Measurement units are a pain, across all disciplines, fields, and walks of life. This is especially true in the United States, where we insist on adhering to the ancient Imperial (called Customary here) measurement systems, while still having to juggle the rest of the world’s metric system for compliance, and of course, there are all those lovely industry-specific units. It’s a headache, and when it comes to roofing and carpentry, no exceptions are to be found.
Take the roof pitch, for example. Roofers and carpenters work in slopes, pitches, and special angle ratios not found in most other disciplines (save some areas of engineering). Meanwhile, the rest of us think in standard 0-360 degrees or 0-180 radians. Those are what our high school math classes taught us. Today, we’re going to learn how to measure the pitch of a roof, and then convert it to a unit we understand better. Thankfully, with computers and scientific calculators, this is a lot easier to do than it would’ve otherwise been.
First, let’s measure the pitch. Don’t walk out onto your roof, that’s dangerous, and makes this harder to do. Climb up on a ladder, and place a carpentry square so that the 12 lines up cleanly with the peak.
Observe the number, on the other side, where the edge of the roof intersects it.
This ratio is a standard roofing pitch, which is run (horizontal distance) per foot of rise.
Example: If the roof crosses the 9 on the other part of the square, you’ve got a ratio of 9/12, or nine inches of run per foot (twelve inches) of rise.
Understanding Things Better
When it comes to the mathematical conversion process, it’s far more beneficial to understand the result of a given equation, rather than how it actually achieves the intended goal. If you’re truly interested in how the math behind this works, there are a great number of quite well-constructed videos on the inner workings of trigonometry and linear algebra.
The question, though, is, why do we need this? Why do carpenters use a seemingly-obtuse measurement in the first place? Honestly, because it’s not actually as obtuse as it seems, and it’s far more practical for them, due to its direct relation to many other variables in their trade. To work in a generic mathematical unit like degrees, would actually require them to be running these conversions constantly, and honestly, they’ve little time for such things.
Note: In other parts of the world where metric is used, degrees are actually commonly used for roof pitch, because the base-10 nature of the standard units converts cleanly with a simple tool.
Running the Conversion
Since we have our pitch (ratio), we’re ready to convert it into degrees. That’s right, that trigonometry you had to take in high school, and swore you’d never use? It’s time to use it. Thankfully, it’s easy to do through a calculator. So, let’s use the Windows calculator since it’s a standard one most people have access to.
- Press Windows+R, type “calc” in the box, and press enter. The calculator will appear.
- In the menu, click “View”, and then “Scientific”.
- Enter the number in your ratio that’s smaller than 12, and then divide that by 12. This will produce a number greater than 0, but less than 1, with several decimal places.
- Click the “Inv” button, and then the “Tan-1” button, which will produce a lengthy decimal number between 1 and 2.
We’ve got a basic decimal/percentage figure now. However, this isn’t the degree unit we want. We have a few more steps ahead of us.
- Take the number on the left-hand side of the decimal (the integer), and subtract it from the original. This will give you a decimal number less than 1. Multiply this by 60, to get your “minutes” component.
- Subtract your “minutes” from that less-than-one decimal number, and multiply that result by 60 as well, to get your seconds. You may need to round this down.
- Now, the initial integer is your degrees, the second number is your minutes, and that remainder, as a whole number, is your seconds.
You just successfully converted your roof pitch into degrees, with just a few simple tasks in the calculator. It’s surprisingly easy, and if you have a tiny bit of programming savvy, you could even write a quick little app that does the entire calculation from entering the ratio in one sweep.
To learn more about unit conversions, and the conventions used by roofers, fill out our contact form today. At JDT Construction, we think it’s important for customers to be in the know!