 This was inevitable – carpenters measure slopes, pitches, and angles by ratios, which is less than intuitive to anyone else. Most people are accustomed to mathematical degrees (or possibly radians) if that. This is worsened by the fact that the unit of measure used in the United States is in increments of 12 when we count in increments of 10, and angles are in increments of 180 or 360.

Today, we’re going to do everything we can to simplify this. A few decades ago, this would be easier said than done. Thankfully, today, there are a host of technologies that can make this pretty easy to do.

Getting Initial Pitch

What you need to do is find the peak of your section of roof, from the side, on a ladder. Line up the level so that the 12 on one end lines up with the peak. Note the other number (it will be vertical) where the line of the roof intersects.

If that line is, for example, 9, then your ration will be 9/12.

A Little Demystification

With concepts like this, it’s generally better to focus mainly on how to get the numbers you need, and not on why the calculations work, or why units are what they are. These are interesting things, and it doesn’t hurt to investigate them later, but it merely adds complication when you need to practically solve a problem in quick order.

That said, why do carpenters use this measurement system? Simply, it’s more practical for them, since they needn’t do calculations back, from more abstract units like degrees. (Note: In metric countries, they generally use degrees flat out, and their tools reflect this). Since roofing measurements are increments of 1 foot of run (12 inches), your ratio is how much vertical rise it has per 12 inches of horizontal distance. In math, this is related to Y-Intercept, if you recall that from high school classes.

Calculating Degree

Now that we have our ratio, we have to use trigonometry, to determine the angle. This is remarkably easy with the use of a scientific calculator. In this example, we’ll assume Windows’ calculator.

• Launch the calculator.
• Divide the first number in your ratio by 12. This will produce a decimal number less than 1.
• Go View->Scientific.
• Click inv and then tan-1. You will get a decimal number greater or equal to 1.

Now, we’re not at degrees just yet, but we have the actual number we’ll be using. Since degrees work by 0-360, we’ll convert this to degrees, minutes, and seconds like on a clock.

• Subtract the integer (the number from the left of the decimal) from your existing number. Multiply this by 60. This will give you minutes.
• Repeat the previous step, which will give you seconds.
• Now, put the first integer down as degrees, the second one down as minutes, and the final calculation (round it if not a whole number) as seconds.

While it takes a few steps and may need you to write down a couple numbers so you don’t lose them, thanks to calculators, it’s just a matter of following instructions. If you’re curious how this works, or about other logic involved in this industry, fill out our contact form below!