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Roof Pitch worksheet

Grades 9–10 · CCSS HSG.SRT.C.8

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- I know the: Slope (%)
- Slope: 50%
- Also find the rafter length: Yes
- Building span (wall to wall): 26 ft
- Eave overhang (horizontal): 2 ft
Find: Roof pitch
Answer
2.
Problem 2.
- I know the: Angle (degrees)
- Roof angle: 24 °
- Also find the rafter length: Yes
- Building span (wall to wall): 24 ft
- Eave overhang (horizontal): 1 ft
Find: Roof pitch
Answer
3.
Problem 3.
- I know the: Angle (degrees)
- Roof angle: 30 °
- Also find the rafter length: Yes
- Building span (wall to wall): 22 ft
- Eave overhang (horizontal): 2 ft
Find: Roof pitch
Answer
4.
Problem 4.
- I know the: Angle (degrees)
- Roof angle: 24 °
- Also find the rafter length: Yes
- Building span (wall to wall): 20 ft
- Eave overhang (horizontal): 1 ft
Find: Roof pitch
Answer
5.
Problem 5.
- I know the: Slope (%)
- Slope: 50%
- Also find the rafter length: Yes
- Building span (wall to wall): 34 ft
- Eave overhang (horizontal): 1 ft
Find: Roof pitch
Answer
6.
Problem 6.
- I know the: Angle (degrees)
- Roof angle: 40 °
- Also find the rafter length: Yes
- Building span (wall to wall): 27 ft
- Eave overhang (horizontal): 1 ft
Find: Roof pitch
Answer
7.
Problem 7.
- I know the: Angle (degrees)
- Roof angle: 30 °
- Also find the rafter length: Yes
- Building span (wall to wall): 26 ft
- Eave overhang (horizontal): 1 ft
Find: Roof pitch
Answer
8.
Problem 8.
- I know the: Pitch (x in 12)
- Pitch: rise per 12 of run: 6 /12
- Also find the rafter length: Yes
- Building span (wall to wall): 16 ft
- Eave overhang (horizontal): 1 ft
Find: Roof pitch
Answer
9.
Problem 9.
- I know the: Pitch (x in 12)
- Pitch: rise per 12 of run: 7 /12
- Also find the rafter length: Yes
- Building span (wall to wall): 20 ft
- Eave overhang (horizontal): 2 ft
Find: Roof pitch
Answer
10.
Problem 10.
- I know the: Pitch (x in 12)
- Pitch: rise per 12 of run: 7 /12
- Also find the rafter length: Yes
- Building span (wall to wall): 16 ft
- Eave overhang (horizontal): 1 ft
Find: Roof pitch
Answer

Answer key: Roof Pitch worksheet

1. Roof pitch: 6/12
1. Find the pitch: a slope percent is the rise per 100 of run, so scale it to a run of 12
  $\frac{12 \times 50}{100}$ $= 6$
2. Write the pitch the way roofers do: rise per 12 of run
  $pitch = 6/12$
3. Find the angle: arctan turns rise ÷ run back into degrees
  $arctan \frac{6}{12}$ $= 26.5651 °$
4. Find the slope percent: the rise for every 100 of run
  $\frac{6}{12} \times 100$ $= 50 %$
5. Find the pitch factor, the sloped length for each foot of flat run. It also turns flat area into roof area
  $\sqrt{1 + {(\frac{6}{12})}^{2}}$ $= 1.118034$
6. Each rafter on a gable roof covers half the span, so halve it to get the rafter run
  $\frac{26}{2}$ $= 13 ft$
7. Find how high the ridge sits above the walls: the rafter run times the rise per foot (pitch ÷ 12)
  $13 \times \frac{6}{12}$ $= 6.5 ft$
8. Add the overhang to the run, then multiply by the pitch factor to get the sloped rafter length
  $13 + 2 \times 1.118034$ $= 16.7705 ft$
2. Roof pitch: 5.34/12
1. Find the pitch: the tangent of the angle is rise ÷ run, so multiply it by 12 to get the rise per 12 of run
  $12 \times tan 24 °$ $= 5.3427$
2. Write the pitch the way roofers do: rise per 12 of run
  $pitch = 5.34/12$
3. Find the angle: arctan turns rise ÷ run back into degrees
  $arctan \frac{5.3427}{12}$ $= 24 °$
4. Find the slope percent: the rise for every 100 of run
  $\frac{5.3427}{12} \times 100$ $= 44.5229 %$
5. Find the pitch factor, the sloped length for each foot of flat run. It also turns flat area into roof area
  $\sqrt{1 + {(\frac{5.3427}{12})}^{2}}$ $= 1.094636$
6. Each rafter on a gable roof covers half the span, so halve it to get the rafter run
  $\frac{24}{2}$ $= 12 ft$
