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Rafter Length worksheet

Grades 8–10 · CCSS 8.G.B.7, HSG.SRT.C.8

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

1.
Problem 1.
- Roof pitch: rise per 12 of run: 8 /12
- Building run (outside of wall to center of ridge): 6 ft
- Ridge board thickness: 1.5 in
- Eave overhang (horizontal, past the wall): 24 in
- Birdsmouth seat cut (bearing on the wall plate): 5.5 in
- Rafter depth (actual): 7.25 in
Find: Rafter length (with overhang, ridge reduction taken)
Answer
2.
Problem 2.
- Roof pitch: rise per 12 of run: 8 /12
- Building run (outside of wall to center of ridge): 14 ft
- Ridge board thickness: 1.5 in
- Eave overhang (horizontal, past the wall): 24 in
- Birdsmouth seat cut (bearing on the wall plate): 3.5 in
- Rafter depth (actual): 7.25 in
Find: Rafter length (with overhang, ridge reduction taken)
Answer
3.
Problem 3.
- Roof pitch: rise per 12 of run: 4 /12
- Building run (outside of wall to center of ridge): 10 ft
- Ridge board thickness: 0 in
- Eave overhang (horizontal, past the wall): 0 in
- Birdsmouth seat cut (bearing on the wall plate): 3.5 in
- Rafter depth (actual): 5.5 in
Find: Rafter length (with overhang, ridge reduction taken)
Answer
4.
Problem 4.
- Roof pitch: rise per 12 of run: 6 /12
- Building run (outside of wall to center of ridge): 14 ft
- Ridge board thickness: 0 in
- Eave overhang (horizontal, past the wall): 0 in
- Birdsmouth seat cut (bearing on the wall plate): 3.5 in
- Rafter depth (actual): 7.25 in
Find: Rafter length (with overhang, ridge reduction taken)
Answer
5.
Problem 5.
- Roof pitch: rise per 12 of run: 8 /12
- Building run (outside of wall to center of ridge): 14 ft
- Ridge board thickness: 0 in
- Eave overhang (horizontal, past the wall): 12 in
- Birdsmouth seat cut (bearing on the wall plate): 5.5 in
- Rafter depth (actual): 9.25 in
Find: Rafter length (with overhang, ridge reduction taken)
Answer
6.
Problem 6.
- Roof pitch: rise per 12 of run: 9 /12
- Building run (outside of wall to center of ridge): 8 ft
- Ridge board thickness: 3 in
- Eave overhang (horizontal, past the wall): 16 in
- Birdsmouth seat cut (bearing on the wall plate): 5.5 in
- Rafter depth (actual): 11.25 in
Find: Rafter length (with overhang, ridge reduction taken)
Answer
7.
Problem 7.
- Roof pitch: rise per 12 of run: 5 /12
- Building run (outside of wall to center of ridge): 14 ft
- Ridge board thickness: 0 in
- Eave overhang (horizontal, past the wall): 12 in
- Birdsmouth seat cut (bearing on the wall plate): 3.5 in
- Rafter depth (actual): 5.5 in
Find: Rafter length (with overhang, ridge reduction taken)
Answer
8.
Problem 8.
- Roof pitch: rise per 12 of run: 4 /12
- Building run (outside of wall to center of ridge): 14 ft
- Ridge board thickness: 1.5 in
- Eave overhang (horizontal, past the wall): 0 in
- Birdsmouth seat cut (bearing on the wall plate): 3.5 in
- Rafter depth (actual): 5.5 in
Find: Rafter length (with overhang, ridge reduction taken)
Answer
9.
Problem 9.
- Roof pitch: rise per 12 of run: 8 /12
- Building run (outside of wall to center of ridge): 16 ft
- Ridge board thickness: 0 in
- Eave overhang (horizontal, past the wall): 24 in
- Birdsmouth seat cut (bearing on the wall plate): 5.5 in
- Rafter depth (actual): 7.25 in
Find: Rafter length (with overhang, ridge reduction taken)
Answer
10.
Problem 10.
