Lesson 5 of 13
Slope, Pitch and Grade
Three trades look at the same slanted line and call it three different things. The roofer says pitch, the excavator says grade, the engineer says degrees. Learn to move between them and you can talk to all three.
Step one
Read the material
Three ideas. They are the same idea in three languages.
Concept one
Slope is rise over run
Every slanted line in the trades is described by two numbers: how far it climbs, and how far it travels sideways while climbing. Rise over run. Nothing else.
What changes between trades is only what you divide by. A roofer always divides by twelve inches. An excavator always divides by one hundred. An engineer converts the ratio to an angle. Same line, same rise, same run, three vocabularies.
Concept two
Pitch is rise per twelve, grade is rise per hundred
Pitch is stated in twelfths because a framing square is twelve inches on the tongue. Six in twelve means six inches up for every twelve across.
Grade is a percent, which means rise per hundred of the same unit. To turn pitch into grade, divide the pitch by twelve and multiply by one hundred. Six in twelve is fifty percent grade. That surprises people, because fifty percent sounds enormous and a 6/12 roof is ordinary. It is only the units talking.
Going the other way, multiply the percent by twelve and divide by one hundred. A two percent fall on a drain line is 0.24 in 12, which is why plumbers say a quarter inch per foot instead.
Concept three
Degrees, and why the trades avoid them
The angle is the arctangent of rise over run. A 6 in 12 roof is 26.57 degrees. A 12 in 12 is exactly 45.
Degrees are correct and almost useless on a job site, because you cannot lay a degree on a board. You can lay twelve and six on a framing square. That is the whole reason the trades kept ratios after the rest of the world went to angles. Use degrees when you set a miter saw, and ratios for everything else.
Step two
Work it with your hands on it
One slope, three readings. Move it and watch all three change together.
Hands on it, off the screen. Put a two foot level on any slope you can reach — a driveway, a ramp, a drain line, a roof you can touch. Hold one end on the surface, level the bubble, and measure the gap under the other end.
That gap over that length is your rise over run. Convert it three ways and check it against the panel.
Step three
Prove you understood it
One question per idea, new numbers every time.
All three solid.
You can read a slope as a ratio, convert between pitch and grade, and give the angle when somebody asks for it. Lesson six puts it on a roof.
Trades Geometry
Lesson five of thirteen. Written by our founder, Dr. Gene A Constant, and donated to the Foundation. Published by Global Sovereign University Press.
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