7. Find how high the ridge sits above the walls: the rafter run times the rise per foot (pitch ÷ 12)
  $12 \times \frac{5.3427}{12}$ $= 5.3427 ft$
8. Add the overhang to the run, then multiply by the pitch factor to get the sloped rafter length
  $12 + 1 \times 1.094636$ $= 14.2303 ft$
3. Roof pitch: 6.93/12
1. Find the pitch: the tangent of the angle is rise ÷ run, so multiply it by 12 to get the rise per 12 of run
  $12 \times tan 30 °$ $= 6.9282$
2. Write the pitch the way roofers do: rise per 12 of run
  $pitch = 6.93/12$
3. Find the angle: arctan turns rise ÷ run back into degrees
  $arctan \frac{6.9282}{12}$ $= 30 °$
4. Find the slope percent: the rise for every 100 of run
  $\frac{6.9282}{12} \times 100$ $= 57.735 %$
5. Find the pitch factor, the sloped length for each foot of flat run. It also turns flat area into roof area
  $\sqrt{1 + {(\frac{6.9282}{12})}^{2}}$ $= 1.154701$
6. Each rafter on a gable roof covers half the span, so halve it to get the rafter run
  $\frac{22}{2}$ $= 11 ft$
7. Find how high the ridge sits above the walls: the rafter run times the rise per foot (pitch ÷ 12)
  $11 \times \frac{6.9282}{12}$ $= 6.3509 ft$
8. Add the overhang to the run, then multiply by the pitch factor to get the sloped rafter length
  $11 + 2 \times 1.154701$ $= 15.0111 ft$
4. Roof pitch: 5.34/12
1. Find the pitch: the tangent of the angle is rise ÷ run, so multiply it by 12 to get the rise per 12 of run
  $12 \times tan 24 °$ $= 5.3427$
2. Write the pitch the way roofers do: rise per 12 of run
  $pitch = 5.34/12$
3. Find the angle: arctan turns rise ÷ run back into degrees
  $arctan \frac{5.3427}{12}$ $= 24 °$
4. Find the slope percent: the rise for every 100 of run
  $\frac{5.3427}{12} \times 100$ $= 44.5229 %$
5. Find the pitch factor, the sloped length for each foot of flat run. It also turns flat area into roof area
  $\sqrt{1 + {(\frac{5.3427}{12})}^{2}}$ $= 1.094636$
6. Each rafter on a gable roof covers half the span, so halve it to get the rafter run
  $\frac{20}{2}$ $= 10 ft$
7. Find how high the ridge sits above the walls: the rafter run times the rise per foot (pitch ÷ 12)
  $10 \times \frac{5.3427}{12}$ $= 4.4523 ft$
8. Add the overhang to the run, then multiply by the pitch factor to get the sloped rafter length
  $10 + 1 \times 1.094636$ $= 12.041 ft$
5. Roof pitch: 6/12
1. Find the pitch: a slope percent is the rise per 100 of run, so scale it to a run of 12
  $\frac{12 \times 50}{100}$ $= 6$
2. Write the pitch the way roofers do: rise per 12 of run
  $pitch = 6/12$
3. Find the angle: arctan turns rise ÷ run back into degrees
  $arctan \frac{6}{12}$ $= 26.5651 °$
4. Find the slope percent: the rise for every 100 of run
  $\frac{6}{12} \times 100$ $= 50 %$
5. Find the pitch factor, the sloped length for each foot of flat run. It also turns flat area into roof area
  $\sqrt{1 + {(\frac{6}{12})}^{2}}$ $= 1.118034$
6. Each rafter on a gable roof covers half the span, so halve it to get the rafter run
  $\frac{34}{2}$ $= 17 ft$
7. Find how high the ridge sits above the walls: the rafter run times the rise per foot (pitch ÷ 12)
  $17 \times \frac{6}{12}$ $= 8.5 ft$
8. Add the overhang to the run, then multiply by the pitch factor to get the sloped rafter length
  $17 + 1 \times 1.118034$ $= 20.1246 ft$
6. Roof pitch: 10.07/12
1. Find the pitch: the tangent of the angle is rise ÷ run, so multiply it by 12 to get the rise per 12 of run
  $12 \times tan 40 °$ $= 10.0692$
2. Write the pitch the way roofers do: rise per 12 of run
  $pitch = 10.07/12$
3. Find the angle: arctan turns rise ÷ run back into degrees
  $arctan \frac{10.0692}{12}$ $= 40 °$
4. Find the slope percent: the rise for every 100 of run
  $\frac{10.0692}{12} \times 100$ $= 83.91 %$
5. Find the pitch factor, the sloped length for each foot of flat run. It also turns flat area into roof area
  $\sqrt{1 + {(\frac{10.0692}{12})}^{2}}$ $= 1.305407$
6. Each rafter on a gable roof covers half the span, so halve it to get the rafter run
