Why is a hip rafter longer than a common rafter?

A hip rafter runs diagonally across the corner instead of straight back, so its horizontal run is the common run times the square root of two, about 1.414 times longer. With the same rise, that makes the hip noticeably longer than a common rafter.

What is the plumb cut on a hip rafter?

The hip plumb cut is shallower than the common plumb cut because the hip travels the longer diagonal. Carpenters often use 17 instead of 12 on the framing square for hips, since the diagonal of a 12 by 12 square is about 17.

What is a jack rafter cheek cut?

Jack rafters run from the wall to the hip and need an angled side cut, called a cheek or side cut, where they meet the hip. For a regular equal pitch hip on a square corner that cheek cut is about 35.26 degrees.

What is the difference between a hip and a valley rafter?

A hip rafter forms an outside corner where two roof planes meet and point up and out. A valley rafter forms an inside corner where two roof planes meet and channel water down. The length and cut geometry are the same; the direction is mirrored.

AngleWise / Hip & Valley

Hip & Valley Rafters:
Lengths & Cuts Made Simple

Hips and valleys are where roof framing gets intimidating — but it's still just triangles, only the rafter runs the diagonal. Give the calculator your roof pitch and common run, and it returns the common and hip lengths, both plumb cuts, and the jack rafter cheek cut.

Hip & Valley Calculator

Enter slope as

Main Roof Pitch — rise in 12

Common Rafter Run — half the building span, to the corner (inches)

The Terms, In Plain English

Common Rafter
The straight rafter that runs from the wall to the ridge, square to the wall. Its run is half the span. Everything else is measured against it.

Hip Rafter
The rafter that runs the outside corner where two roof planes meet, pointing up and out. Because it travels diagonally, it's longer than a common rafter and sits at a shallower angle.

Valley Rafter
The mirror image of a hip — an inside corner where two roof planes meet and funnel water down. Same lengths and cuts as a hip, just running the other way.

Jack Rafter
A shortened rafter that runs from the wall up to the hip (or down from the ridge to the valley). Each one needs an angled cheek cut where it lands on the hip.

Why the Hip Runs Longer

Here's the one idea that makes hips click: a common rafter runs straight back, but a hip runs the diagonal of the corner. Picture the square footprint under the corner — the common rafter follows the side, the hip follows the diagonal across it.

That diagonal is longer by a factor of about 1.414 (the square root of 2). So with the same rise, the hip covers more horizontal distance, which makes it longer and gives it a shallower plumb cut than the common rafter. That's the whole secret.

The "17" shortcut: carpenters frame commons using 12 on the square (the run unit), but hips using 17 — because the diagonal of a 12×12 square is about 17 (actually 16.97). Same pitch, longer run per unit. The calculator uses the exact value, but "17 for hips" is the rule of thumb on the square.

How to Cut a Hip, Step by Step

Set the main roof pitch. The hip is driven by the same pitch as the common rafters — enter it as rise-in-12 or degrees.
Enter the common run. That's half the building span, out to the corner.
Read the hip length. The calculator gives the true diagonal length of the hip rafter.
Cut the hip plumb cut at the shallower angle shown — it leans against the ridge like a common, but at the hip's own angle.
Cut the jack cheek angles. Each jack rafter meeting the hip gets the side (cheek) cut the calculator gives, so it lands flush against the hip.

Common Mistakes

Using common-rafter length for the hip. The hip is longer because of the diagonal. Cut it to the hip length, not the common length, or it'll fall short.
Using the common plumb cut on the hip. The hip's plumb cut is shallower. Mixing them up leaves a gap at the ridge.
Forgetting the cheek cut on jacks. Jacks need an angled side cut to sit flush against the hip — a square cut leaves a wedge gap.
Skipping the test rafter. Cut one hip and one jack, fit them, then use them as patterns. Hips are expensive to get wrong in a stack.

Frequently Asked Questions

Why is a hip rafter longer than a common rafter?: It runs the diagonal of the corner, so its horizontal run is about 1.414× longer. Same rise, longer run, longer rafter.
What is the plumb cut on a hip rafter?: A shallower plumb cut than the common, because the hip travels the longer diagonal. Carpenters use "17" on the square for hips instead of 12.
What is a jack rafter cheek cut?: The angled side cut where a jack rafter meets the hip — about 35.26° for a regular equal-pitch hip on a square corner.
What's the difference between a hip and a valley?: A hip is an outside corner pointing up and out; a valley is an inside corner channeling water down. Same lengths and cuts, mirrored direction.

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