# How to measure the diameter of an electrical wire [closed]

I'm working on a project and I need to measure the diameter of a thin bare copper wire but I don't know how. Can you please tell me a way to measure the diameter of a wire.

Is there a way to measure it using diffraction?

## closed as off-topic by Carl Witthoft, Kyle Kanos, Kyle Oman, ACuriousMind♦, MartinJun 25 '15 at 9:59

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• With a caliper ? – David Jun 24 '15 at 11:20
• Did you put the optics tag because you whish to use its diffraction pattern? – Snaporaz Jun 24 '15 at 11:21
• I'm voting to close this question as off-topic because it shows insufficient prior research. – Kyle Kanos Jun 24 '15 at 12:52
• At this point there is a serious disconnect between "I just want a number as the diameter of my wire", and your complaining measuring many turns won't give a good answers below. The wrapping approach is the classic method (and can give you an answer in "gauge" directly if you care for that sort of thing) and can be very accurate if combined with either a vernier caliper or a micrometer. – dmckee Jun 24 '15 at 13:57
• @david2000, you keep saying that people aren't answering with methods that give you high enough accuracy... but you haven't said what accuracy you need so the question is too vague. Also, please can you explain why it has to be an optical method? Which techniques have you considered, and why weren't they suitable? – Alex Valavanis Jun 24 '15 at 13:58

Laser pointer, wire, screen at known distance.

You will see the following diffraction pattern:

(not trying to make the best image... exposure could have been better, and I could have put a beam stop in in order to avoid the overexposure of the central beam.)

The point is that I can see a series of "blobs" that correspond to diffraction peaks from light that goes around my wire. I count slightly less than 10 peaks for 3 squares on my paper (1/4" squares), with a green laser pointer (wavelength 532 nm) at a distance of about 2.5 m from the screen.

From this you can calculate the thickness of the wire. By increasing the distance, and in particular by increasing the distance until you get an integer number of peaks falling on an integer number of squares on your grid, you can get almost any accuracy you want with things you already have lying around. And if you can't bend your wire, or you don't have enough to stack it up, that doesn't matter either.

The equation for the peak spacing is given from basic straight slit diffraction: for wire thickness $d$, distance to the screen $D$, wavelength $\lambda$, the spacing $w$ between peaks is given by

$$w = \frac{\lambda D}{d}$$

And so the thickness of the wire can be deduced from

$$d = \frac{\lambda D}{w}$$

In the above case, I calculate that $d = 0.69 mm$ diameter - indeed, it was a pretty thin wire I had lying around (somewhat smaller than 1 mm).

You can get quite good accuracy with this method, assuming that you have a known wavelength for your laser pointer. For greater control over the measurement, you could rotate the graph paper until you exactly found an integer number of blobs between your lines; the angle would give you some "fine tuning" of the measurement. And you can see quite easily see all the way out to the 20th peak; if we assume you can center these peaks better than 1/4 of their spacing (really that is not hard) your accuracy will be better than 2% ($\frac{\sqrt{2}}{4 \cdot 20}$). With a bit of care you can do even better. With stuff you have lying around your office.

Postscript

I just repeated this slightly more carefully with a wire I had at home. Measured diameter was 0.46 - 0.49 mm (often wire is not perfectly circular... As this measurement just confirmed). I set the pointer and wire up much further from the wall (28.5 1 foot tiles - right across the big room) and could see 26 fringes (you lose count near the middle but can extrapolate by counting what you can: I see 9 peaks on 14 squares, and N peaks on just over 40. I conclude N=26).

I determine the wire to be 0.47 mm diameter from this measurement - right where the calipers put it...

• Really helpful it was, sir – David 2000 Jun 24 '15 at 22:06
• Not that there is anything wrong with this technique, of course, but a 1% measurement isn't a patch on what could be accomplished with 50-100 wraps and a caliper. – dmckee Jun 25 '15 at 2:08
• @dmckee of course you are right. But this was a method I could perform at my desk, with a very small piece of wire and no calipers... I think most of the time 1% is good enough - slide rule rule... – Floris Jun 25 '15 at 2:11
• I'm just suggesting that the OP is exhibiting an inconsistent set of expectations in his responses to various suggestions. Getting 1% with stuff found in your desk is way cool. – dmckee Jun 25 '15 at 2:13
• cool, I want to do this too! – an offer can't refuse Jun 25 '15 at 3:59

I don't know what accuracy you need, but you can wind (densely), say, 100 turns of wire on a cylinder and measure the length of the coil. EDIT: another approach (which can be more accurate, if you know what material you have): take a long piece of wire and weigh it. There are some ways to measure density as well.

