Hip roof framing geometry

Hip Rafter Calculator

Calculate the hip rafter length for a square 90° hip roof corner from common rafter run, pitch, and overhang. The page shows the plan diagonal so the formula is easy to check.

Units

Common rafter run (ft)Roof pitch rise per 12 run Horizontal overhang (ft)Hip rafters to order Waste / extra hips (%)Cost per hip rafter ($)

Hip rafter length

Plan diagonal

Hip pitch angle

Rough cost

Hip roof assumption

This assumes an equal-pitch roof meeting at a square 90° corner. It does not size structural members, jack rafters, birdsmouth cuts, shortening allowances, or complex unequal-pitch hips.

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Rafter Length Calculator

Calculate the common rafter length before hip layout.

Valley Rafter Calculator

Compare hip and valley geometry for square roof intersections.

Roof Pitch Calculator

Convert pitch to angle, grade, and multiplier.

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Hip rafter formula

Roof rise = (common run + overhang) × pitch ÷ 12

Plan diagonal = (common run + overhang) × √2

Hip rafter length = sqrt(plan diagonal² + rise²)

Order count = hip count × (1 + waste %)

Sample takeoff

A 10 ft common run with 1 ft overhang on a 6/12 roof gives a 15.56 ft plan diagonal and a 16.50 ft hip rafter length for the equal-pitch corner.A 3 m common run with 0.3 m overhang on a 6/12 roof gives a 4.67 m plan diagonal and a 4.95 m hip rafter length for the equal-pitch corner.

Hip Rafter Calculator FAQ

How do I calculate hip rafter length?+

For an equal-pitch 90° hip, multiply common run plus overhang by √2 to get the plan diagonal, calculate rise from pitch, then use the Pythagorean theorem with diagonal and rise.For an equal-pitch 90° hip, multiply common run plus overhang by √2 to get the plan diagonal, calculate rise from pitch, then use the Pythagorean theorem with diagonal and rise.

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

The core geometry is similar on equal-pitch square corners, but the framing context, cuts, shortening, and jack layout are different enough to plan separately.The core geometry is similar on equal-pitch square corners, but the framing context, cuts, shortening, and jack layout are different enough to plan separately.

Does this include birdsmouth or ridge allowances?+

No. It gives the geometric line length before field cut allowances. Use your framing plan, lumber size, and local practice for cut details.No. It gives the geometric line length before field cut allowances. Use your framing plan, lumber size, and local practice for cut details.