Rafter Length Calculator

Professional rafter calculator to compute common rafter length, rise, roof angle, and overhang. Supports span or run, pitch (rise-in-12) or angle, and both metric and imperial units. WCAG-accessible and mobile-first.

Full original guide (expanded)

Rafter Length Calculator

Calculate common rafter length, roof rise, and overhang length from span/run and pitch or angle in metric or imperial units.

Interactive Calculator

Select the unit system for all length inputs.
Known dimension
ft
Pitch method
in per 12 in
in
When checked, the calculator subtracts (ridge ÷ 2) adjusted along the slope.
in
Controls the rounding of feet/inches results.

Results

Roof angle
—
Pitch factor (length per unit run)
—
Total rise (for run)
—
—
Common rafter length to ridge centerline
—
—
Cut length (after ridge deduction)
—
—
Total length incl. overhang
—
—

Authoritative Content & Methodology

Data Source and Methodology

Primary reference for trigonometric identities used in roof geometry: NIST Digital Library of Mathematical Functions (DLMF), Chapter 4: Trigonometric Functions, 2010–2024. Direct link: https://dlmf.nist.gov/4.

All calculations are rigorously based on the formulas and data provided by this source.

Note: This tool performs geometric computation only; it does not perform structural sizing or code checks.

The Formulas Explained

$$\theta = \begin{cases} \arctan\!\left(\dfrac{p}{12}\right), & \text{if pitch } p \text{ (rise-in-12) is given} \\ \theta_{\text{deg}} \cdot \dfrac{\pi}{180}, & \text{if angle in degrees is given} \end{cases} $$ $$\text{run} = \begin{cases} \dfrac{\text{span}}{2}, & \text{if span is known} \\ \text{run}, & \text{if run is known} \end{cases} $$ $$\text{rise} = \text{run}\cdot\tan(\theta) \quad\quad \text{pitch factor} = \sec(\theta) = \dfrac{1}{\cos(\theta)} $$ $$L_{\text{center}} = \dfrac{\text{run}}{\cos(\theta)}$$ $$\Delta_{\text{ridge}} = \dfrac{t/2}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{cut}} = L_{\text{center}} - \Delta_{\text{ridge}} $$ $$\Delta_{\text{overhang}} = \dfrac{\text{overhang}_\text{horizontal}}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{total}} = L_{\text{cut}} + \Delta_{\text{overhang}} $$

Glossary of Variables

Span
Total building width (outside to outside). Run = span ÷ 2.
Run
Horizontal distance from wall plate to centerline of the roof.
Pitch (p)
Rise in inches per 12 inches of run (e.g., 6-in-12).
Angle (θ)
Roof angle from the horizontal in radians or degrees.
Ridge thickness (t)
Thickness of the ridge board. Half of this is often deducted along the slope.
Overhang
Horizontal projection beyond the wall face to the fascia; converted to a sloped tail length.
Lcenter
Rafter length from wall plate to ridge centerline along the top edge.
Lcut
Rafter cut length after ridge deduction.
Ltotal
Total rafter length including overhang.

How It Works: A Step-by-Step Example

Scenario: A garage with a 24 ft span and a 6-in-12 roof pitch. Ridge thickness is 1.5 in; overhang is 18 in.

  1. Run = span ÷ 2 = 24 ft ÷ 2 = 12 ft.
  2. Angle: θ = arctan(6/12) ≈ 26.565°.
  3. Pitch factor: sec(θ) ≈ 1.1180.
  4. Lcenter = run ÷ cos(θ) = 12 ft × 1.1180 ≈ 13.416 ft.
  5. Ridge deduction: Δridge = (1.5 in ÷ 2) ÷ cos(θ) ≈ (0.75 in) ÷ 0.8944 ≈ 0.838 in ≈ 0.0698 ft.
  6. Lcut = 13.416 − 0.0698 ≈ 13.346 ft.
  7. Overhang tail: Δoverhang = 18 in ÷ cos(θ) ≈ 18 ÷ 0.8944 ≈ 20.12 in ≈ 1.676 ft.
  8. Total: Ltotal = 13.346 + 1.676 ≈ 15.022 ft ≈ 15′ 0 1/4″.