- Roof pitch: rise per 12 of run: 5 /12
- Building run (outside of wall to center of ridge): 14 ft
- Ridge board thickness: 3 in
- Eave overhang (horizontal, past the wall): 24 in
- Birdsmouth seat cut (bearing on the wall plate): 5.5 in
- Rafter depth (actual): 11.25 in
Find: Rafter length (with overhang, ridge reduction taken)
Answer

Answer key: Rafter Length worksheet

1. Rafter length (with overhang, ridge reduction taken): 114.48 in
1. Find the pitch factor: how many inches of sloped rafter you need for each inch of level run
  $\sqrt{1 + {(\frac{8}{12})}^{2}}$ $= 1.20185$
2. Turn the run into inches and take off half the ridge board, because rafters stop at its face, not its center
  $6 \times 12 - \frac{1.5}{2}$ $= 71.25 in$
3. Multiply that run by the pitch factor to get the sloped length from the wall to the ridge
  $71.25 \times 1.20185$ $= 85.6318 in$
4. Multiply the overhang by the pitch factor too, since the tail slopes at the same angle
  $24 \times 1.20185$ $= 28.8444 in$
5. Add the main length and the tail to get the whole rafter
  $85.6318 + 28.8444$ $= 114.4763 in$
6. Find the roof angle from the pitch. That angle sets both the top (plumb) cut and the seat cut
  $arctan \frac{8}{12}$ $= 33.6901 °$
7. Find the height of the notch's upright cut (the heel): the seat length times the rise per inch
  $5.5 \times \frac{8}{12}$ $= 3.6667 in$
8. Find how much wood stays above the wall: the rafter's upright depth minus the heel
  $7.25 \times 1.20185 - 3.6667$ $= 5.0467 in$
2. Rafter length (with overhang, ridge reduction taken): 229.85 in
1. Find the pitch factor: how many inches of sloped rafter you need for each inch of level run
  $\sqrt{1 + {(\frac{8}{12})}^{2}}$ $= 1.20185$
2. Turn the run into inches and take off half the ridge board, because rafters stop at its face, not its center
  $14 \times 12 - \frac{1.5}{2}$ $= 167.25 in$
3. Multiply that run by the pitch factor to get the sloped length from the wall to the ridge
  $167.25 \times 1.20185$ $= 201.0095 in$
4. Multiply the overhang by the pitch factor too, since the tail slopes at the same angle
  $24 \times 1.20185$ $= 28.8444 in$
5. Add the main length and the tail to get the whole rafter
  $201.0095 + 28.8444$ $= 229.8539 in$
6. Find the roof angle from the pitch. That angle sets both the top (plumb) cut and the seat cut
  $arctan \frac{8}{12}$ $= 33.6901 °$
7. Find the height of the notch's upright cut (the heel): the seat length times the rise per inch
  $3.5 \times \frac{8}{12}$ $= 2.3333 in$
8. Find how much wood stays above the wall: the rafter's upright depth minus the heel
  $7.25 \times 1.20185 - 2.3333$ $= 6.3801 in$
3. Rafter length (with overhang, ridge reduction taken): 126.49 in
1. Find the pitch factor: how many inches of sloped rafter you need for each inch of level run
  $\sqrt{1 + {(\frac{4}{12})}^{2}}$ $= 1.054093$
2. Turn the run into inches and take off half the ridge board, because rafters stop at its face, not its center
  $10 \times 12 - \frac{0}{2}$ $= 120 in$
3. Multiply that run by the pitch factor to get the sloped length from the wall to the ridge
  $120 \times 1.054093$ $= 126.4911 in$
4. Multiply the overhang by the pitch factor too, since the tail slopes at the same angle
  $0 \times 1.054093$ $= 0 in$
5. Add the main length and the tail to get the whole rafter
  $126.4911 + 0$ $= 126.4911 in$
6. Find the roof angle from the pitch. That angle sets both the top (plumb) cut and the seat cut
  $arctan \frac{4}{12}$ $= 18.4349 °$
7. Find the height of the notch's upright cut (the heel): the seat length times the rise per inch
  $3.5 \times \frac{4}{12}$ $= 1.1667 in$
8. Find how much wood stays above the wall: the rafter's upright depth minus the heel
  $5.5 \times 1.054093 - 1.1667$ $= 4.6308 in$
4. Rafter length (with overhang, ridge reduction taken): 187.83 in
