Inputs
White theme • Client-side computationApplies to span/run/overhang.
Choose how you enter slope.
For rise per 12, enter rise like 6.
Choose which you will enter.
Run will be span ÷ 2 for equal-pitch valley.
Horizontal distance perpendicular to ridge.
Horizontal; tail adds length along valley.
Results
Valley length (to ridge, no tail)
—
Total length (including overhang tail)
—
Plan diagonal (corner to ridge)
—
Hip/valley factor (√(2 + s²))
—
Common factor: —
Plumb angle θ
—
Cheek bevel β (valley): —
How to use
- Select your length units.
- Choose span or run as the base input.
- Enter pitch as rise-per-12, angle, or percent.
- Add overhang if the tail extends beyond the plate.
- Press Calculate. Optionally add to history.
- Export history as CSV or print to PDF.
Tip: For equal-pitch valleys meeting at right angles, run = span ÷ 2.
Formula used
Let slope be s (rise per unit horizontal).
For rise-per-12 input, s = rise / 12.
For angle input, s = tan(θ).
For percent grade, s = % / 100.
With common horizontal run R and overhang O (same units), the
45° valley length to the ridge is:
Lcore = R · √( 2 + s² )
Ltotal = (R + O) · √( 2 + s² )
Plan diagonal: D = √2 · R
Angles: plumb θ = atan(s), cheek bevel (valley) β = atan( s / √2 ).
Equal pitches and 90° plan assumed.
how to find the length of a valley rafter
- Decide your base: enter total span or the common run.
- Convert pitch to slope
s:- Rise-per-12:
s = rise / 12 - Angle:
s = tan(θ) - Percent:
s = % / 100
- Rise-per-12:
- For equal pitches meeting at 90°, set
R = run(orspan ÷ 2). - Compute the hip/valley factor
FHV = √(2 + s²). - Length to ridge (no tail):
Lcore = R · FHV. - If an eave tail exists, use total:
Ltotal = (R + O) · FHV. - Angles for cuts:
- Plumb:
θ = atan(s) - Cheek bevel (valley):
β = atan( s / √2 )
- Plumb:
Worked example — span = 20 ft, pitch = 6-in-12, overhang = 1 ft.
Run
Hip/valley factor
Valley to ridge
Total with tail
Plumb angle
Run
R = span ÷ 2 = 10 ft, slope s = 6/12 = 0.5.Hip/valley factor
FHV = √(2 + 0.5²) = √2.25 = 1.5.Valley to ridge
Lcore = 10 × 1.5 = 15.000 ft.Total with tail
Ltotal = (10 + 1) × 1.5 = 16.500 ft.Plumb angle
θ ≈ 26.565°, cheek bevel β ≈ 19.471°.
Use local code requirements and manufacturer literature for final detailing.
Valley rafter factors (quick table)
| Pitch (in/12) | Slope s | √(2 + s²) | Plumb angle θ (°) | Cheek bevel β (°) |
|---|---|---|---|---|
| 3 | 0.2500 | 1.436141 | 14.036 | 10.025 |
| 4 | 0.3333 | 1.452966 | 18.435 | 13.263 |
| 5 | 0.4167 | 1.474317 | 22.620 | 16.416 |
| 6 | 0.5000 | 1.500000 | 26.565 | 19.471 |
| 8 | 0.6667 | 1.563472 | 33.690 | 25.239 |
| 10 | 0.8333 | 1.641476 | 39.806 | 30.509 |
| 12 | 1.0000 | 1.732051 | 45.000 | 35.264 |
Use the factor to multiply by run for core length.
Sample core lengths for common runs (no overhang)
| Run (ft) | 4/12 | 6/12 | 8/12 |
|---|---|---|---|
| 8 | 11.624 ft | 12.000 ft | 12.508 ft |
| 10 | 14.530 ft | 15.000 ft | 15.635 ft |
| 12 | 17.436 ft | 18.000 ft | 18.762 ft |
Core length = run × √(2 + s²). Add tail length if applicable.
Length added per foot of overhang
Each 1 ft of horizontal overhang increases valley length by the factor.
| Pitch (in/12) | Added length per 1 ft overhang |
|---|---|
| 4/12 | ≈ 1.453 ft |
| 6/12 | ≈ 1.500 ft |
| 8/12 | ≈ 1.563 ft |
General: ΔL = O × √(2 + s²), where O is overhang.
Example data
Click a row to load its inputs.
| # | Units | Mode | Span | Run | Pitch type | Pitch value | Overhang |
|---|---|---|---|---|---|---|---|
| 1 | ft | span | 20 | — | rise per 12 | 6 | 1 |
| 2 | ft | run | — | 14 | rise per 12 | 8 | 1.5 |
| 3 | m | span | 7.2 | — | angle | 26.565 | 0.25 |
History (for CSV/PDF)
| Timestamp | Units | Mode | Span | Run | Pitch type | Pitch | Overhang | Hip factor | Core length | Total length | Plan diagonal | Plumb θ | Bevel β |
|---|
Add rows after each calculation, then export.