Calculation Result
Results update after submission or live input changes.
Roof Triangle Diagram
Formula Used
Angle = atan(rise ÷ run) Slope % = (rise ÷ run) × 100 Pitch per 12 = (rise ÷ run) × 12 Rafter = √(rise² + run²)
Result Summary
Automatic Unit Conversions
Formula Used
| Calculation | Formula |
|---|---|
| Angle | θ = atan(rise ÷ run) × 180 ÷ π |
| Slope percentage | (rise ÷ run) × 100 |
| Pitch per twelve | (rise ÷ run) × 12 |
| Rafter length | √(rise² + run²) |
| Rise from angle | run × tan(θ) |
| Run from angle | rise ÷ tan(θ) |
Roof pitch compares vertical rise with horizontal run. Degrees describe the same slope using an angle. Both formats support accurate planning and material estimates.
How to Use
Select the mode matching your available measurements. Enter values using one consistent linear unit. Press calculate to produce every related roof measurement.
Choose live calculations for immediate updates while typing. Preset buttons quickly load common twelve-unit roof pitches. Review the diagram before copying or exporting results.
Worked Example
A roof rises six inches over twelve inches. The ratio equals one-half, producing a fifty-percent slope. Its angle measures approximately 26.565 degrees.
| Input or result | Example value |
|---|---|
| Rise | 6 in |
| Run | 12 in |
| Pitch | 6:12 |
| Angle | 26.565° |
| Slope | 50% |
| Rafter length | 13.416 in |
Common Roof Pitch Reference
| Pitch | Degrees | Slope | General classification |
|---|---|---|---|
| 1:12 | 4.764° | 8.33% | Conventional slope |
| 2:12 | 9.462° | 16.67% | Conventional slope |
| 3:12 | 14.036° | 25% | Steep slope |
| 4:12 | 18.435° | 33.33% | Steep slope |
| 5:12 | 22.62° | 41.67% | Steep slope |
| 6:12 | 26.565° | 50% | Steep slope |
| 8:12 | 33.69° | 66.67% | Very steep slope |
| 9:12 | 36.87° | 75% | Very steep slope |
| 10:12 | 39.806° | 83.33% | Very steep slope |
| 12:12 | 45° | 100% | Very steep slope |
| 16:12 | 53.13° | 133.33% | Very steep slope |
| 18:12 | 56.31° | 150% | Very steep slope |
| 24:12 | 63.435° | 200% | Very steep slope |
Pitch labels provide convenient comparisons between common roof slopes. Classifications shown here are broad planning references only. Local building rules may use different limits and terminology.
Frequently Asked Questions
What does a 6:12 roof pitch mean?
The roof rises six units for twelve horizontal units. Any matching unit may describe both measurements. This pitch equals about 26.565 degrees.
How are roof pitch degrees calculated?
Divide rise by run before applying inverse tangent. Convert the resulting radian value into degrees. The calculator performs both steps automatically.
Can I enter fractions?
Yes, common fractions and mixed numbers are accepted. Examples include 6/12 and 4 1/2. Avoid denominators equal to zero.
Does the selected unit affect the angle?
No, angles depend on the rise-to-run ratio. Rise and run must use matching units. Mixed units create incorrect ratios and results.
What is slope percentage?
Slope percentage compares rise against run as a percentage. A 6:12 pitch produces a fifty-percent slope. It describes steepness without using degrees.
How is rafter length calculated?
Rise and run form perpendicular triangle sides. Rafter length becomes the triangle hypotenuse. The Pythagorean theorem supplies that length.
Are roof classifications universal?
No, classifications vary across codes and roofing systems. This calculator uses broad descriptive ranges. Always check applicable local requirements first.
Can this calculator size roofing materials?
It supplies geometry useful for early estimates. Complete material quantities require roof area and waste allowances. Openings and overhangs also affect totals.
Is measuring an existing roof safe?
Roof access can cause serious falls and injuries. Prefer plans or ground-based measuring methods. Use qualified professionals for elevated measurements.
Safety and Code Notice
This tool provides estimates for planning and learning. It does not approve structural or roofing designs. Verify every project with qualified local professionals.