How long does machine embroidery take

There are a lot of different factors you are correct.

Everyone has some moderately varied results depending on their experiences. I usually account for approximately 10-15 min startup (setting files/threads and framing the first run of hats).
Almost always the lowest runs end up being 4-5 min. where you can frame the next set. change-out time is 1 minute.
The running rate of the machine is measured in stitches per minute. 500-750 are standards. and usually its a minimum of 3000 stitches for some of the smallest logos.

5-6min. is a bare minimum time per run.

The longest run I have ever had on some hats was over 1-hr but they were 2.5 x 5.5 logos.

The actual number of colors is less of a factor (it is one but only because it adds in trims and setup time)
Color changes adds in 3-8 seconds on top of a trim.
Trims add in 10-12 Seconds.
A general number I usually use for trims and color changes is 15-seconds for calculation.

So in summary:

Shortest time to do a single "one off" hat on a single head.
Assuming the machine is set to hat mode already.

1st hat: 14-21 minutes. = 10-15min. startup + 4-6 run. Assuming everything runs perfect.
2nd hat: 6min./run

Longest time I have run on a 2.5"x 2.5" logo that I can think of
17,000 stitches @ 750spm
35 trims
31+minutes/run.

That said it can be as much as much as an hr or more depending on detail.

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Problems or questions
How fast are embroidery machines?
How long does it take to master embroidery?
Why does embroidery take so long?
How much is 1000 stitches in embroidery?

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How fast are embroidery machines?

The majority of machines run around 600-750 stitches per minute on average embroidery designs. If a design has plenty of color changes and trims, it will take significantly longer to embroidery the design. All these stops slow down embroidering. Embroidery digitizing cuts back on stops.

How long does it take to master embroidery?

I estimate it takes roughly 3-6 hours to learn the very basics of using your embroidery machine interface and to stitch your first built-in design. As you grow in your embroidery journey, you will continue to learn new things about your machine and become more proficient.

Why does embroidery take so long?

The bigger the order, the longer it will take to embroider. Most embroidery machines can embroider between 500 - 1000 stitches per minute, and the most items you're embroidering, the more stitches the machine makes.

How much is 1000 stitches in embroidery?

Typically the cost per 1,000 stitches can vary from as little as 50 cents to $4.00 depending on the size of the design, the number of colour changes and the number of garments to be embroidered. Usually as the number or size of the stitch count increases the cost per 1,000 stitches goes down.