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Check my math

Minnesota Dave, and anyone else;

Is my math correct?

We express roof pitches as 6:12, 3:12 12:12 For 12' measured horizontal, how much rise, or fall?

We express grades as % A 10% grade falls away 10' in 100' of horizontal.

Both of these are ratios. We can convert.

Also inclines are expressed in degrees. We can measure an angle, in this case deviation from horizontal with a protractor, but how do we turn that number into percent, or ratio?

A circle 200 feet in diameter has a circumference of 200x Pie, or 3.1416, or 628.32 feet. As a circle has 360 degrees, each degree is 628.32/360 or 1.7453333333333......

Therefore, a 10% grade is 10x1.7453333333333333.......or a 17.4533333333... degree angle.

A circle 24' in diameter has a circumference of 24x3.1416 or 75.3984' As this circle is also 360 degrees, we can divide. 75.3984/360= .20944. therefore a 6:12 pitch is 6/.20944=28.6478 degrees.

I have a new phone. It tells me the angle as a deviation from level. I always need it expressed as ratio, or percent for it to make sense to me.

I understand this won't work very accurately as my units of measure are circular, and these measurements need to be straight.

What is the proper way to convert?

Willie

An optimist is usually wrong, and when the unexpected happens is unprepared. A pessimist is usually right, when wrong, is delighted, and well prepared.