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BuyCommon Rafter vs Hip / Valley
When the simple common-rafter math applies — and when it does not
The Rafter Length & Roof Pitch Calculator sizes a common rafter: square to the ridge, same pitch as the roof, run = half the span (or the actual plate-to-ridge run you type). A hip or valley is a different stick — use the Hip / Valley Rafter Length Calculator (diagonal run = common run × 1.4142). Feeding a hip into the common calculator will give you a confident, wrong length and the wrong plumb angle.
How to mark a common: rafter length and pitch guide. Hip/valley method: diagonal-run guide. If you already cut the wrong one: common troubleshooting or hip/valley troubleshooting.
Two calculators now. Commons: span or run, pitch, overhang. Hips and valleys: common run × 1.4142, then a new hypotenuse.
Open Hip / Valley Calculator →Jump to what you need
When the Simple Common-Rafter Math Applies
Use the calculator when the rafter runs perpendicular to the ridge (or to the bearing wall on a shed) and the pitch of that rafter is the roof pitch. Gable commons, jack commons that still sit square to the ridge (the length shortens, the pitch does not), and a shed common with a known run all share the same triangle: run, rise, hypotenuse.
- Centered gable commons — span ÷ 2 = run. This is the calculator default.
- Shed / single slope commons — enter run directly (plate to upper bearing). Do not use span mode unless there is a centered ridge.
- Common jacks on a hip roof — same pitch and same plumb as a full common; only the length shortens as they step to the hip. The calculator still gives the full common. You shorten each jack by the jack layout, not by switching to hip math.
If you can set a framing square to 12 and the roof pitch and walk a plumb and a seat that match the roof, you are in common-rafter land. That is the same family of square work as a stair stringer — one right triangle, equal steps or one long hypotenuse.
Why Hip Rafters Need Different Geometry
A hip runs to the corner in plan. On a square-corner building the hip's plan run is not the common run. It is the diagonal of the common run: hip run = common run × √2 (for a 90° corner). The rise is the same as the common. So hip length = √((common run × √2)² + rise²). That is longer than the common, and the plumb cut is not the common pitch angle.
hip plan run = common run × √2 (90° corner)
hip length = √(hip run² + rise²)
hip plumb ≠ common pitch angle
hip length = √(hip run² + rise²)
hip plumb ≠ common pitch angle
Same 24 ft building, 6/12Common run 12 ft, common line 13′ 5", common plumb 26.57°. Hip plan run = 12 × 1.414 = 16.97 ft. Hip line ≈ 18.00 ft. Hip plumb is flatter than 26.57° because you spread the same rise over a longer run. Backing bevels and a different seat sit on top of that. None of those numbers come out of the common calculator.
Hips also take a backing bevel so the jack edges land on a plane, and the birdsmouth is skewed in plan. That is a second layout on top of length. For the length itself, use the Hip / Valley Rafter Length Calculator — do not type a hip into the common tool. Walkthrough: diagonal-run guide.
Valley Rafters Are Not Commons Either
A valley is the inside corner. In plan it is the same kind of diagonal as a hip: longer run, same rise, different plumb, plus bevels so the valley can receive the jacks. A valley is often dropped or doubled; none of that is common-rafter length.
If you need a valley length, use the Hip / Valley Rafter Length Calculator (same diagonal-run math as a regular hip). Do not use the common rafter calculator. Using common length on a valley leaves a gap at the inside corner or a valley that sits high and throws every jack off.
The common calculator covers common rafters only. Hip and valley are a distinct calculation: different plan run, different plumb, backing or cheek bevels, and usually a different birdsmouth. Use the hip/valley calculator for length and hip plumb. Still cross-check backing on a square. How-to: diagonal-run guide.
Common vs Hip / Valley — What Changes
| Common rafter | Hip / valley | |
|---|---|---|
| Plan direction | Square to the ridge | To the corner (typically 45° in plan) |
| Run | Span/2 or plate-to-ridge | Common run × √2 (square corner) |
| Rise | Plate to ridge | Same rise as the common |
| Length | √(run² + rise²) | √(hip run² + rise²) — longer |
| Plumb cut | Pitch angle (arctan rise/run) | Flatter / different; not the common degree |
| Birdsmouth | Plumb heel + level seat | Skewed; plus backing or cheek bevels |
| Calculator | Common rafter tool | Hip / valley tool |
Jack rafters that land on a hip still use common plumb and common pitch. Only their length steps down. Cut the full common from the calculator first, then shorten jacks on layout. Do not invent a new pitch for each jack.
Square to the ridge? Common calculator. Runs to a corner? Hip/valley calculator. Two tools, two triangles.
Open Hip / Valley Calculator →FAQ
Can I multiply the common length by 1.414 to get a hip?
No. That scales the hypotenuse as if rise scaled too. Rise does not scale; only the plan run does. Use hip run = common run × √2, then a new hypotenuse with the same rise. And you still need the hip plumb, not the common plumb.
What about a 45° roof (12/12) hip?
A 12/12 common is 45°. The hip is still a different run and a different plumb. 12/12 does not make a hip into a common.
Irregular hips (different pitches each side)?
Worse, not better. The plan angle is not 45° and both pitches feed the hip. The hip/valley calculator is regular (equal-pitch, 90°) only. Unequal pitches still need a dedicated irregular-hip method.
Is a ridge beam the same as a ridge board for run?
You still subtract half the ridge thickness from each common run. A structural ridge beam is thicker, so the subtraction is larger. The calculator lets you enter run directly if you already deducted it.
Where do stairs fit?
They do not. Stringers are a different triangle with code rise/run. Use the Stair Stringer Calculator or Deck Stair Calculator.
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Rafter Layout Gear
Lock 12 and the pitch on a framing square. The calculator is the numbers; the square is the line.
Swanson Speed Square
Pivot to the pitch degree for the ridge plumb cut. Confirm it against the calculator angle so the pair meets the ridge.
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16×24 Framing Square
12 on the body, pitch on the tongue. Same walk as a stringer, different triangle.
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Johnson Stair Gauges
Clamp the pitch so the square cannot drift while you tick plumb and seat lines.
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7-1/4" Circular Saw
Bevel to the plumb-cut angle. Stop the birdsmouth kerfs short of the crotch so remaining depth stays in the board.
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48" Box Beam Level
Prove plate and ridge before the first pair. A rolling plate shows up as a rafter that is “too short” on one side.
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Get the Numbers First
Span or run, pitch or rise, overhang. Common rafter only.
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