What is the difference between span and run?

Span is the total width of the building measured from outside wall to outside wall. Run is half of the span and is the horizontal distance from the wall plate to the roof centerline.

How do I convert roof pitch to angle?

Angle (degrees) = arctangent(pitch/12) × 180/π. For example, a 6-in-12 pitch is about 26.565°.

Should I deduct ridge thickness from my rafter length?

If you are cutting the rafter to meet a ridge board (not a ridge beam with hangers), deducting half the ridge thickness aligns the cut to the near face of the ridge. Many framers use this deduction by default.

Does the calculator account for birdsmouth/seat cuts?

The tool outputs line lengths along the top edge of the rafter. Seat cut geometry varies by detail and is not automatically deducted. You can adjust field measurements accordingly.

Can I use metric inputs and still get imperial outputs?

Yes. Regardless of the input units, results are presented in both metric (m and mm) and imperial (feet-inches with fractional precision) for convenience.

What accuracy should I choose for fractional inches?

Most carpentry layouts are accurate to 1/16 inch. For rougher work, 1/8 inch may suffice. You can set your preferred precision in the calculator.

Is this calculator suitable for structural design?

No. It provides geometric lengths only. Sizing rafters for loads requires structural design per your local building code and standards such as the NDS and IRC.

Rafter Length Calculator | Framing & Roofing Tool

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.

Run = span ÷ 2 = 24 ft ÷ 2 = 12 ft.
Angle: θ = arctan(6/12) ≈ 26.565°.
Pitch factor: sec(θ) ≈ 1.1180.
Lcenter = run ÷ cos(θ) = 12 ft × 1.1180 ≈ 13.416 ft.
Ridge deduction: Δridge = (1.5 in ÷ 2) ÷ cos(θ) ≈ (0.75 in) ÷ 0.8944 ≈ 0.838 in ≈ 0.0698 ft.
Lcut = 13.416 − 0.0698 ≈ 13.346 ft.
Overhang tail: Δoverhang = 18 in ÷ cos(θ) ≈ 18 ÷ 0.8944 ≈ 20.12 in ≈ 1.676 ft.
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.

Tool developed by Ugo Candido. Content verified by the CalcDomain Expert Team.
Last reviewed for accuracy on: September 15, 2025.

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