1. Find the pitch factor: how many inches of sloped rafter you need for each inch of level run
  $\sqrt{1 + {(\frac{6}{12})}^{2}}$ $= 1.118034$
2. Turn the run into inches and take off half the ridge board, because rafters stop at its face, not its center
  $14 \times 12 - \frac{0}{2}$ $= 168 in$
3. Multiply that run by the pitch factor to get the sloped length from the wall to the ridge
  $168 \times 1.118034$ $= 187.8297 in$
4. Multiply the overhang by the pitch factor too, since the tail slopes at the same angle
  $0 \times 1.118034$ $= 0 in$
5. Add the main length and the tail to get the whole rafter
  $187.8297 + 0$ $= 187.8297 in$
6. Find the roof angle from the pitch. That angle sets both the top (plumb) cut and the seat cut
  $arctan \frac{6}{12}$ $= 26.5651 °$
7. Find the height of the notch's upright cut (the heel): the seat length times the rise per inch
  $3.5 \times \frac{6}{12}$ $= 1.75 in$
8. Find how much wood stays above the wall: the rafter's upright depth minus the heel
  $7.25 \times 1.118034 - 1.75$ $= 6.3557 in$
5. Rafter length (with overhang, ridge reduction taken): 216.33 in
1. Find the pitch factor: how many inches of sloped rafter you need for each inch of level run
  $\sqrt{1 + {(\frac{8}{12})}^{2}}$ $= 1.20185$
2. Turn the run into inches and take off half the ridge board, because rafters stop at its face, not its center
  $14 \times 12 - \frac{0}{2}$ $= 168 in$
3. Multiply that run by the pitch factor to get the sloped length from the wall to the ridge
  $168 \times 1.20185$ $= 201.9109 in$
4. Multiply the overhang by the pitch factor too, since the tail slopes at the same angle
  $12 \times 1.20185$ $= 14.4222 in$
5. Add the main length and the tail to get the whole rafter
  $201.9109 + 14.4222$ $= 216.3331 in$
6. Find the roof angle from the pitch. That angle sets both the top (plumb) cut and the seat cut
  $arctan \frac{8}{12}$ $= 33.6901 °$
7. Find the height of the notch's upright cut (the heel): the seat length times the rise per inch
  $5.5 \times \frac{8}{12}$ $= 3.6667 in$
8. Find how much wood stays above the wall: the rafter's upright depth minus the heel
  $9.25 \times 1.20185 - 3.6667$ $= 7.4504 in$
6. Rafter length (with overhang, ridge reduction taken): 138.13 in
1. Find the pitch factor: how many inches of sloped rafter you need for each inch of level run
  $\sqrt{1 + {(\frac{9}{12})}^{2}}$ $= 1.25$
2. Turn the run into inches and take off half the ridge board, because rafters stop at its face, not its center
  $8 \times 12 - \frac{3}{2}$ $= 94.5 in$
3. Multiply that run by the pitch factor to get the sloped length from the wall to the ridge
  $94.5 \times 1.25$ $= 118.125 in$
4. Multiply the overhang by the pitch factor too, since the tail slopes at the same angle
  $16 \times 1.25$ $= 20 in$
5. Add the main length and the tail to get the whole rafter
  $118.125 + 20$ $= 138.125 in$
6. Find the roof angle from the pitch. That angle sets both the top (plumb) cut and the seat cut
  $arctan \frac{9}{12}$ $= 36.8699 °$
7. Find the height of the notch's upright cut (the heel): the seat length times the rise per inch
  $5.5 \times \frac{9}{12}$ $= 4.125 in$
8. Find how much wood stays above the wall: the rafter's upright depth minus the heel
  $11.25 \times 1.25 - 4.125$ $= 9.9375 in$
7. Rafter length (with overhang, ridge reduction taken): 195 in
1. Find the pitch factor: how many inches of sloped rafter you need for each inch of level run
  $\sqrt{1 + {(\frac{5}{12})}^{2}}$ $= 1.083333$
2. Turn the run into inches and take off half the ridge board, because rafters stop at its face, not its center
  $14 \times 12 - \frac{0}{2}$ $= 168 in$
3. Multiply that run by the pitch factor to get the sloped length from the wall to the ridge
  $168 \times 1.083333$ $= 182 in$
4. Multiply the overhang by the pitch factor too, since the tail slopes at the same angle
  $12 \times 1.083333$ $= 13 in$
