Hip & Valley Rafter Length Calculator

A hip and valley rafter length calculator returns the rafter's length from your common rafter run and roof pitch. It multiplies the common run by the square root of 2 (about 1.414) to get the diagonal run, then takes the hypotenuse of that run and the rise. The result is the hip or valley length.

Last reviewed September 2026Method & sources Report an error

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Hip/Valley Rafter Length

18.000 ft

Breakdown
Hip/Valley Rafter Length	18.000 ft
Hip/Valley Run	16.971 ft
Rise	6.000 ft

How to Calculate Hip & Valley Rafter Length

A hip or valley rafter runs diagonally in plan view, across the square corner formed by two adjacent common rafter runs at 45° to each. By the Pythagorean theorem, that diagonal run is the common rafter's run times √2 (about 1.414). The hip/valley rafter reaches the same total rise (roof height) as the common rafter over that longer diagonal run. So its actual length is the hypotenuse of a triangle formed by that diagonal run and the shared rise: `√((common run × √2)² + rise²)`.

Example: Roof with a 12 ft common rafter run, 6

A roof with a 12 ft common rafter run, 6:12 pitch: 1. Rise: 12 × (6 ÷ 12) = 6 ft 2. Hip/valley run: 12 × √2 ≈ 16.97 ft 3. Hip/valley length: √(16.97² + 6²) = √(288 + 36) = √324 = 18.0 ft That hip or valley rafter needs to be 18.0 ft long. That is a clean number for this specific pitch and run combination.

Hip & Valley Rafter Length: Compare Scenarios

Scenario	Hip/Valley Rafter Length	Hip/Valley Run	Rise
Small (6 ft run, 4:12 pitch)	8.718 ft	8.485 ft	2.000 ft
Medium (12 ft run, 6:12 pitch)	18.000 ft	16.971 ft	6.000 ft
Large (20 ft run, 8:12 pitch)	31.269 ft	28.284 ft	13.333 ft

What Is Hip & Valley Rafter Length?

A hip and valley rafter length calculator extends the same rafter-length geometry the Rafter Length calculator uses for common rafters. It applies that math to the diagonal hip (roof corner) and valley (roof intersection) rafters found on a hip roof or an L-shaped roof intersection. Both use the same underlying math. A valley is just a hip rafter's mirror image, where two roof planes meet instead of two roof planes ending.

Hip & Valley Rafter Length: Pros and Cons

Pros

Uses the correct diagonal-run relationship (√2 times the common run) rather than treating the hip/valley the same as a common rafter
Works for any common rafter run and roof pitch combination
The same formula applies to both hip rafters (roof corners) and valley rafters (roof intersections), which share identical geometry

Cons

Assumes an equal-pitch roof (both intersecting roof planes have the same pitch). An unequal-pitch hip or valley (where two roof sections have different pitches) needs more advanced roof framing geometry than this calculator covers
Doesn't account for the hip/valley rafter's own ridge-end and tail-end cuts (the compound angle cheek cuts specific to hip/valley framing), which are a separate layout step from the length calculated here
Assumes a standard 45° hip/valley (the common rafter runs meeting at a square corner). An irregular hip at a different plan angle needs different trigonometry

Hip & Valley Rafter Length: What a Pro Checks

The compound angle cheek cuts at a hip or valley rafter's ridge and tail ends are a separate layout step from the length calculated here. They are typically done with a speed square or a hip/valley-specific rafter framing table.
This assumes an equal-pitch roof on both sides of the hip or valley. An unequal-pitch intersection needs more advanced framing geometry than this formula covers.

Frequently Asked Questions

How do you calculate hip rafter length?

First find the hip's horizontal run (the common rafter's run × √2, about 1.414), then find the hip's length as the hypotenuse of that run and the roof's total rise: √(hip run² + rise²).

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

Yes, for the same common rafter run and pitch. A hip and a valley rafter share identical geometry, just at opposite roles. A hip is an outside corner where two roof planes end, and a valley is an inside intersection where two roof planes meet.

Why is a hip rafter longer than a common rafter?

Because it travels a longer horizontal run to reach the same rise. A hip's run is the common rafter's run times √2 (about 1.414), so a hip rafter is meaningfully longer than the common rafters on the same roof.

What's the difference between a hip and a valley?

A hip is an external roof corner where two roof planes slope away from each other (common on a hip roof). A valley is an internal intersection where two roof planes slope toward each other and meet (common where an L-shaped house's two roof sections join). Both use the same length formula.

Does this calculator give me the cut angles for a hip rafter?

No. It calculates the hip or valley rafter's length only. The compound angle cuts at the ridge and tail ends of a hip/valley rafter are a separate layout step, typically done with a speed square or a rafter framing table specific to hip/valley cuts.

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