Hip Rafter Calculator

A hip rafter runs diagonally across the plan, so it covers 16.97 inches for every 12 inches a common rafter covers. Most framers round that to 17 on the square, which is close enough on a small roof and off by nearly half an inch on a large one. This calculator uses the true figure, shows what the shortcut would have given, and works out the two things that are almost never published: the backing bevel that keeps the hip below the roof planes, and the common difference that lets you cut every jack rafter without measuring one of them.

Hip rafter length: 20' 10 7/8" Ridge to the outside corner of the plate, 1.5" ridge shortening removed and 24" of eave carried around the corner. Theoretical length before adjustments is 18' 0".
Hip unit run: 16.9706" A hip travels diagonally in plan, so for every 12 inches of common run it covers √(12² + 12²) = 16.97 inches. Using 12 here — treating the hip like a common rafter — makes it far too short.
Using 17 instead of 16.97: +0.333" long The framing square shortcut gives 18' 0 5/16" against a true 18' 0". On this span the difference is about 5/16 of an inch — enough to matter if you are cutting to a line.
Hip plan run: 16' 11 5/8" 12' 0" of common run × √2. This is the horizontal distance from the corner to the point below the ridge end.
Hip plumb cut: 19.5° The hip is shallower than the commons on the same roof — those cut at 26.6°. Same rise, longer run. Level cut is 70.5°.
Backing bevel: 18.4° each side The two roof planes meet above the hip's top edge, so a square-topped hip stands proud of the sheathing. Bevel both sides at 18.4°, or drop the hip instead.
Or drop the hip: 0.250" Deepening the birdsmouth by 0.250" lowers the hip until its top corners sit in the roof planes. Faster than backing and structurally equivalent, at the cost of a slightly deeper seat cut.
Ridge shortening: 1.125" Half the ridge thickness measured on the 45° diagonal, converted along the slope. A hip meets the ridge corner at an angle, so it loses more than a common rafter does at the same ridge.
Jack rafter common difference: 17.889" Each jack at 16" on centre is this much shorter than the one before it. Cut the longest, then step down by this figure — no jack needs measuring individually.
Common rafter, for comparison: 13' 5" Theoretical common length on the same roof, before ridge shortening and overhang. The hip is 34% longer.

Why the hip runs 16.97 while the common runs 12

The hip is a different pitch from the roof it belongs to

A common rafter climbs its rise over a run measured straight across the building. A hip climbs the same rise over a run measured diagonally, from the corner of the plate to the point beneath the end of the ridge. That diagonal is longer by a factor of the square root of two.

So on a 6/12 roof the commons cut at 26.6 degrees and the hip cuts at 19.5. Both reach the same ridge height, but the hip takes a longer path to get there. Every cut on the hip — plumb, level, birdsmouth — is set from the hip angle, not the roof pitch.

This is where the number 17 comes from. Twelve times the square root of two is 16.97, and a framing square marked in whole inches cannot show that, so the trade rounds up. On a 24 foot span the rounding adds about three eighths of an inch to the hip; on a 40 foot span it adds over half an inch.

Whether that matters depends on how you are working. A hip cut long and scribed in place absorbs it. A hip cut to a calculated length in a shop does not.

Backing, dropping, and why a square hip does not fit

Set a rectangular hip rafter into the corner with its top edge on the hip line, and its two top corners will stand above the roof planes on either side. Sheathing laid across it will rock on those corners instead of bearing on the jacks.

There are two fixes and framers argue about which is better. Backing means beveling both top edges at the calculated angle so the hip presents a ridge that matches the two planes. It is correct, it looks right from below on an exposed structure, and it takes a saw pass down a long heavy timber.

Dropping means leaving the hip square and deepening its birdsmouth so the whole rafter sits lower, until the top corners fall into the roof planes. It takes seconds, it is structurally equivalent for normal spans, and it is what most production framers do. The only cost is a seat cut that removes slightly more of the rafter depth.

Both figures come from the same angle, and both are given above. On a 6/12 roof with 2x stock the drop is about a quarter of an inch — small enough that framers who skip it entirely often get away with it, and large enough to see in the finished sheathing on a low pitch.

Jack rafters step by a fixed amount

The rafters that run from the plate to the hip get shorter as they approach the corner, and they get shorter by exactly the same amount each time.

That amount is the jack spacing multiplied by the slope factor of the common rafter — not the hip. A jack is a common rafter that has been cut short, so it climbs at the common pitch, and moving one spacing along the plate shortens it by one spacing measured along that slope.

This means you never measure more than one jack. Cut the longest, then take the common difference off each successive pair. On 16 inch centres at a 6/12 pitch that step is a fraction under eighteen inches, and it repeats until you run out of plate.

Each jack also needs a single cheek cut where it meets the hip, at 45 degrees in plan for an equal pitch roof, and a shortening of half the hip thickness measured on that same diagonal. The cheek cut angle does not change from jack to jack; only the length does.

What this is based on

Hip unit run — the diagonal of a 12 inch square, 16.9706 inches
Backing angle derived from the dihedral between the roof plane and the vertical plane through the hip line
Jack rafter common difference — spacing × common rafter slope factor

Layout geometry for an equal pitch hip roof. It does not size the hip rafter, which carries jack loads and often needs to be deeper or doubled compared with a common rafter, and it does not cover irregular hips, unequal pitches or structural connections at the corner.

Frequently asked questions

Why is the hip unit run 17 and not 12?

The hip runs diagonally across the corner, so for every 12 inches of common run it covers the diagonal of a 12 inch square — 16.97 inches. Framing squares are marked in whole inches, so the trade uses 17. The rounding adds roughly three eighths of an inch on a 24 foot span.

Is the hip the same pitch as the roof?

No. It reaches the same ridge height over a longer run, so it is always shallower. A 6/12 roof has a hip at about 19.5 degrees against 26.6 for the commons, and every hip cut is set from the hip angle.

Should I back the hip or drop it?

Either works. Backing bevels both top edges so the hip matches the roof planes and is the traditional answer. Dropping leaves the hip square and deepens the birdsmouth so it sits lower, which is faster and structurally equivalent for normal spans. Production framing almost always drops.

What is the jack rafter common difference?

The fixed amount each jack is shorter than the previous one — the jack spacing multiplied by the common rafter slope factor. Cut the longest jack, then step down by this figure for every pair, and none of the others need measuring.

Does this work for an irregular hip?

No. All of this assumes equal pitches on both sides, which puts the hip at 45 degrees in plan. An irregular or bastard hip sits at a different plan angle, has different cheek cuts on each face and needs a separate layout.