5. Add the main length and the tail to get the whole rafter
  $182 + 13$ $= 195 in$
6. Find the roof angle from the pitch. That angle sets both the top (plumb) cut and the seat cut
  $arctan \frac{5}{12}$ $= 22.6199 °$
7. Find the height of the notch's upright cut (the heel): the seat length times the rise per inch
  $3.5 \times \frac{5}{12}$ $= 1.4583 in$
8. Find how much wood stays above the wall: the rafter's upright depth minus the heel
  $5.5 \times 1.083333 - 1.4583$ $= 4.5 in$
8. Rafter length (with overhang, ridge reduction taken): 176.3 in
1. Find the pitch factor: how many inches of sloped rafter you need for each inch of level run
  $\sqrt{1 + {(\frac{4}{12})}^{2}}$ $= 1.054093$
2. Turn the run into inches and take off half the ridge board, because rafters stop at its face, not its center
  $14 \times 12 - \frac{1.5}{2}$ $= 167.25 in$
3. Multiply that run by the pitch factor to get the sloped length from the wall to the ridge
  $167.25 \times 1.054093$ $= 176.297 in$
4. Multiply the overhang by the pitch factor too, since the tail slopes at the same angle
  $0 \times 1.054093$ $= 0 in$
5. Add the main length and the tail to get the whole rafter
  $176.297 + 0$ $= 176.297 in$
6. Find the roof angle from the pitch. That angle sets both the top (plumb) cut and the seat cut
  $arctan \frac{4}{12}$ $= 18.4349 °$
7. Find the height of the notch's upright cut (the heel): the seat length times the rise per inch
  $3.5 \times \frac{4}{12}$ $= 1.1667 in$
8. Find how much wood stays above the wall: the rafter's upright depth minus the heel
  $5.5 \times 1.054093 - 1.1667$ $= 4.6308 in$
9. Rafter length (with overhang, ridge reduction taken): 259.6 in
1. Find the pitch factor: how many inches of sloped rafter you need for each inch of level run
  $\sqrt{1 + {(\frac{8}{12})}^{2}}$ $= 1.20185$
2. Turn the run into inches and take off half the ridge board, because rafters stop at its face, not its center
  $16 \times 12 - \frac{0}{2}$ $= 192 in$
3. Multiply that run by the pitch factor to get the sloped length from the wall to the ridge
  $192 \times 1.20185$ $= 230.7553 in$
4. Multiply the overhang by the pitch factor too, since the tail slopes at the same angle
  $24 \times 1.20185$ $= 28.8444 in$
5. Add the main length and the tail to get the whole rafter
  $230.7553 + 28.8444$ $= 259.5997 in$
6. Find the roof angle from the pitch. That angle sets both the top (plumb) cut and the seat cut
  $arctan \frac{8}{12}$ $= 33.6901 °$
7. Find the height of the notch's upright cut (the heel): the seat length times the rise per inch
  $5.5 \times \frac{8}{12}$ $= 3.6667 in$
8. Find how much wood stays above the wall: the rafter's upright depth minus the heel
  $7.25 \times 1.20185 - 3.6667$ $= 5.0467 in$
10. Rafter length (with overhang, ridge reduction taken): 206.38 in
1. Find the pitch factor: how many inches of sloped rafter you need for each inch of level run
  $\sqrt{1 + {(\frac{5}{12})}^{2}}$ $= 1.083333$
2. Turn the run into inches and take off half the ridge board, because rafters stop at its face, not its center
  $14 \times 12 - \frac{3}{2}$ $= 166.5 in$
3. Multiply that run by the pitch factor to get the sloped length from the wall to the ridge
  $166.5 \times 1.083333$ $= 180.375 in$
4. Multiply the overhang by the pitch factor too, since the tail slopes at the same angle
  $24 \times 1.083333$ $= 26 in$
5. Add the main length and the tail to get the whole rafter
  $180.375 + 26$ $= 206.375 in$
6. Find the roof angle from the pitch. That angle sets both the top (plumb) cut and the seat cut
  $arctan \frac{5}{12}$ $= 22.6199 °$
7. Find the height of the notch's upright cut (the heel): the seat length times the rise per inch
  $5.5 \times \frac{5}{12}$ $= 2.2917 in$
8. Find how much wood stays above the wall: the rafter's upright depth minus the heel
  $11.25 \times 1.083333 - 2.2917$ $= 9.8958 in$