How long is a valley rafter?

For a 24 ft intersecting roof at 6/12, the valley rafter line length is 18 ft before any ridge or tail adjustment. It runs the diagonal of the corner, so it is longer than the common rafter on the same roof.

Is a valley rafter the same length as a hip rafter?

For a regular roof, yes. A regular hip and a regular valley on the same pitch and run have the same line length and the same plumb, seat, and cheek cuts. They differ in how they sit in the roof, an inside versus an outside corner, and in that a hip gets backed or dropped while a valley usually does not.

What is the jack rafter common difference?

It is how much each jack changes from the next. At 6/12 with jacks 16 in on center it is 17-7/8 in: the first jack off the corner is that long, the second is twice that, and so on up the hip or valley.

Does this handle irregular (unequal pitch) valleys?

This page solves the regular valley, where both roof planes share one pitch. The app also solves irregular valleys, where the two planes run different pitches, with a separate plan angle and cut on each face. That case is in the app.

Which way do valley jacks run?

From the valley up to the ridge, growing longer as they step away from the inside corner. Hip jacks are the mirror: they run from the plate up to the hip, growing shorter toward the outside corner. The common difference is identical; only the direction changes.

Roof framing

Valley rafter calculator

Valley rafter length, run, and every cut angle from an intersecting roof span and a pitch, plus the jack rafter common difference and run-down. The same framing math the CutOnce app runs, no trig on your part.

Updated 2026-08-08

Intersecting roof span (ft)

Roof pitch (rise / 12)

Jack spacing (in OC)

Span is the width of the roof that dies into the valley; its half is the common run. Pitch is the common rafter's rise per 12 in of run. Both roof planes share one pitch here (a regular valley).

Valley rafter length: 18 ft
Valley run: 16 ft 11-5/8 in
Ridge height: 6 ft
Plumb cut: 19.5°
Seat cut: 70.5°
Cheek cut: 43.3°
Jack common difference: 17-7/8 in
Jack side cut: 41.8°

First jacks (long to short): 13 ft 5 in · 11 ft 11-1/8 in · 10 ft 5-1/4 in · 8 ft 11-5/16 in

Cheek cut angles are measured from the board's top edge. Subtract from 90° for the angle from square.

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How a valley rafter is calculated

A valley runs diagonally down the inside corner where two roof planes meet, so for every 12 inches a common rafter runs, the valley runs 12 times the square root of 2, about 16.97 inches. Its length is that longer unit run and the roof's rise worked through the Pythagorean theorem. On a regular valley both planes share one pitch, and the common run is half the span of the roof that dies into the valley. That is the same length and cut math as a regular hip, just turned into the corner instead of out of it.

A worked example

A 24 ft wide intersecting roof at 6/12, with jacks 16 in on center. Every number below is computed by the same function that drives the calculator above.

Valley run (diagonal to the corner)	16 ft 11-5/8 in
Valley rafter length	18 ft
Ridge height	6 ft
Plumb cut	19.5°
Seat cut	70.5°
Cheek (side) cut	43.3°
Jack common difference	17-7/8 in

Valley vs hip: same length, opposite corner

A hip sheds water off an outside corner; a valley collects it in an inside corner, where an L-shaped or T-shaped roof, an addition, or a dormer meets the main roof. Geometrically they are mirror images: a regular valley and a regular hip on the same pitch have the same line length and the same plumb, seat, and cheek cuts. The difference is in the assembly. A hip is backed or dropped so the sheathing planes meet flush over its top edge; a valley is usually a doubled member, or a single board left square with the sheathing and shingles woven over it, so there is no backing angle to cut.

Jack rafters: hip, valley, and cripple

Jack rafters are the shortened rafters that fill the triangle between a hip or valley and the plate or ridge. They come in three kinds, and all of them step by the same common difference: each jack is one spacing's worth of common-rafter length longer or shorter than its neighbor, and every one shares a single side (cheek) cut where it meets the hip or valley.

01
Hip jacks
Run from the wall plate up to the hip, getting shorter toward the corner. The run-down below is exactly this series.
02
Valley jacks
Run from the valley up to the ridge, getting longer as they move away from the corner. Same common difference, read the other direction.
03
Cripple jacks
Span hip to valley (or valley to ridge) touching neither plate nor ridge, cut with a cheek on both ends. The app lays these out; this page covers the hip and valley jacks.

Jack run-down for the worked example

At 6/12 with jacks 16 in on center, each jack steps by one common difference. Here are the first jacks, longest to shortest, before any tail or side-cut shortening.

Jack	Length
1	13 ft 5 in
2	11 ft 11-1/8 in
3	10 ft 5-1/4 in
4	8 ft 11-5/16 in
5	7 ft 5-7/16 in
6	5 ft 11-9/16 in

Valley length and cut angles by pitch

Per foot of common run, a valley is this long, with these plumb and cheek cut angles. The length grows with run; the angles are set by pitch alone. Take half your intersecting span as the common run, then scale the length here.

Pitch	Valley length / ft run	Plumb cut	Cheek cut
3/12	17-1/4 in	10.0°	44.6°
4/12	17-7/16 in	13.3°	44.2°
5/12	17-11/16 in	16.4°	43.8°
6/12	18 in	19.5°	43.3°
7/12	18-3/8 in	22.4°	42.8°
8/12	18-3/4 in	25.2°	42.1°
9/12	19-3/16 in	27.9°	41.5°
10/12	19-11/16 in	30.5°	40.7°
12/12	20-13/16 in	35.3°	39.2°

Common questions

How long is a valley rafter?: For a 24 ft intersecting roof at 6/12, the valley rafter line length is 18 ft before any ridge or tail adjustment. It runs the diagonal of the corner, so it is longer than the common rafter on the same roof.
Is a valley rafter the same length as a hip rafter?: For a regular roof, yes. A regular hip and a regular valley on the same pitch and run have the same line length and the same plumb, seat, and cheek cuts. They differ in how they sit in the roof, an inside versus an outside corner, and in that a hip gets backed or dropped while a valley usually does not.
What is the jack rafter common difference?: It is how much each jack changes from the next. At 6/12 with jacks 16 in on center it is 17-7/8 in: the first jack off the corner is that long, the second is twice that, and so on up the hip or valley.
Does this handle irregular (unequal pitch) valleys?: This page solves the regular valley, where both roof planes share one pitch. The app also solves irregular valleys, where the two planes run different pitches, with a separate plan angle and cut on each face. That case is in the app.
Which way do valley jacks run?: From the valley up to the ridge, growing longer as they step away from the inside corner. Hip jacks are the mirror: they run from the plate up to the hip, growing shorter toward the outside corner. The common difference is identical; only the direction changes.

Cut the whole roof, offline

The app frames regular and irregular hips and valleys, lays out every hip, valley, and cripple jack, and prints a cut list, all working with no signal. Part of the one-time toolbox, no subscription.