These steps match the calculator’s output within rounding precision.

Frequently Asked Questions (FAQ)

What inputs do I need?

Provide span or run, then choose either roof pitch (rise-in-12) or angle in degrees. Optionally add ridge thickness (to deduct half) and overhang (horizontal).

Which is more accurate: pitch or angle?

They are equivalent when correctly converted. Pitch is common on plans; angles are convenient for protractors and layout tools. The calculator handles both precisely.

Do I need to include sheathing or fascia thickness?

This tool reports the line length along the rafter’s top edge. If your detail requires adding or subtracting materials (e.g., fascia thickness), adjust on site or incorporate it into the overhang allowance.

Can I calculate hip or valley rafters?

This version focuses on common rafters. Hip/valley lengths require plan geometry across two axes. We plan to add an advanced module with those features.

How precise are the conversions?

Internally, calculations use double-precision floating point with unit conversions. Imperial outputs are rounded to your selected fractional precision (1/16″ or 1/8″).

Will this pass building inspection?

Inspections focus on structural adequacy and code compliance. Use this tool for geometry and layout only. For sizing, consult the IRC/IBC and NDS span tables or a licensed engineer.

Can I save or share my results?

Use the “Copy results” button to place a formatted summary on your clipboard for quick sharing in notes, emails, or job cards.

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted LaTeX)
\[\theta = \begin{cases} \arctan\!\left(\dfrac{p}{12}\right), & \text{if pitch } p \text{ (rise-in-12) is given} \\ \theta_{\text{deg}} \cdot \dfrac{\pi}{180}, & \text{if angle in degrees is given} \end{cases}\]
\theta = \begin{cases} \arctan\!\left(\dfrac{p}{12}\right), & \text{if pitch } p \text{ (rise-in-12) is given} \\ \theta_{\text{deg}} \cdot \dfrac{\pi}{180}, & \text{if angle in degrees is given} \end{cases}
Formula (extracted LaTeX)
\[\text{run} = \begin{cases} \dfrac{\text{span}}{2}, & \text{if span is known} \\ \text{run}, & \text{if run is known} \end{cases}\]
\text{run} = \begin{cases} \dfrac{\text{span}}{2}, & \text{if span is known} \\ \text{run}, & \text{if run is known} \end{cases}
Formula (extracted LaTeX)
\[\text{rise} = \text{run}\cdot\tan(\theta) \quad\quad \text{pitch factor} = \sec(\theta) = \dfrac{1}{\cos(\theta)}\]
\text{rise} = \text{run}\cdot\tan(\theta) \quad\quad \text{pitch factor} = \sec(\theta) = \dfrac{1}{\cos(\theta)}
Formula (extracted LaTeX)
\[L_{\text{center}} = \dfrac{\text{run}}{\cos(\theta)}\]
L_{\text{center}} = \dfrac{\text{run}}{\cos(\theta)}
Formula (extracted LaTeX)
\[\Delta_{\text{ridge}} = \dfrac{t/2}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{cut}} = L_{\text{center}} - \Delta_{\text{ridge}}\]
\Delta_{\text{ridge}} = \dfrac{t/2}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{cut}} = L_{\text{center}} - \Delta_{\text{ridge}}
Formula (extracted text)
$\theta = \begin{cases} \arctan\!\left(\dfrac{p}{12}\right), & \text{if pitch } p \text{ (rise-in-12) is given} \\ \theta_{\text{deg}} \cdot \dfrac{\pi}{180}, & \text{if angle in degrees is given} \end{cases} $ $\text{run} = \begin{cases} \dfrac{\text{span}}{2}, & \text{if span is known} \\ \text{run}, & \text{if run is known} \end{cases} $ $\text{rise} = \text{run}\cdot\tan(\theta) \quad\quad \text{pitch factor} = \sec(\theta) = \dfrac{1}{\cos(\theta)} $ $L_{\text{center}} = \dfrac{\text{run}}{\cos(\theta)}$ $\Delta_{\text{ridge}} = \dfrac{t/2}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{cut}} = L_{\text{center}} - \Delta_{\text{ridge}} $ $\Delta_{\text{overhang}} = \dfrac{\text{overhang}_\text{horizontal}}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{total}} = L_{\text{cut}} + \Delta_{\text{overhang}} $
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Rafter Length Calculator

Calculate common rafter length, roof rise, and overhang length from span/run and pitch or angle in metric or imperial units.

