Roof Pitch Calculator
Solve for angle (°), pitch (in/12), slope (%), rise, run, or rafter length. Pick a method, enter the required values, and get a step-by-step solution.
Calculation Steps
Practical Guide
Roof Pitch Calculator: Convert Pitch, Slope, Angle, Rise/Run, and Rafter Length
This guide mirrors the calculator above. Learn the relationships between pitch (in/12), slope (%), angle (°), rise, run, and common rafter length—plus fast field methods, worked examples, and the gotchas that move your numbers.
Quick Start
- 1 In Solve for, choose the unknown you need: Angle (°), Pitch (in/12), Slope (%), Rise, Run, or Rafter length.
- 2 Pick a Mode that matches the inputs you already have (e.g., compute angle from rise & run, or from pitch, or from slope).
- 3 Set Output Units for length results (mm, cm, m, in, ft) and enter your known values. The form only shows the inputs required for your chosen mode.
- 4 Review the Calculated Result, then skim the Calculation Steps to see formulas, unit conversions, and rounding assumptions.
- 5 If you need surface area for material estimating, use the pitch multiplier (explained below) to convert plan area to roof area.
Tip: For a quick field reading, place a 12-inch level on the shingle and measure rise at the free end. That number is the pitch “in/12”. A 6-inch rise at 12 inches of run is a 6:12 roof.
Watch-out: Adding length units to angle/pitch/slope results won’t make sense—those are dimensionless displays. Only rise, run, and rafter length carry units.
Variables & Symbols
- \(r\) Rise (vertical)
- \(x\) Run (horizontal)
- \(\theta\) Angle to horizontal (degrees or radians)
- \(P\) Pitch in inches per 12 in of run (e.g., \(P=6\) for 6:12)
- \(s\%\) Slope in percent \((100\,r/x)\)
- \(L\) Common rafter length over run \(\sqrt{x^2+r^2}\)
- \(M\) Pitch multiplier for surface area \(\sqrt{1+(P/12)^2}\)
Choosing Your Method
Method A — From Rise & Run
Best when you can measure directly with a level, tape, or laser.
- Direct geometry; no lookups required.
- Outputs all forms (°, in/12, %, rafter length).
- Works for any units (keep them consistent).
- Access to the roof needed for true readings.
- Short runs amplify measurement error.
Method B — From Pitch (in/12) or Slope (%)
Fast for US residential work where pitch is standard vernacular.
- One box number describes the roof (e.g., 4:12, 7:12).
- Easy to convert to angle and rafter length.
- Still need a run to get actual lengths.
- “Percent slope” is sometimes misread as degrees.
What Moves the Number the Most
Stick to one length unit for rise and run. Mixing inches and feet without converting is the #1 error.
Measuring over 12 in is convenient but noisy; double-check over 24–48 in when you can.
Pitch is often rounded to the nearest 0.5 in/12; angles to 0.5°. Declare your convention up front.
Build-up layers, sheathing thickness, and underlayments slightly change true rise/run from framing geometry.
Make sure you’re using horizontal run, not slope length. The calculator expects horizontal run \(x\).
Remote readings (from the ground with angle finders or photos) are safer but need careful alignment to avoid parallax.
Worked Examples
Example 1 — Convert 6:12 Pitch to Angle, Slope, and Rafter per Foot
- Given: Pitch \(P=6\) (i.e., 6 in rise per 12 in run)
- Find: \(\theta\) (degrees), slope (%), rafter length per foot of run
To get a total common rafter length, multiply that per-foot factor by your actual horizontal run to the ridge.
Example 2 — From Rise & Run to Pitch, Angle, and Rafter (Metric Input, Imperial Output)
- Given: Rise \(r = 0.90\ \text{m}\), Run \(x=2.40\ \text{m}\)
- Output units: ft/in for length, degrees for angle
The calculator handles unit conversions internally—set your preferred display units before reviewing results.
Ratios, Conversions & Variations
Use this table to translate among common notations and to understand practical implications of each range.
| Item | Formula / Conversion | Practical Notes |
|---|---|---|
| Pitch → Angle | \(\theta = \arctan(P/12)\) | Example: 4:12 ≈ 18.43°, 6:12 ≈ 26.57°, 9:12 ≈ 36.87°. |
| Angle → Pitch | \(P = 12\,\tan\theta\) | Example: 30° ≈ 6.93:12 (≈ 7:12). |
| Pitch → Slope (%) | \(s\% = 100\,P/12\) | Rule of thumb: each 1 in/12 ≈ 8.333% slope. |
| Rafter per 1 ft run | \(L_{/ft}=\sqrt{1+(P/12)^2}\) | Multiply by horizontal run to get total common rafter length. |
| Roof area multiplier | \(M=\sqrt{1+(P/12)^2}\) | Surface area = plan area × \(M\) for a single-slope plane (no hips/valleys). |
| Common ranges | Low: 2:12–4:12; Moderate: 4:12–6:12; Steep: 7:12+ | Material choices and underlayment requirements often depend on these ranges. |
- Use horizontal run, not slope length, in all formulas.
- Convert fractional inches to decimals before multiplying.
- Document where you measured rise (top of rafter vs top of sheathing).
- For hips/valleys, use the manufacturer’s multipliers or derive from 3-D geometry.
- When estimating shingles, apply waste for cuts, hips/valleys, and starter/ ridge.
- If local rules specify minimum pitch for a product, verify before ordering.
Materials, Logistics & Sanity Checks
Selecting Materials
- Pitch suitability: Many shingles list a minimum pitch; metal panels often accommodate lower slopes with sealed seams.
- Underlayment: Steeper pitches shed water faster; low slopes may require peel-and-stick membranes.
- Snow & rain: In heavy snow/rain zones, moderate to steep pitches improve shedding and reduce ponding risk.
On-Site Practices
- Confirm pitch at multiple locations; framing can vary across spans.
- Use harnesses and roof jacks on steep pitches; work from staging where possible.
- Record measurement points and a quick sketch—future change orders go faster.
Sanity Checks
- Does \(\theta\) match the stated pitch? (e.g., 6:12 ≈ 26.6°)
- Does rafter length recompute your rise when you back-solve?
- Do units stay consistent through every step?
Building codes and manufacturer literature govern minimum slope, underlayment, and fastening. Use this guide for planning; defer to the governing documents for compliance decisions.