Electronic – How far can mains voltage arc in air

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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.

Best Answer

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.