Interactive Calculator

Select the unit system for all length inputs.
Known dimension
ft
Pitch method
in per 12 in
in
When checked, the calculator subtracts (ridge ÷ 2) adjusted along the slope.
in
Controls the rounding of feet/inches results.

Results

Roof angle
—
Pitch factor (length per unit run)
—
Total rise (for run)
—
—
Common rafter length to ridge centerline
—
—
Cut length (after ridge deduction)
—
—
Total length incl. overhang
—
—

Authoritative Content & Methodology

Data Source and Methodology

Primary reference for trigonometric identities used in roof geometry: NIST Digital Library of Mathematical Functions (DLMF), Chapter 4: Trigonometric Functions, 2010–2024. Direct link: https://dlmf.nist.gov/4.

All calculations are rigorously based on the formulas and data provided by this source.

Note: This tool performs geometric computation only; it does not perform structural sizing or code checks.

The Formulas Explained

$$\theta = \begin{cases} \arctan\!\left(\dfrac{p}{12}\right), & \text{if pitch } p \text{ (rise-in-12) is given} \\ \theta_{\text{deg}} \cdot \dfrac{\pi}{180}, & \text{if angle in degrees is given} \end{cases} $$ $$\text{run} = \begin{cases} \dfrac{\text{span}}{2}, & \text{if span is known} \\ \text{run}, & \text{if run is known} \end{cases} $$ $$\text{rise} = \text{run}\cdot\tan(\theta) \quad\quad \text{pitch factor} = \sec(\theta) = \dfrac{1}{\cos(\theta)} $$ $$L_{\text{center}} = \dfrac{\text{run}}{\cos(\theta)}$$ $$\Delta_{\text{ridge}} = \dfrac{t/2}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{cut}} = L_{\text{center}} - \Delta_{\text{ridge}} $$ $$\Delta_{\text{overhang}} = \dfrac{\text{overhang}_\text{horizontal}}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{total}} = L_{\text{cut}} + \Delta_{\text{overhang}} $$

Glossary of Variables

Span
Total building width (outside to outside). Run = span ÷ 2.
Run
Horizontal distance from wall plate to centerline of the roof.
Pitch (p)
Rise in inches per 12 inches of run (e.g., 6-in-12).
Angle (θ)
Roof angle from the horizontal in radians or degrees.
Ridge thickness (t)
Thickness of the ridge board. Half of this is often deducted along the slope.
Overhang
Horizontal projection beyond the wall face to the fascia; converted to a sloped tail length.
Lcenter
Rafter length from wall plate to ridge centerline along the top edge.
Lcut
Rafter cut length after ridge deduction.
Ltotal
Total rafter length including overhang.

How It Works: A Step-by-Step Example

Scenario: A garage with a 24 ft span and a 6-in-12 roof pitch. Ridge thickness is 1.5 in; overhang is 18 in.

  1. Run = span ÷ 2 = 24 ft ÷ 2 = 12 ft.
  2. Angle: θ = arctan(6/12) ≈ 26.565°.
  3. Pitch factor: sec(θ) ≈ 1.1180.
  4. Lcenter = run ÷ cos(θ) = 12 ft × 1.1180 ≈ 13.416 ft.
  5. Ridge deduction: Δridge = (1.5 in ÷ 2) ÷ cos(θ) ≈ (0.75 in) ÷ 0.8944 ≈ 0.838 in ≈ 0.0698 ft.
  6. Lcut = 13.416 − 0.0698 ≈ 13.346 ft.
  7. Overhang tail: Δoverhang = 18 in ÷ cos(θ) ≈ 18 ÷ 0.8944 ≈ 20.12 in ≈ 1.676 ft.
  8. Total: Ltotal = 13.346 + 1.676 ≈ 15.022 ft ≈ 15′ 0 1/4″.

These steps match the calculator’s output within rounding precision.

Frequently Asked Questions (FAQ)

What inputs do I need?

Provide span or run, then choose either roof pitch (rise-in-12) or angle in degrees. Optionally add ridge thickness (to deduct half) and overhang (horizontal).

