Roof Rafter Birdsmouth Seat Cut, Plumb Angle & Height Above Plate (HAP) Calculator

Compute exact framing square angles and Height Above Plate (HAP) for rafters.

Height Above Plate (HAP)
6.36 in
Plumb Cut Angle (Miter Saw) 26.57 deg
Level Seat Cut Angle 63.43 deg
Birdsmouth Heel Plumb Cut Depth 1.75 in
Inputs
in/12"
Roof slope rise in inches per 12 inches of run.
in
Actual dressed rafter lumber width in inches (5.5" for 2×6, 7.25" for 2×8, 9.25" for 2×10).
in
Horizontal birdsmouth seat cut resting on the top plate (e.g., 3.5" for 2×4 wall).
Results & Graph
Height Above Plate (HAP)
6.36 in
Plumb Cut Angle (Miter Saw)
26.57 deg
Level Seat Cut Angle
63.43 deg
Birdsmouth Heel Plumb Cut Depth
1.75 in

Height Above Plate (HAP)

Graph 1 • Pitch Rise Per12 Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 in 3.6 in 7.1 in 50%: 6.6 in 6.6 50% 75%: 6.43 in 6.4 75% 100%: 6.36 in 6.4 100% 125%: 6.36 in 6.4 125% 150%: 6.44 in 6.4 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Height Above Plate (HAP) 6.36 in Plumb Cut Angle (Miter Saw) 26.57 deg Level Seat Cut Angle 63.43 deg Birdsmouth Heel Plumb Cut Depth 1.75 in
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Height Above Plate (HAP)6.36 inPlumb Cut Angle (Miter Saw)26.57 degLevel Seat Cut Angle63.43 degBirdsmouth Heel Plumb Cut Depth1.75 in
Summary: On a 6:12 roof with a 7.25" rafter and 3.5" level seat cut, plumb angle is 26.57°, seat angle is 63.43°, and HAP is 6.36".
Summary: On a 6:12 roof with a 7.25" rafter and 3.5" level seat cut, plumb angle is 26.57°, seat angle is 63.43°, and HAP is 6.36".
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Interactive chart & math engine powered by CalculatorGraph

Formula & Mathematical Methodology: Rafter Birdsmouth & HAP Formula

PlumbAngle = arctan(Pitch / 12)
SeatAngle = 90° − PlumbAngle
HAP = (RafterWidth / cos θ) − SeatCut × tan θ
PlumbAngle = arctan(Pitch / 12); SeatAngle = 90° − PlumbAngle; HAP = (RafterWidth / cos θ) − SeatCut × tan θ
  • pitchRisePer12: Pitch Rise Per12 (in/12")
  • rafterActualWidthIn: Rafter Actual Width In (in)
  • seatLevelCutIn: Seat Level Cut In (in)

Rounding: Physical package counts round up where appropriate; continuous measurements round to 2 decimal places.

Worked Example: Practical Benchmark: Rafter Birdsmouth & HAP

Compute exact framing square angles and Height Above Plate (HAP) for rafters.

  1. Enter your project dimensions, machining speeds, or recipe weights.
  2. Compute the governing equation: PlumbAngle = arctan(Pitch / 12); SeatAngle = 90° − PlumbAngle; HAP = (RafterWidth / cos θ) − SeatCut × tan θ.
  3. Review the primary result, supporting dimensions, and 3 SVG visualizations.
Result: Computes Rafter Birdsmouth & HAP via PlumbAngle = arctan(Pitch / 12); SeatAngle = 90° − PlumbAngle; HAP = (RafterWidth / cos θ) − SeatCut × tan θ.

Frequently Asked Questions

How does the Roof Rafter Birdsmouth Seat Cut, Plumb Angle & Height Above Plate (HAP) Calculator calculate results?

It evaluates PlumbAngle = arctan(Pitch / 12); SeatAngle = 90° − PlumbAngle; HAP = (RafterWidth / cos θ) − SeatCut × tan θ directly in your browser and plots three custom SVG visualizations.

Can I compare different material dimensions or batch sizes side by side?

Yes. Click "Compare (0/3)" in the results toolbar to pin up to 3 scenarios side by side.

Can I print a clean shop or kitchen reference sheet?

Yes. Click the Print button in the results toolbar for a distraction-free worksheet.

Construction & Home · Roofing & Framing

Roof Rafter Birdsmouth Seat Cut, Plumb Angle & Height Above Plate (HAP) Calculator: inputs, method, and how to read the result

Compute exact framing square angles and Height Above Plate (HAP) for rafters.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Pitch Rise Per12: Roof slope rise in inches per 12 inches of run.
  • Rafter Actual Width In: Actual dressed rafter lumber width in inches (5.5" for 2×6, 7.25" for 2×8, 9.25" for 2×10).
  • Seat Level Cut In: Horizontal birdsmouth seat cut resting on the top plate (e.g., 3.5" for 2×4 wall).

What the calculation includes

With the default values shown, Height Above Plate (HAP) is 6.36 in. The calculation follows Rafter Birdsmouth & HAP Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Pitch Rise Per12 from 6 in/12" to 7 in/12" changes Height Above Plate (HAP) from 6.36 in to 6.35 in. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard North American & metric trade dimensions, Machinery’s Handbook formulas, and culinary weight ratios.
  • Verify local municipal building codes, tool manufacturer limits, and food-safety time/temperature tables before execution.

Scope: Trade, Shop & Culinary Science Reference Standard Check the assumptions and limitations against your situation before relying on the estimate.

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