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What is a formula for building stair steps?

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Quick Answer

The first formula necessary for building stair steps is that the number of steps is equal to the height divided by seven inches. Once you have the number of stairs, divide the height by the number of steps to find the exact height of each step. With this formula, the height of each step plus the run of each stair must equal 17.5 inches, so subtract the height of a step from 17.5 to get the run.

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Full Answer

Another possible formula to determine the run of each stair is that twice the height of each step plus the run of each stair must equal between 24 and 25 inches.

As an example for applying these formulas, imagine you need to construct stairs to climb a vertical distance of 10 feet. Ten feet is equal to 120 inches, and 120 divided by 7 is 17.14. Rounding down, this means that you need 17 steps total. To find the exact height of the steps, divide 120 by 17 to get approximately 7.06 inches tall. Finally, using the first formula for run, subtract 7.06 from 17.5 to find that each stair measures 10.44 inches in depth. This answer also fulfills the alternative formula, because 7.06 inches times two is 14.12 inches, and 14.12 plus 10.44 is 24.56, which falls between 24 and 25 inches.

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