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I've read that that the output voltage available at the Vout pin is approximately equal to the Vcc applied to pin 8 minus 1.7V. This is for an input voltage of +15V.

I wanted to know if there is an equation for Vout in terms of input based on threshold/trigger?

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Vout should be largely independent from the threshold / trigger voltage.

Also, if anything like this exists: it'd be in the NE555 datasheet.

Also, the NE555 can't drive arbitrarily large loads, so make sure you don't try to figure out an output voltage while drawing a lot of current.

Also, the NE555 is largely obsolete, if you need 555 functionality, I'd recommend looking into CMOS variants (LMC555, TLC555, many others), which can give you rail-to-rail output (i.e. you reach +Vcc and 0V on the output), at least as long as you're not significantly loading the output.

If you're building something that isn't really dependent on being based on a 555 (for example, you just want to trigger something periodically), I'd recommend looking into Is the NE555 the IC I need, and if not, what do I replace it with?.

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