General Building (B) · Lesson 2 of 7

Rafter and Stair Math: Rise, Run, and Pitch

"Rafter and Stair Math: Rise, Run, and Pitch" is lesson 2 of 7 in the General Building (B) Learning Hub. It opens with "Rafter Length Is a Right Triangle" and works through 5 short steps, then a worked example you can check yourself against.

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Steps in this lesson

  1. Rafter Length Is a Right Triangle
  2. Finding Rise From Pitch
  3. Stair Math Starts With Total Rise
  4. The Code Numbers That Bound the Math
  5. Total Run for the Stair

The worked example in the course applies this lesson to a realistic job in 5 steps, from "Find the rise" through "Find the number of treads and total run".

What you'll be able to do

  • Explain the main idea of "Rafter and Stair Math: Rise, Run, and Pitch" in plain language you can use on the exam.
  • Apply this step with confidence: "Stair Math Starts With Total Rise".
  • Apply this step with confidence: "The Code Numbers That Bound the Math".
  • Apply this step with confidence: "Total Run for the Stair".
  • Test yourself on the worked example and the quick-check quiz inside the classroom.
RAFTER AND STAIR MATH Rise, run, and pitch - both are right-triangle problems RUN = 168" RISE = 84" RAFTER 187.8" RAFTER FORMULA Rise = (Run/12) x Pitch Length^2 = Run^2 + Rise^2 6:12 pitch, 168" run: Rise = 14 x 6 = 84" Rafter = sqrt(168^2+84^2) = 187.8" STAIR MATH (CRC R311.7) Max riser height7 3/4" Min tread depth10" Riser/tread uniformity tolerance3/8" 9 FT FLOOR-TO-FLOOR (108") 1 108 / 7.75 = 13.9 -> 14 risers 2 108 / 14 = 7.71" per riser (under the 7.75" max) 3 Treads = 14 - 1 = 13 4 Total run = 13 x 10" = 130" (about 10'-10") CC
The diagram for this lesson, exactly as it appears in the Learning Hub.

The first steps of this lesson

Step 1: Rafter Length Is a Right Triangle

A common rafter forms the hypotenuse of a right triangle: the RUN is the horizontal distance from the wall plate to the ridge centerline, and the RISE is the vertical distance the roof climbs over that run. Once you know rise and run, the rafter's line length comes straight from the Pythagorean theorem - the same hypotenuse math used for hip and valley framing, just at the plumb-cut angle instead of 45 degrees.

Step 2: Finding Rise From Pitch

Roof pitch is expressed as rise per 12 inches of run (like 6:12 or 8:12 - see the Pitch & Slope lesson for the ratio itself). To find total rise for a given run: divide the run by 12, then multiply by the pitch's rise number. Rise = (Run / 12) x Pitch Rise Number.

The remaining 3 steps, the worked example and the quiz are in the course. This is a preview. The full lesson, with the step-by-step explanations, a worked example and a quick-check quiz, is inside the classroom.

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