Quick answer
A pitch of x:12 has an angle of arctan(x ÷ 12) and a rafter factor √(1 + (x ÷ 12)²). A 6:12 pitch is 26.57°, a 50% slope and 1.118 feet of rafter per foot of run.
Choose what you know (rise per 12 inches, angle or slope) and enter the value. The calculator returns the others. Use this roof pitch calculator to check your own figures.
Related tools: Roof Shingles Calculator: Squares and bundles of shingles for a roof area. Roof Sheathing Calculator: Sheets of plywood or OSB for a roof area. Roof Area Calculator: Roof surface area from the building footprint, overhang and pitch.
How to use the Roof Pitch Calculator
- Choose i know the: Rise per 12 in of run (x:12) and Angle in degrees.
- Enter value (between 0 and 1000).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| I know the | Choose one: Rise per 12 in of run (x:12); Angle in degrees | Starts at Rise per 12 in of run (x:12) |
| Value | A number | > 0, ≤ 1000 |
Formula and method
Formula
pitch x:12 → angle = arctan(x ÷ 12); rafter factor = √(1 + (x ÷ 12)²)
IEEE-754 double precision; shown to the decimals indicated.
Rafter length equals the run times the factor. Plan geometry only; confirm quantities with your supplier and local code before ordering.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: I know the = Rise per 12 in of run (x:12); Value = 6.
| Result | Value |
|---|---|
| Pitch | 6:12 |
| Angle | 26.57° |
| Slope | 50% |
| Rafter length per ft of run | 1.118 |
Example 2
Inputs: I know the = Angle in degrees; Value = 30.
| Result | Value |
|---|---|
| Pitch | 6.93:12 |
| Angle | 30° |
| Slope | 57.74% |
| Rafter length per ft of run | 1.1547 |
Example 3
Inputs: I know the = Rise per 12 in of run (x:12); Value = 12.
| Result | Value |
|---|---|
| Pitch | 12:12 |
| Angle | 45° |
| Slope | 100% |
| Rafter length per ft of run | 1.4142 |
The first line is the headline result (pitch). Below it the roof Pitch Calculator lists angle, slope and rafter length per ft of run, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Three ways to say the same slope
Pitch 6:12 means 6 inches of rise per 12 inches of run. Slope as a percentage is rise ÷ run: 6 ÷ 12 = 50%. The angle is arctan(0.5) = 26.57°.
Why it matters
Pitch decides roofing materials: shingles generally need at least 2:12 or 4:12, depending on underlayment. Steeper roofs shed snow but need more material and safer work practices.
How the result changes with value
Holding every other input at the first worked example, this table changes only value. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Value | Pitch | Angle | Slope |
|---|---|---|---|
| 3 | 3:12 | 14.04° | 25% |
| 6 | 6:12 | 26.57° | 50% |
| 12 | 12:12 | 45° | 100% |
| 24 | 24:12 | 63.43° | 200% |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Value: entering "90" shows "The angle must be below 90°." beside that field and no result.
Choosing between the Roof Pitch Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Roof Shingles Calculator](/construction/roof-shingles-calculator/) | roof area, bundles per square and waste allowance | Bundles needed |
| [Roof Sheathing Calculator](/construction/roof-sheathing-calculator/) | roof area, sheet size and waste allowance | Sheets needed |
| [Roof Area Calculator](/construction/roof-area-calculator/) | building length, building width and overhang on every side | Roof area |
| [Metal Roofing Calculator](/construction/metal-roofing-material-calculator/) | roof width to cover, panel coverage width and panel length | Panels needed |
| [Ice and Water Shield Calculator](/construction/ice-water-shield-calculator/) | area to cover, coverage per roll and waste allowance | Rolls needed |
Background: construction estimates
Material quantities are geometry plus a margin. Calculate the exact volume or area, add an allowance for waste, spillage, cuts and uneven ground (calculator pages commonly mention 5 to 10 percent, a rule of thumb that varies by material and job) and round up to whole units. One cubic yard is exactly 27 cubic feet.
Suppliers often have minimum order sizes and may charge for small loads, so confirm quantities, product yields and local code with your supplier or a qualified estimator before ordering.
Assumptions and limitations
- Angles must be below 90°
Quantities are estimates. Add allowances for waste and site conditions, and follow local codes and a qualified professional's instructions for structural or safety-critical work.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for value to confirm this.
Frequently asked questions
What is a 12/12 roof?
A 12/12 roof rises 12 inches per 12 inches of run, a 45° angle.
How do I measure the pitch?
Use a level and a tape: measure the rise over 12 inches.
Can I convert angle to pitch?
Yes, pitch = 12 × tan(angle).
What does the Roof Pitch Calculator calculate?
Roof pitch as rise per 12 inches, angle, slope percent and rafter length factor. It returns Pitch, Angle, Slope and Rafter length per ft of run.
What formula does the Roof Pitch Calculator use?
pitch x:12 → angle = arctan(x ÷ 12); rafter factor = √(1 + (x ÷ 12)²). Rafter length equals the run times the factor.
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Angles must be below 90°.
What does the “I know the” option change?
It sets how the roof Pitch is worked out. The choices are Rise per 12 in of run (x:12) and Angle in degrees.
What is an example of a roof Pitch result?
With i know the Rise per 12 in of run (x:12) and value 6, the pitch is 6:12.
Can I rely on this calculator for a decision?
Quantities are estimates. Add allowances for waste and site conditions, and follow local codes and a qualified professional's instructions for structural or safety-critical work. For this calculator in particular: Angles must be below 90°.
Related calculators
- Roof Shingles Calculator — Squares and bundles of shingles for a roof area.
- Roof Sheathing Calculator — Sheets of plywood or OSB for a roof area.
- Roof Area Calculator — Roof surface area from the building footprint, overhang and pitch.
- Metal Roofing Calculator — Number of metal roofing panels across a roof width.
- Ice and Water Shield Calculator — Rolls of ice and water membrane for an area.
- Gutter Length Calculator — Total gutter length and number of sections from your eave lengths.
- Thread Pitch Calculator — Convert between threads per inch and pitch in millimeters.
Sources
- OpenStax, Prealgebra 2e (Rice University): perimeter, area, volume, circumference and the Pythagorean theorem
- NIST Special Publication 811, Guide for the Use of the International System of Units (SI), Appendix B conversion factors (international foot 0.3048 m, inch 25.4 mm, US gallon 3.785411784 L)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.