Which is more accurate: pitch or angle?

They are equivalent when correctly converted. Pitch is common on plans; angles are convenient for protractors and layout tools. The calculator handles both precisely.

Do I need to include sheathing or fascia thickness?

This tool reports the line length along the rafter’s top edge. If your detail requires adding or subtracting materials (e.g., fascia thickness), adjust on site or incorporate it into the overhang allowance.

Can I calculate hip or valley rafters?

This version focuses on common rafters. Hip/valley lengths require plan geometry across two axes. We plan to add an advanced module with those features.

How precise are the conversions?

Internally, calculations use double-precision floating point with unit conversions. Imperial outputs are rounded to your selected fractional precision (1/16″ or 1/8″).

Will this pass building inspection?

Inspections focus on structural adequacy and code compliance. Use this tool for geometry and layout only. For sizing, consult the IRC/IBC and NDS span tables or a licensed engineer.

Can I save or share my results?

Use the “Copy results” button to place a formatted summary on your clipboard for quick sharing in notes, emails, or job cards.

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted LaTeX)
\[\theta = \begin{cases} \arctan\!\left(\dfrac{p}{12}\right), & \text{if pitch } p \text{ (rise-in-12) is given} \\ \theta_{\text{deg}} \cdot \dfrac{\pi}{180}, & \text{if angle in degrees is given} \end{cases}\]
\theta = \begin{cases} \arctan\!\left(\dfrac{p}{12}\right), & \text{if pitch } p \text{ (rise-in-12) is given} \\ \theta_{\text{deg}} \cdot \dfrac{\pi}{180}, & \text{if angle in degrees is given} \end{cases}
Formula (extracted LaTeX)
\[\text{run} = \begin{cases} \dfrac{\text{span}}{2}, & \text{if span is known} \\ \text{run}, & \text{if run is known} \end{cases}\]
\text{run} = \begin{cases} \dfrac{\text{span}}{2}, & \text{if span is known} \\ \text{run}, & \text{if run is known} \end{cases}
Formula (extracted LaTeX)
\[\text{rise} = \text{run}\cdot\tan(\theta) \quad\quad \text{pitch factor} = \sec(\theta) = \dfrac{1}{\cos(\theta)}\]
\text{rise} = \text{run}\cdot\tan(\theta) \quad\quad \text{pitch factor} = \sec(\theta) = \dfrac{1}{\cos(\theta)}
Formula (extracted LaTeX)
\[L_{\text{center}} = \dfrac{\text{run}}{\cos(\theta)}\]
L_{\text{center}} = \dfrac{\text{run}}{\cos(\theta)}
Formula (extracted LaTeX)
\[\Delta_{\text{ridge}} = \dfrac{t/2}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{cut}} = L_{\text{center}} - \Delta_{\text{ridge}}\]
\Delta_{\text{ridge}} = \dfrac{t/2}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{cut}} = L_{\text{center}} - \Delta_{\text{ridge}}
Formula (extracted text)
$\theta = \begin{cases} \arctan\!\left(\dfrac{p}{12}\right), & \text{if pitch } p \text{ (rise-in-12) is given} \\ \theta_{\text{deg}} \cdot \dfrac{\pi}{180}, & \text{if angle in degrees is given} \end{cases} $ $\text{run} = \begin{cases} \dfrac{\text{span}}{2}, & \text{if span is known} \\ \text{run}, & \text{if run is known} \end{cases} $ $\text{rise} = \text{run}\cdot\tan(\theta) \quad\quad \text{pitch factor} = \sec(\theta) = \dfrac{1}{\cos(\theta)} $ $L_{\text{center}} = \dfrac{\text{run}}{\cos(\theta)}$ $\Delta_{\text{ridge}} = \dfrac{t/2}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{cut}} = L_{\text{center}} - \Delta_{\text{ridge}} $ $\Delta_{\text{overhang}} = \dfrac{\text{overhang}_\text{horizontal}}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{total}} = L_{\text{cut}} + \Delta_{\text{overhang}} $
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Rafter Length Calculator

Calculate common rafter length, roof rise, and overhang length from span/run and pitch or angle in metric or imperial units.

