256 Shades of Grey - How to Calculate Cutting Depth

Any possible mention of the words plunge, depth, speed, thickness, or size are meant to be purely scientific and not any kind of innuendo whatsoever. :hear_no_evil: :see_no_evil: :speak_no_evil:

As you’ve probably seen by now, Easel uses the 256-shade grey scale to represent the depth of a cut. White means no cut at all, and black means cut all the way through. Any shade of grey in between will, more or less, correlate to a particular depth. We can use this to our advantage when working in other graphics software like Illustrator or Inkscape - using some very simple math, you can calculate how deep a particular shade of grey will be when your SVG file is imported into Easel. There’s a little bit of slop involved, because you’ll almost invariably end up rounding some numbers up or down, but we’re talking very small fractions. Any fine adjustment can be made in Easel if needed.

This is all going to be in fractions of an inch, but the same math applies to metric values as well.

Using the grey scale, we’ll have 256 possible cut depths in any given material. The thicker the material is, the greater the distance between each successive shade. An easy way to visualize this is with a one-inch thick piece of material - at 1.0 inches, we’ll have roughly 4/1000th of an inch of depth per shade. Simply divide the thickness of the material by 256 to find that number:

1.0 / 256 = 0.0039 (we’ll just round this up to 0.004)

If you reverse the math, you’ll see how close we are:

0.004 * 256 = 1.024

Again, a little bit of slop involved, but unless you’re designing press-fit parts it’s probably going to be OK.

A more common thickness to be working with is a quarter of an inch , so let’s see what our depth per grey shade is at that thickness:

0.25 / 256 = .00097 (we’ll go with .001 here)

Seems about right, yeah? We had four thousandths at one inch, and now we have one thousandth at a quarter inch. I can work with these numbers.

Using this knowledge, it’s now pretty easy to find out how many of those miniscule steps it’ll take to reach a particular depth. I want to cut a 1/16" deep circle in this 1/4" material, so I’m just going to divide the decimal version of 1/16" by our 0.001 value:

0.0625 / 0.001 = 62.5 (call it 63)

Now we know that it will take 63(ish) shades of grey to reach a depth of 1/16" in our 1/4" material. There’s one last step now - since white has an RGB value of 255/255/255 (black is 0/0/0), we need to subtract those 63 shades from our 255 white:

255 - 63 = 192

Set the RGB value of our imaginary circle object to 192/192/192, and…well, that’s pretty much it. If all the stars and planets align properly, that 192RGB circle should cut to a depth of 1/16", give or take a couple of thousandths. Again - if true precision is needed, just apply the absolute value in Easel.

Is everyone still with me? :smile:

Let’s do one more math run. I want to take a nice, hearty 3/8" chunk out of a 5/8" thick board. First, let’s once again figure out our depth per gray shade by dividing the material thickness by 256:

0.625" / 256 = 0.002441 (…that’s a tough call, so I’m going to stay with 4 decimal places on this one and use 0.0024)

Next, calculate the number of grey shades there are in a 3/8" cut:

0.375 / 0.0024 = 156.25 (this is easier to call, let’s go with 156)

Subtract those 156 shades from 255 to get the actual RGB value we need:

256 - 156 = 99

And there you have it, we’ve determined the RGB value to apply to our object to get down 3/8" from the surface of a 5/8" board.

Easy peasy. (what does that even mean? :confused: )

This method is pretty good for getting an idea of how relatively deep a cut will be in a given thickness of material. If you’re designing a sign, and you know approximately how much depth offset you want between different elements, you can do a reasonable approximation right in your graphics software rather than trying to isolate, select, and tweak everything after the fact. Chances are fair that you’ll still need to do that to some extent, but…perhaps not! :smile:

Someone who’s good with any kind of programming language could probably whip up a small widget to do the math in no time flat. I am not that person. :smile:

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:grinning: I think i now have a headache

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It might be easier to work out the depths in your head if you can get your graphics editor to show grayscale values as percentages instead of 0-255.

It’s been done. Check out dmap2gcode.

This is great! Following up with this… so it should be theoretically possible to carve continously smooth in the Z-axis if the .svg uses a continously smooth gray-scale?

I’m thinking about trying to eliminate the regular steps in a 3D contour map. I guess the challenge would be to get my digital elevation model converted to a manageable .svg file. Teeny tiny vector squares ? :slight_smile:

Hi @Paul

With this method of carving 2.5D the machine will still do a watering style cut and the z-axis will step down for each level. If you have enough steps to the grey scale then it can get pretty smooth…

See some examples here:
https://discuss.inventables.com/t/tip-jar-bounty-500-claimed-by-sketch42-iphone-6-case/9122/14

And here:
New to CNC Machining

Not sure if this still applies directly as they have changed things related to depth (no longer a percentage of thickness).

I think it is still a percentage of thickness for the initial import of the SVG and then after that the depths are set to actual fixed values.

eg. when importing an SVG with 50% grey it sets the depth of cut to 50% the depth of the material that is set in Easel… 10mm thick material means that 50% grey will cut to 5mm, but if you change the thickness of your piece, then it will still cut to 5mm unless you re-import your SVG.

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Yes, that’s correct.