Hip and Valley Factor • Hip & Valley Rafter Slope Chart

By Roof Online Staff • Updated September 27, 2023

Table of Contents

Note: The values discussed on this page and given in the hip and valley factor table apply to regular hips and valleys, where the roof sections have the same slope and meet to form a 90-degree angle and the hip or valley forms a 45-degree angle with the eave. The information on this page will not apply to the hip rafters on an octagonal roof, for example.

What is a Hip and Valley Factor?

The hip and valley factor is a number that is multiplied by the run, or horizontal distance covered, of a common rafter to determine the length of a hip or valley rafter. Repeat, the horizontal distance covered, not the length, of a common rafter.

For precision, the thickness of the ridge board and any eave overhang should be taken into account when determining the run.

The hip and valley factor varies according to the slope of the roof, as shown in the table below.

Hip and Valley Factor Formula

For a roof slope expressed as “X-in-12” (rise-in-run), the hip and valley factor is determined by finding the square root of ((rise/run)² + 2) for the slope of the adjacent roof sections.

Divide the rise by the run (the run is 12). Square the result. Add 2. Find the square root of the result. 

You need to know the hip and valley factor to determine the hip rafter length on hip roofs like this.
A roof hip!
You need to know the hip and valley factor to determine the valley rafter length for roof valleys like this.
A roof valley!

Hip and Valley Rafter Pitch is Different from the Roof Pitch

On a related note, the pitch (properly the “slope”) of a hip or valley rafter will not be the same as the pitch of the adjacent roof sections. The slope of the hip or valley rafter will be lower than the slope of the adjacent roof sections.

This is because the hip or valley rafter has to rise the exact same total amount, from the height of the eaves to the height of the ridge, but it has to do it over a longer distance.

Where common rafters (the regular rafters) rise a certain distance over 12 inches, the hip or valley rafter will rise the same distance over 16.97 inches.

While the slopes of the common rafters are expressed as “X-in-12″, the slope of the hip and valley rafter on the same roof will be “X-in-16.97“.

So where two roof sections intersect to form a 90° angle (a regular hip or valley), and each roof section has, for example, a 6-in-12 slope, the hip or valley rafter at that intersection will have a slope of 6-in-16.97.

Expressing the same thing using degrees: the roof sections in the above example have a 26.57° slope, while the hip or valley rafter will have a 19.47° slope.

Remember that the heel cut, seat cut, and head cut for a hip and valley rafter will have angles that reflect this difference in slope. Do not cut them according to a template you have been using for the common rafters.

Roof Pitch Measurement Tools

If you want to verify the slope of your rafters to an amazing degree of accuracy and you like cool new tools, you should check out this digital level.

It’s probably be way too expensive for what you need. This is what professionals use. It will tell you the rafter’s slope in degrees, rise/run, or percentage, and automatically convert from one to the other.

As a (much) cheaper alternative, we recommend this slope finder. It’s very inexpensive and very accurate.

One more thing: if you’re using this table, you should consider getting yourself a construction calculator. This one is very good.

Table: Hip and Valley Factors

Hip and Valley Factor Table
Roof Slope
Roof Slope
(In Degrees)
Hip or Valley
Rafter Slope
Hip or Valley
Rafter Slope
(In Degrees)
Hip and Valley Factor
1-in-12 4.76° 1-in-16.97 3.37° 1.4167
1.5-in-12 7.13° 1.5-in-16.97 5.05° 1.4197
2-in-12 9.46° 2-in-16.97 6.72° 1.4240
2.5-in-12 11.77° 2.5-in-16.97 8.38° 1.4295
3-in-12 14.04° 3-in-16.97 10.03° 1.4362
3.5-in-12 16.26° 3.5-in-16.97 11.65° 1.4440
4-in-12 18.43° 4-in-16.97 13.26° 1.4529
4.5-in-12 20.56° 4.5-in-16.97 14.85° 1.4631
5-in-12 22.62° 5-in-16.97 16.42° 1.4743
5.5-in-12 24.62° 5.5-in-16.97 17.96° 1.4866
6-in-12 26.57° 6-in-16.97 19.47° 1.5
6.5-in-12 28.44° 6.5-in-16.97 20.96° 1.5144
7-in-12 30.26° 7-in-16.97 22.42° 1.5298
7.5-in-12 32.01° 7.5-in-16.97 23.84° 1.5462
8-in-12 33.69° 8-in-16.97 25.24° 1.5635
8.5-in-12 35.31° 8.5-in-16.97 26.61° 1.5817
9-in-12 36.87° 9-in-16.97 27.94° 1.6008
9.5-in-12 38.37° 9.5-in-16.97 29.24° 1.6207
10-in-12 39.81° 10-in-16.97 30.51° 1.6415
10.5-in-12 41.19° 10.5-in-16.97 31.75° 1.6630
11-in-12 42.51° 11-in-16.97 32.95° 1.6853
11.5-in-12 43.78° 11.5-in-16.97 34.12° 1.7083
12-in-12 45° 12-in-16.97 35.27° 1.7321
12.5-in-12 46.17° 12.5-in-16.97 36.38° 1.7564
13-in-12 47.29° 13-in-16.97 37.45° 1.7815
13.5-in12 48.37° 13.5-in-16.97 38.50° 1.8071
14-in-12 49.4° 14-in-16.97 39.52° 1.8333
14.5-in-12 50.39° 14.5-in-16.97 40.51° 1.8601
15-in-12 51.34° 15-in-16.97 41.47° 1.8874
15.5-in-12 52.25° 15.5-in-16.97 42.41° 1.9153
16-in-12 53.13° 16-in-16.97 43.31° 1.9437
16.5-in-12 53.97° 16.5-in-16.97 44.20° 1.9725
17-in-12 54.78° 17-in-16.97 45.05° 2.0017
17.5-in-12 55.56° 17.5-in-16.97 45.88° 2.0314
18-in-12 56.31° 18-in-16.97 46.69° 2.0616
18.5-in-12 57.03° 18.5-in-16.97 47.47° 2.0921
19-in-12 57.72° 19-in-16.97 48.23° 2.1230
19.5-in-12 58.39° 19.5-in-16.97 48.97° 2.1542
20-in-12 59.04° 20-in-16.97 49.69° 2.1858
20.5-in-12 59.66° 20.5-in-16.97 50.38° 2.2177
21-in-12 60.26° 21-in-16.97 51.06° 2.25
21.5-in-12 60.83° 21.5-in-16.97 51.72° 2.2826
22-in-12 61.39° 22-in-16.97 52.35° 2.3154
22.5-in-12 61.93° 22.5-in-16.97 52.98° 2.3485
23-in-12 62.45° 23-in-16.97 53.58° 2.3819
23.5-in-12 62.95° 23.5-in-16.97 54.17° 2.4156
24-in-12 63.43° 24-in-16.97 54.74° 2.4495
24.5-in-12 63.90° 24.5-in-16.97 55.29° 2.4836