Interactive Calculator

Select the unit system for all length inputs.
Known dimension
ft
Pitch method
in per 12 in
in
When checked, the calculator subtracts (ridge ÷ 2) adjusted along the slope.
in
Controls the rounding of feet/inches results.

Results

Roof angle
—
Pitch factor (length per unit run)
—
Total rise (for run)
—
—
Common rafter length to ridge centerline
—
—
Cut length (after ridge deduction)
—
—
Total length incl. overhang
—
—

Authoritative Content & Methodology

Data Source and Methodology

Primary reference for trigonometric identities used in roof geometry: NIST Digital Library of Mathematical Functions (DLMF), Chapter 4: Trigonometric Functions, 2010–2024. Direct link: https://dlmf.nist.gov/4.

All calculations are rigorously based on the formulas and data provided by this source.

Note: This tool performs geometric computation only; it does not perform structural sizing or code checks.

The Formulas Explained

$$\theta = \begin{cases} \arctan\!\left(\dfrac{p}{12}\right), & \text{if pitch } p \text{ (rise-in-12) is given} \\ \theta_{\text{deg}} \cdot \dfrac{\pi}{180}, & \text{if angle in degrees is given} \end{cases} $$ $$\text{run} = \begin{cases} \dfrac{\text{span}}{2}, & \text{if span is known} \\ \text{run}, & \text{if run is known} \end{cases} $$ $$\text{rise} = \text{run}\cdot\tan(\theta) \quad\quad \text{pitch factor} = \sec(\theta) = \dfrac{1}{\cos(\theta)} $$ $$L_{\text{center}} = \dfrac{\text{run}}{\cos(\theta)}$$ $$\Delta_{\text{ridge}} = \dfrac{t/2}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{cut}} = L_{\text{center}} - \Delta_{\text{ridge}} $$ $$\Delta_{\text{overhang}} = \dfrac{\text{overhang}_\text{horizontal}}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{total}} = L_{\text{cut}} + \Delta_{\text{overhang}} $$

Glossary of Variables

Span
Total building width (outside to outside). Run = span ÷ 2.
Run
Horizontal distance from wall plate to centerline of the roof.
Pitch (p)
Rise in inches per 12 inches of run (e.g., 6-in-12).
Angle (θ)
Roof angle from the horizontal in radians or degrees.
Ridge thickness (t)
Thickness of the ridge board. Half of this is often deducted along the slope.
Overhang
Horizontal projection beyond the wall face to the fascia; converted to a sloped tail length.
Lcenter
Rafter length from wall plate to ridge centerline along the top edge.
Lcut
Rafter cut length after ridge deduction.
Ltotal
Total rafter length including overhang.

How It Works: A Step-by-Step Example

Scenario: A garage with a 24 ft span and a 6-in-12 roof pitch. Ridge thickness is 1.5 in; overhang is 18 in.

  1. Run = span ÷ 2 = 24 ft ÷ 2 = 12 ft.
  2. Angle: θ = arctan(6/12) ≈ 26.565°.
  3. Pitch factor: sec(θ) ≈ 1.1180.
  4. Lcenter = run ÷ cos(θ) = 12 ft × 1.1180 ≈ 13.416 ft.
  5. Ridge deduction: Δridge = (1.5 in ÷ 2) ÷ cos(θ) ≈ (0.75 in) ÷ 0.8944 ≈ 0.838 in ≈ 0.0698 ft.
  6. Lcut = 13.416 − 0.0698 ≈ 13.346 ft.
  7. Overhang tail: Δoverhang = 18 in ÷ cos(θ) ≈ 18 ÷ 0.8944 ≈ 20.12 in ≈ 1.676 ft.
  8. Total: Ltotal = 13.346 + 1.676 ≈ 15.022 ft ≈ 15′ 0 1/4″.

These steps match the calculator’s output within rounding precision.

Frequently Asked Questions (FAQ)

What inputs do I need?

Provide span or run, then choose either roof pitch (rise-in-12) or angle in degrees. Optionally add ridge thickness (to deduct half) and overhang (horizontal).

Which is more accurate: pitch or angle?

They are equivalent when correctly converted. Pitch is common on plans; angles are convenient for protractors and layout tools. The calculator handles both precisely.

