, here is the Wiki writeup on “preferred numbers” used for resistor values:

Am I not correct that a 150Ω (10%) might be 135-144 or 156-165 but is unlikely to be 145-155? A resister with such a value would have been binned as a slightly more expensive “5%” part.

Seeing no smiley-face, I assume you’re serious. But you’re also probably seriously wrong.

The phenomenon you speak of is valid, and may once have applied to resistors, but today the “binning” cost probably exceeds any manufacturing advantage.

:dubious:

Someone needs to give us a history lesson here. In the old days, when these schemes were first come up with, was it just to have an equally spaced set of resistors, or was it because their quality control sucked?

If the later (which I kind of assumed), did they shoot for some value, say 100, and a few percent were out of speck, so they tested and moved those to another bin? Or did they have barely a clue, just making a bunch of resistors and binning them after the fact?