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my question is how would I find the length of an uncoiled spring?

I hope that is clear enough, but other ways of explaining what i'm looking for look like this: How would I find the length of a line that made a spring x meters high?

Or how would you know how long a piece of metal must be to manufacture a spring x meters high.

A little background info. I'm studying architecture and have been thinking about spiral stair cases. Knowing the elevation you hope to achieve via the staircase is useful for knowing how high/how many steps are required. But for knowing how "deep" a step must be (ie the horizontal element that you step on), it seems to me that it would be useful to calculate the entire "length" of your staircase.

I have considered thinking about the problem as having a step placed at regular intervals on a circle. So you would have x amount of circles stacked on top of each other, with steps that form a spiral. However i'd really like to know if there's some maths that can help me with my problem.

Thanks in advance for any help you can give! Lntz.