Do I need to include sheathing or fascia thickness?

This tool reports the line length along the rafter’s top edge. If your detail requires adding or subtracting materials (e.g., fascia thickness), adjust on site or incorporate it into the overhang allowance.

Can I calculate hip or valley rafters?

This version focuses on common rafters. Hip/valley lengths require plan geometry across two axes. We plan to add an advanced module with those features.

How precise are the conversions?

Internally, calculations use double-precision floating point with unit conversions. Imperial outputs are rounded to your selected fractional precision (1/16″ or 1/8″).

Will this pass building inspection?

Inspections focus on structural adequacy and code compliance. Use this tool for geometry and layout only. For sizing, consult the IRC/IBC and NDS span tables or a licensed engineer.

Can I save or share my results?

Use the “Copy results” button to place a formatted summary on your clipboard for quick sharing in notes, emails, or job cards.

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted LaTeX)
\[\theta = \begin{cases} \arctan\!\left(\dfrac{p}{12}\right), & \text{if pitch } p \text{ (rise-in-12) is given} \\ \theta_{\text{deg}} \cdot \dfrac{\pi}{180}, & \text{if angle in degrees is given} \end{cases}\]
\theta = \begin{cases} \arctan\!\left(\dfrac{p}{12}\right), & \text{if pitch } p \text{ (rise-in-12) is given} \\ \theta_{\text{deg}} \cdot \dfrac{\pi}{180}, & \text{if angle in degrees is given} \end{cases}
Formula (extracted LaTeX)
\[\text{run} = \begin{cases} \dfrac{\text{span}}{2}, & \text{if span is known} \\ \text{run}, & \text{if run is known} \end{cases}\]
\text{run} = \begin{cases} \dfrac{\text{span}}{2}, & \text{if span is known} \\ \text{run}, & \text{if run is known} \end{cases}
Formula (extracted LaTeX)
\[\text{rise} = \text{run}\cdot\tan(\theta) \quad\quad \text{pitch factor} = \sec(\theta) = \dfrac{1}{\cos(\theta)}\]
\text{rise} = \text{run}\cdot\tan(\theta) \quad\quad \text{pitch factor} = \sec(\theta) = \dfrac{1}{\cos(\theta)}
Formula (extracted LaTeX)
\[L_{\text{center}} = \dfrac{\text{run}}{\cos(\theta)}\]
L_{\text{center}} = \dfrac{\text{run}}{\cos(\theta)}
Formula (extracted LaTeX)
\[\Delta_{\text{ridge}} = \dfrac{t/2}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{cut}} = L_{\text{center}} - \Delta_{\text{ridge}}\]
\Delta_{\text{ridge}} = \dfrac{t/2}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{cut}} = L_{\text{center}} - \Delta_{\text{ridge}}
Formula (extracted text)
$\theta = \begin{cases} \arctan\!\left(\dfrac{p}{12}\right), & \text{if pitch } p \text{ (rise-in-12) is given} \\ \theta_{\text{deg}} \cdot \dfrac{\pi}{180}, & \text{if angle in degrees is given} \end{cases} $ $\text{run} = \begin{cases} \dfrac{\text{span}}{2}, & \text{if span is known} \\ \text{run}, & \text{if run is known} \end{cases} $ $\text{rise} = \text{run}\cdot\tan(\theta) \quad\quad \text{pitch factor} = \sec(\theta) = \dfrac{1}{\cos(\theta)} $ $L_{\text{center}} = \dfrac{\text{run}}{\cos(\theta)}$ $\Delta_{\text{ridge}} = \dfrac{t/2}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{cut}} = L_{\text{center}} - \Delta_{\text{ridge}} $ $\Delta_{\text{overhang}} = \dfrac{\text{overhang}_\text{horizontal}}{\cos(\theta)} \quad\Rightarrow\quad L_{\text{total}} = L_{\text{cut}} + \Delta_{\text{overhang}} $
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn
Formulas

(Formulas preserved from original page content, if present.)

Version 0.1.0-draft
Citations

Add authoritative sources relevant to this calculator (standards bodies, manuals, official docs).

Changelog
  • 0.1.0-draft — 2026-01-19: Initial draft (review required).