Rain amount equivalent to running sprinklers?

How does rainfall amount compare to watering with the sprinklers?

Like is 1 inch of rain equivalent to 10 minutes of sprinklers?

Sprinklers are usually measured in Precipitation Rate (PR). The units are Inches/Hour (In/Hr) and it varies for each sprinkler model, nozzle, and water pressure.

For a quick example, a sprinkler with a PR of 0.5 in/hr would take 120 minutes to put down 1 inch of water.

You can determine the PR of your sprinklers by either looking up there data online, or, doing a Catch Cup test.

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And unless your irrigation installer checked the pressure at each head, go catchcup

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As mentioned above, it varies. But will add - it varies greatly! It can vary from 10 to 60 min to put down the same amount of water depending on above mentioned factors.

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I assume that rain would have the same absorption issues that the sprinklers would have, meaning that if an inch of rain falls in 30 minutes, maybe (arbitrary) half an inch would be absorbed, and the rest is lost to runoff.