Jack rafters step down by a constant common difference toward the hip corner

On the roof plane each jack rafter is shorter than the last by a constant common difference: Δ = (spacing ÷ 12) × the pitch multiplier. Cut them in a stepped set from the longest.

A developed, unrolled view of a hip roof plane. The eave runs along the bottom and the hip rafter rises as a diagonal to the ridge. Evenly spaced jack rafters run from the eave up to the hip, and their true lengths shrink by a constant amount toward the corner. That amount, the common difference, equals the rafter spacing divided by twelve times the common pitch multiplier — the square root of one plus the pitch over twelve squared. Each jack toward the corner is shorter than the last by this fixed difference, so they are field-cut from the longest. — Source: Common-difference method (spacing × pitch multiplier)

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A developed, unrolled view of a hip roof plane. The eave runs along the bottom and the hip rafter rises as a diagonal to the ridge. Evenly spaced jack rafters run from the eave up to the hip, and their true lengths shrink by a constant amount toward the corner. That amount, the common difference, equals the rafter spacing divided by twelve times the common pitch multiplier — the square root of one plus the pitch over twelve squared. Each jack toward the corner is shorter than the last by this fixed difference, so they are field-cut from the longest.

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    <img src="https://remodelcalculators.com/api/figure-embed/rafter-jacks" alt="A developed, unrolled view of a hip roof plane. The eave runs along the bottom and the hip rafter rises as a diagonal to the ridge. Evenly spaced jack rafters run from the eave up to the hip, and their true lengths shrink by a constant amount toward the corner. That amount, the common difference, equals the rafter spacing divided by twelve times the common pitch multiplier — the square root of one plus the pitch over twelve squared. Each jack toward the corner is shorter than the last by this fixed difference, so they are field-cut from the longest." width="800" height="460" style="width:100%;height:auto;border:0" loading="lazy">
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    Diagram: <a href="https://remodelcalculators.com/construction-diagrams/rafter-jacks" target="_blank" rel="noopener">Jack rafters step down by a constant common difference toward the hip corner</a> — courtesy of <a href="https://remodelcalculators.com" target="_blank" rel="noopener">RemodelCalculators.com</a>
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Free rafter length calculator: common, hip, valley & jack rafter lengths, plumb/seat cut angles, birdsmouth depth, and board count. Per IRC R802. No signup.

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