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So is there a standard rule of thumb, or equation about the distance the end of a screw will travel per rotation?

Conversely, how many turns it will take to travel a specific distance?

Say I have an M3 screw and I want to make absolutely no more than 3mm into an object and avoid hitting electronics. Looking at the M# screws in my toolbox they appear to have a standard pitch ratio for the threads?

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Metric bolts use thread pitch in millimeters. Your M3 screw likely uses the standard pitch of 0.5 millimeters. One complete rotation of the screw will advance the screw into the work piece by that amount.

According to the Bolt Depot chart, there is only one standard pitch for M3 screws, although other sizes will have standard, fine, super fine pitches available.

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A metric thread table is what you want.

Table 1. Source: Anzor.

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So is there a standard rule of thumb, or equation about the distance the end of a screw will travel per rotation?

It's not a rule of thumb - it's defined by the pitch.

Conversely, how many turns it will take to travel a specific distance?

Turns required = distance / pitch.

Say I have an M3 screw and I want to make absolutely no more than 3mm into an object and avoid hitting electronics.

Max turns = 3 / 0.5 = 6.

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