  $\frac{27}{2}$ $= 13.5 ft$
7. Find how high the ridge sits above the walls: the rafter run times the rise per foot (pitch ÷ 12)
  $13.5 \times \frac{10.0692}{12}$ $= 11.3278 ft$
8. Add the overhang to the run, then multiply by the pitch factor to get the sloped rafter length
  $13.5 + 1 \times 1.305407$ $= 18.9284 ft$
7. Roof pitch: 6.93/12
1. Find the pitch: the tangent of the angle is rise ÷ run, so multiply it by 12 to get the rise per 12 of run
  $12 \times tan 30 °$ $= 6.9282$
2. Write the pitch the way roofers do: rise per 12 of run
  $pitch = 6.93/12$
3. Find the angle: arctan turns rise ÷ run back into degrees
  $arctan \frac{6.9282}{12}$ $= 30 °$
4. Find the slope percent: the rise for every 100 of run
  $\frac{6.9282}{12} \times 100$ $= 57.735 %$
5. Find the pitch factor, the sloped length for each foot of flat run. It also turns flat area into roof area
  $\sqrt{1 + {(\frac{6.9282}{12})}^{2}}$ $= 1.154701$
6. Each rafter on a gable roof covers half the span, so halve it to get the rafter run
  $\frac{26}{2}$ $= 13 ft$
7. Find how high the ridge sits above the walls: the rafter run times the rise per foot (pitch ÷ 12)
  $13 \times \frac{6.9282}{12}$ $= 7.5056 ft$
8. Add the overhang to the run, then multiply by the pitch factor to get the sloped rafter length
  $13 + 1 \times 1.154701$ $= 16.1658 ft$
8. Roof pitch: 6/12
1. Write the pitch the way roofers do: rise per 12 of run
  $pitch = 6/12$
2. Find the angle: arctan turns rise ÷ run back into degrees
  $arctan \frac{6}{12}$ $= 26.5651 °$
3. Find the slope percent: the rise for every 100 of run
  $\frac{6}{12} \times 100$ $= 50 %$
4. Find the pitch factor, the sloped length for each foot of flat run. It also turns flat area into roof area
  $\sqrt{1 + {(\frac{6}{12})}^{2}}$ $= 1.118034$
5. Each rafter on a gable roof covers half the span, so halve it to get the rafter run
  $\frac{16}{2}$ $= 8 ft$
6. Find how high the ridge sits above the walls: the rafter run times the rise per foot (pitch ÷ 12)
  $8 \times \frac{6}{12}$ $= 4 ft$
7. Add the overhang to the run, then multiply by the pitch factor to get the sloped rafter length
  $8 + 1 \times 1.118034$ $= 10.0623 ft$
9. Roof pitch: 7/12
1. Write the pitch the way roofers do: rise per 12 of run
  $pitch = 7/12$
2. Find the angle: arctan turns rise ÷ run back into degrees
  $arctan \frac{7}{12}$ $= 30.2564 °$
3. Find the slope percent: the rise for every 100 of run
  $\frac{7}{12} \times 100$ $= 58.3333 %$
4. Find the pitch factor, the sloped length for each foot of flat run. It also turns flat area into roof area
  $\sqrt{1 + {(\frac{7}{12})}^{2}}$ $= 1.157704$
5. Each rafter on a gable roof covers half the span, so halve it to get the rafter run
  $\frac{20}{2}$ $= 10 ft$
6. Find how high the ridge sits above the walls: the rafter run times the rise per foot (pitch ÷ 12)
  $10 \times \frac{7}{12}$ $= 5.8333 ft$
7. Add the overhang to the run, then multiply by the pitch factor to get the sloped rafter length
  $10 + 2 \times 1.157704$ $= 13.8924 ft$
10. Roof pitch: 7/12
1. Write the pitch the way roofers do: rise per 12 of run
  $pitch = 7/12$
2. Find the angle: arctan turns rise ÷ run back into degrees
  $arctan \frac{7}{12}$ $= 30.2564 °$
3. Find the slope percent: the rise for every 100 of run
  $\frac{7}{12} \times 100$ $= 58.3333 %$
4. Find the pitch factor, the sloped length for each foot of flat run. It also turns flat area into roof area
  $\sqrt{1 + {(\frac{7}{12})}^{2}}$ $= 1.157704$
5. Each rafter on a gable roof covers half the span, so halve it to get the rafter run
  $\frac{16}{2}$ $= 8 ft$
6. Find how high the ridge sits above the walls: the rafter run times the rise per foot (pitch ÷ 12)
  $8 \times \frac{7}{12}$ $= 4.6667 ft$
7. Add the overhang to the run, then multiply by the pitch factor to get the sloped rafter length
  $8 + 1 \times 1.157704$ $= 10.4193 ft$