# Measuring High Voltage in Millimeters (and Other HV Probe Tricks)

I work a lot with high voltages and others frequently replicate my projects, so I often get asked “What voltage is needed?”. That means I need to be able to measure high voltages. Here’s how I do it using a Fluke high voltage probe as well as my own homemade probe. And what if you don’t have a probe? I have a solution for that too.

## How Long Is Your Spark?

The simplest way to measure high voltage is by spark length. If your circuit has a spark gap then when a spark occurs, that’s a short-circuit, dumping all your built up charge. When your spark gap is at the maximum distance at which you get a spark then just before the spark happens is when you have your maximum voltage. During the spark the voltage rapidly goes to zero and depending on your circuit it may start building up again. The voltage before the spark occurred is related to the spark length, which is also the spark gap width.

The oscilloscope photo below shows this changing voltage. This method is good for a rough estimate. I’ll talk about doing more precise measurements when I talk about high voltage probes further down.

But it’s not quite so simple. The shape of the electrodes plays a big part, as does the pressure and temperature of whatever is in the gap, usually air. For flat electrodes, or spherical electrodes whose diameter is significantly greater than the gap size, in air at 25C (77F), the following formula can be used:

`voltage (kV) = 3 x pressure x spark length + 1.3√spark length`

The pressure is in units of atmospheres and the spark length is in millimeters. Most hackers work at atmospheric pressure which is 1 atm, so that can be left out of the formula. Also, for a 10mm spark gap, for example, taking the square root of 10mm and multiplying by 1.3 means you’re adding an insignificant 4.1. And so the formula is usually simplified to just:

`voltage (kV) = 3 x spark length (in mm)`

or for centimeters:

`voltage (kV) = 30 x spark length (in cm)`

That’s just another way of saying that there’s 30kV/cm. For inches, the formula is:

`voltage (kV) = 11.8 x spark length (in inches)`

In the photos above, the measured voltage is 17kV. The spark gap width (i.e. the spark length) is measured as just under 5mm. If we apply the formula for a 5mm spark gap, we get 3 x 5mm = 15kV. The larger the spheres, the closer the measurement should match the formula, for a certain voltage range, but more on that below.

However, if you use sharper electrodes such as needles or rods, then at sufficient voltages the electric field between the electrodes will be less uniform and in places will be strong enough to ionize some of the air in the gap. That essentially creates a high resistance short-circuit which means your voltage will be lowered. The formula above will no longer apply. In that case you can try looking up your spark length and electrode configuration in a chart.

The above chart summarizes all of this. The bottom line in dark blue is the line according to the formula (essentially 30kV/cm):

`voltage (kV) = 30 x spark length (in cm)`

That formula defines a linear relationship between spark length and voltage. It looks like there’s a bend upward at 50kV but that’s because the voltage scale below 50kV increments by 5 and above 50kV it increments by 10. Above that is the real data. As you can see, needle electrodes follow the formula the least. The larger the sphere diameter, the higher the voltage they get to before they no longer closely follow the 30kV/cm line. Most of my work these days is below 30kV, though my electrodes are rarely big spheres, as is the case for most hackers. That is unless you’re working with Van de Graaff generators, but even then usually only the dome is spherical and the other electrode isn’t.

## Using A Fluke High Voltage Probe

For more precise measurements I use a Fluke 80K-40 high voltage probe. This one is designed for use from 1kV to 40kV DC, with accuracy varying from 1% to 2% depending on the temperature, and not including the accuracy of the meter. For AC it’s designed for peak AC, 20kV RMS and gives an accuracy at 60Hz of +/-5%. The input resistance is 1000MΩ. It’s for use with a 10MΩ +/-1.0% voltmeter, or oscilloscope as in the photos above. Meters with other impedances can be used with the help of an external shunt or a correction factor, all of which is described in the probe’s documentation.

When making the measurement, take the reading on the meter or oscilloscope and multiply it by 1000. That’s how I went from the 17V shown on the scope to 17kV in the example above.

Here are two more photos of where I’ve used the Fluke probe. One is with a 10MΩ FET analog meter for measuring the voltage across a smoke precipitator. The other is with the analog meter again but I’m holding the probe in my hand. I’m measuring the voltage across a lifter that’s being provided by a PC monitor power supply.

## A Homemade High Voltage Probe

The Fluke is good for up to 40kV DC but I’ve had to measure higher and so I made my own probe. The highest I’ve used it for is 75kV DC, though it’s designed for a maximum of 150V at the meter, which equates to an input voltage of 150kV.

The above is how it was designed. R1 has a very high resistance compared to the meter’s impedance of 10MΩ (R3) and the resistor that the meter is measuring across, also 10MΩ (R2). It can be done without R2 but that would put the meter in danger of having a high voltage across it.

R2 and R3 are two resistors in parallel and combined can be counted as a single 5MΩ resistor as shown in the first formula in the diagram. Together they’re usually labelled as R2||R3. The schematic on the right is a simplified way of looking at the circuit with R3 pulled out of the meter and combined with R2.

R1 and R2||R3 form a voltage divider. The second formula in the diagram shows how the voltage across R2||R3 is calculated. Notice that the result, 74.9V is almost 1/1000th of 75,000V, the voltage being measured. It’s only 0.1% off, which is smaller than the meter accuracy. That means we can say that to get the actual voltage you simply multiply the measured voltage by 1000 (75V x 1000 = 75,000V).

The value of R1 was selected so that it wouldn’t load down the circuit being measured. High voltage circuits often don’t have much spare current for measuring purposes. R1 was also selected such that there wouldn’t be a problem with leakage over its surface. In my case R1 is made up of 25 smaller resistors and so with the voltage divided among them, I figured there’d be no leakage problem. R1 was lastly selected so that R2||R3 would have a useful voltage range across it. 3000V is measured as 3V, 20,000V is measured as 20V, and 75,000V is measured as 75V, and so on, which are reasonable values for a meter.