Is there a formula to calculate the step width vs. riser height?
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you can get parts for stair casings at a home improvement store- pre cut. there was a city code in play the last time i had new stairs were put in.
http://www.finehomebuilding.com/2016/08/04/2-rules-comfortable-stairs
https://www.mycarpentry.com/stair-calculator.html
http://www.ez-stairs.com/widgets/stair_calculator/index.html
Here, these links will help. Check your local building codes for compliance for your specific application.
https://m.wikihow.com/Measure-for-Stairs
http://www.calculator.net/stair-calculator.html
https://www.thespruce.com/code-requirements-risers-treads-stair-width-and-more-4120151
This makes it simple! http://www.calculator.net/stair-calculator.html
Hey, I understand that the thread is old, but I found this page in goole so I'm sure my post will be useful.
As per the topics question about the stair formula, I found this page has all the formulae needed to calculate each part of the stair - https://concalculator.com/stair-calculator/. There is also a good calculator.
Riser height depends on the total height and number of steps. As said here, pay attention to the regulations. General guidelines recommends the rise to be no more than 7.75 inches and run no less than 10 inches.