# How far can mains voltage arc in air?

I wondered this while soldering a mains voltage circuit board and was surprised by how close together the traces were. It has obvious implications in design of electrical plugs, and the proximity of wires when doing anything to do with mains voltage.

I've tried asking search engines sensible questions like "how far can 240V arc at 1 atmosphere" and "how far can electricity jump" but I haven't found any easy answer. This calculator states that it only takes voltages between 400 and 3000VDC.

By asking this question, I hope future people will be able to find the answer quickly and simply.

My research suggests that the arcing distance is dependant on the medium and the pressure, so let's assume air (~79% nitrogen, ~20% oxygen, ~1% argon and a few other things) at 1 atmosphere or 1.01325 Bar.
An answer has also drawn my attention to the affect of temperature and humidity. Assuming that higher temperatures and higher humidities both increase the possible arcing distance, let's choose something harsh like 40 degrees Celsius and 95% humidity.

Given a mains voltage of 230VAC in the UK, how close would two uninsulated copper wires (as an example) need to be before an arc could form between them?

Is this different for traces on a circuit board, or pins in a plug?

For bonus points, could answers be given for 120VAC too? Would 240V arc significantly farther than 230V? How about 110V compared to 120V?

I'm looking for fairly concise answers, but perhaps the reason I haven't found a simple answer is because there isn't one...

This question is just out of curiosity. I'm not going to start rewiring mains fixtures or designing 240V circuit boards any time soon.

• Somebody once told me, as a general rule of thumb, on earth every 1000volts is 1mm .. – Piotr Kula Apr 25 '17 at 12:27
• @ppumkin: so given a linear scale, that would mean 240V could arc about 0.24mm through air, but no answer has given this figure yet. – M_M Apr 25 '17 at 12:31
• Under ideal conditions probably. But the problem is to start the arc'ing process, since if there is a less resistive route, like a PCB trace the chances of arc'ing are less likely. If there is no other route and electrons are getting crammed up on the PCB route they could possibly micro'arc at these conditions. But PCB insulation is another barrier(since insulation does not count as air gap anymore). How far apart are these PCB traces you talking about? and what voltage is going in there. – Piotr Kula Apr 25 '17 at 12:38

The breakdown voltage of air varies significantly due to changes in humidity, pressure, and temperature. However, a rough guide is that it takes 1 kV per millimeter.

Since that's about where arcs happen, you want to be nowhere near that in a real circuit. On a circuit board, you also have to consider conduction along the surface. This is why you often see talk of clearance and creapage in the same discussion.

Clearance is the straightest path between two conductors. This is where the rough guide of 1 kV/mm for arcing applies.

Creapage is the shortest distance between to conductors along a surface. The breakdown gradient for creapage is lower than for clearance since dirt can accumulate on surfaces. Some dirt is partially conductive on its own, but many things can provide leakage paths after soaking up some humidity. Take a look at specs for medical power supplies, for example, and you'll see large minimum creapage requirements to guarantee low leakage currents.

There are various safety standards out there that require minimum clearance and creapage distances according to application, voltage, and sometimes environmental parameters. For most ordinary consumer equipment, 5 mm clearance is good enough isolation between user-touchable parts and 120 V AC power. However, you really should look at the relevant standards, especially if you are doing something out of the ordinary.

• I've repeatedly read DRY AIR arcs between smooth flat plates at 3,000 volts per millimeter. – analogsystemsrf Apr 21 '17 at 12:08
• Maybe note that coating and potting can reduce the required distances by quite a bit. Coating can sometimes be hard to spot for someone not familiar with the topic, so distances might seem awfully close. – Arsenal Apr 21 '17 at 14:20
• Thanks for your informative answer. The information on creepage is very interesting, and I can see how it deserves consideration when putting traces on a circuit board. Though it was the traces that got me thinking, the question is really about arcing through air (Given a mains voltage of 230VAC in the UK, how close would two uninsulated copper wires [...] need to be before an arc could form between them?). Assuming that a higher temperature and higher humidity both increase the distance, let's choose a fairly harsh example like 40 degrees Celsius and 95% humidity. I'll edit the question. – M_M Apr 25 '17 at 12:27

Given a mains voltage of 230VAC in the UK, how close would two uninsulated copper wires (as an example) need to be before an arc could form between them?

The answer is: it depends. There are a variety of factors including air, pressure\elevation, humidity, and dirt from the environment all affect the distance that an arc can form between two conductors.

International standards boards (namely IPC, and IEC) have come up with minimum distances between insulated conductors. Uninsulated conductors are not safe for use in products so those distances are not provided. Uninsulated conductors in PCB's or connectors are covered in the clearance section of the table. These specs are to prevent arcing or any kind of fire hazard. It should also be noted that to view the actual specs you'll need to buy them from IEC (like IEC 61010-1), but there is a lot of information regarding the content of these specifications available on the web.

It should also be noted that the distance changes depending on the environment (pollution degree), an environment that sees more dirt/humidity will have a shorter spacing. The distances in the table above are for a pollution degree 2 which would probably cover most designs, if not, find a table (or buy the spec) for the pollution degree your designing for.

Is this different for traces on a circuit board, or pins in a plug?

Yes. In the first table, the distance essentially doubles for off PCB conductors.

For bonus points, could answers be given for 120VAC too? Would 240V arc significantly farther than 230V? How about 110V compared to 120V?

In the table above, if only designing for 120V the distance is shorter.

The minimum voltage required to initiate an electrical arc in gas is described by Paschen's Law.

At large gaps it depends roughly linearly on distance, and also depends on the composition, temperature and pressure of the gas. For air at standard temperature and pressure it's about 3.3MV/m. As the gap gets very small the voltage to create a spark actually increases again. The spark is caused by free electrons that are accelerated by the voltage knocking other electrons off air molecules. If the gap is too small they can't get enough of a run up to knock off another electron before hitting the positive electrode. This means that there's a minimum sparking voltage of 327V at 7.5µm in normal air.

240VAC has a peak voltage of ~340V, so you might be able to get it to briefly spark near the peak with a gap close to 7.5µm. 120VAC won't spark in air.

In the real world there can be transient overvoltages, contaminants, condensation, etc. You shouldn't rely on the above for safety purposes.

• It hasn't been mentioned by anyone yet, but would a point discharge be easier to start on, for example, the point of a stray strand of wire given the same distance as a smooth conductor? This is the principle of operation of the lightning rod where electrical stress is concentrated at the tip. – Transistor Aug 21 '18 at 14:57
• Paschen's Law is for uniform fields, and field strengths are indeed greater on surfaces with a small radius of curvature. I don't know of an easy way to calculate the breakdown voltage in a nonuniform field, but the same physical effects that cause the minimum will still apply. On a practical level, even a sewing needle has a tip that's 10s of µm across, so the field between two needles separated by 7.5µm will still be fairly uniform. I expect that you'd need something really unusually sharp to strongly affect the minimum voltage. – patstew Aug 21 '18 at 16:25