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Roof Pitch Calculator

Calculate roof pitch ratio (rise/run), slope angle in degrees, grade percentage, and rafter length multiplier.

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How to Use the Roof Pitch Calculator – Pitch, Angle & Multiplier

1Enter the vertical rise in inches.
2Enter the horizontal run in inches (standard construction run is 12 inches).
3Read the standard pitch ratio (e.g., 6:12), slope angle in degrees, and slope percentage.
4Check the rafter multiplier factor to determine true slanted rafter lengths.

Formula & How It Works

Trigonometric Slope & Rafter Factor Math

Pitch = Rise:12 | Angle = arctan(Rise ÷ Run) × (180 ÷ π) | Rafter Factor = √(Rise² + Run²) ÷ Run

Pitch ratio is expressed as Rise:Run (standardized to 12 inches of run). The pitch angle is calculated using the arctangent function: θ = arctan(Rise / Run). The rafter length factor equals √(1 + (Rise/Run)²), which multiplies horizontal span to yield true rafter length.

Worked Examples

Standard Residential Roof Pitch (6:12)

Input: Rise: 6 inches, Run: 12 inches

Explanation: arctan(6/12) = arctan(0.5) = 26.565°. Rafter factor = √(36 + 144) / 12 = 1.1180.

Result: Pitch: 6:12 | Angle: 26.57° | Slope: 50.0% | Rafter Factor: 1.1180x

Steep Gable Roof (10:12)

Input: Rise: 10 inches, Run: 12 inches

Explanation: arctan(10/12) = 39.8056°. Rafter factor = √(100 + 144) / 12 = 1.3017.

Result: Pitch: 10:12 | Angle: 39.81° | Slope: 83.3% | Rafter Factor: 1.3017x

Low-Slope Modern Roof (2:12)

Input: Rise: 2 inches, Run: 12 inches

Explanation: Requires membrane or standing seam metal roofing because slope is below standard shingle minimums.

Result: Pitch: 2:12 | Angle: 9.46° | Slope: 16.7% | Rafter Factor: 1.0138x

45-Degree High Pitch (12:12)

Input: Rise: 12 inches, Run: 12 inches

Explanation: Rise equals run, creating a 45-degree right isosceles triangle with rafter multiplier √2.

Result: Pitch: 12:12 | Angle: 45.00° | Slope: 100.0% | Rafter Factor: 1.4142x (√2)

Frequently Asked Questions

What does a 6:12 roof pitch mean?▼

A 6:12 roof pitch means the roof plane rises 6 inches vertically for every 12 inches of horizontal run distance (a 26.57° slope angle).

What is the minimum roof pitch for standard asphalt shingles?▼

Building codes generally require a minimum pitch of 2:12 with double underlayment, and 4:12 for standard single underlayment application.

How do you calculate rafter length from horizontal run?▼

Multiply the horizontal building run by the rafter factor. For example, on a 15-foot horizontal run with a 6:12 pitch: 15 ft × 1.1180 = 16.77 ft rafter.

What is the difference between roof pitch and roof slope?▼

While often used interchangeably in the US, slope specifically refers to the ratio of rise over run (X:12), whereas pitch historically meant rise over the entire building span.

What pitch is considered a 'walkable' roof?▼

Pitches of 6:12 and lower are typically walkable with rubber-soled footwear. Pitches of 7:12 and above generally require roof jacks and safety harnesses.

Does this tool work completely client-side?▼

Yes, all trigonometric formulas run locally in your web browser with zero server latency.

Last reviewed & updated: 2026-11-01

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