• No, I need more accuracy! – David 2000 Jun 24 '15 at 11:54
• @David2000 Do you have a beam balance? You simply choose the length of wire so that the uncertainty in the mass implies the required accuracy of the diameter. IMO I would do this as well as a micrometer (I know you don't have one - but everyone is howling that this is the "right method") for the simple reasons that (1) it can be made be more accurate than a micrometer, for very fine wire and (2) you need to be very careful with fine copper wire (40 SWG and finer) and mirometers: the latter will easily crush the former a few percent so you need to have a very experienced "feel" for their use. – WetSavannaAnimal Jun 24 '15 at 13:54
• @WetSavannaAnimalakaRodVance - not to mention the fact that wire often is not perfectly round... A good balance (and knowledge of the density) will give a better measure of the average cross sectional area for sure. – Floris Jun 25 '15 at 2:52

You can first measure the length of the wire, then put the wire into the water, and see the volume change of the water. Then use $\pi r^2 = V/L$ to get the diameter.

# edit

• If you need more accuracy, maybe you can either coil the wire on a pencil or some other object many times, then you can measure the the length of many diameters, like in this graph. Then the error could be decrease.

• Or you can investigate about the interference pattern about your wire, this is just a proposal, here is a link about diffraction of hair and wire, see if it helps(it should be useful if your wire is very thin and it should provide a good precision).

• Need a real high accuracy and in other word, impossible – David 2000 Jun 24 '15 at 13:33
• @David2000 see the edit. – an offer can't refuse Jun 24 '15 at 13:55

You can also measure the electric resistance of a long piece of the wire and the calculate the cross section of the wire using the fact that the specific resistivity of copper (at 20 C) is $1.68\times 10^{-8}$ Ohm m.

Technically Micrometers or more commonly called as Screw Gauge are used to calculate diameter or radius of thin wires in physics labs you can refer to this article: https://en.wikipedia.org/?title=Micrometer

• Sorry but I don't have a Micrometer! – David 2000 Jun 24 '15 at 13:35
• david if you want high level of precision and less error you have to use micrometer this is standard equipment used today when i was in senior secondary class we had these types of experiments this is fairly common experiment in physics! – user84155 Jun 24 '15 at 13:40

A micrometer would be the preferred method. A caliper would not be appropriate because it would not give you enough precision.

• But I don't have a Micrometer – David 2000 Jun 24 '15 at 13:36
• Come on, a caliper can give you a precision high enough (0.1mm or even 0.01mm) – David Jun 24 '15 at 13:52
• @David , it depends on what he means by "thin wire" I guess. The difference in diameter between 30 AWG and 31 AWG is 0.0011 inches (nominal). Most calipers would be fine with that. Smaller wire than that and I would use a micrometer. And if you start throwing in half gauges and other wire gauge standards, a micrometer really becomes necessary. But ultimately whether or not it is enough precision is a question for David2000. Additionally, I've seen too many people flatten wire with a caliper because they push too hard. It is easier to prevent that by using a micrometer. – Eric Jun 24 '15 at 16:48

Using optics, you say? Well, you make a Michelson interferometer, with the movable mirror referenced to a mechanical stop. You move the mirror away from the stop, insert the wire and close the gap until the wire is held lightly between the base of the mirror and the stop. Now pull out the wire and slowly close the gap until the mirror makes contact with the base, counting fringes as you do so.

Alternatively, you can make a small aperture and lay parallel wires across the aperture with the wires touching each other. Remove every other wire and you have made a diffraction grating. Use a laser pointer as a light source and measure the diffraction angle. This can be used to calculate the wire spacing and therefore the wire size.

copper wires can be measured by using screw gauge. read your text for how to use screw gauge. and use moving microscope to measure the same by optically