When you stand outside and look at a roof, you may wonder:
“How steep is that roof?” or “What angle is that?”

Roof angle matters in many situations—installing solar panels, estimating materials, rainwater flow, snow load, or even designing a small shed.
The good thing is: calculating roof angle is easier than it looks.

This guide explains everything in a simple, practical way.

What Is Roof Angle?

The roof angle is the angle (in degrees) between the roof surface and a perfectly horizontal line.

Most people describe roof steepness using roof pitch, like:

• 4/12 (mild slope)
• 6/12 (standard slope)
• 12/12 (very steep)

But pitch is only a ratio.
To convert that into an actual angle, we use a simple formula.

1. Understanding Roof Pitch

Roof pitch is written as:

Pitch = Rise / Run

• Rise = vertical height (in inches or centimeters)
• Run = horizontal distance
  • In the USA, run is usually 12 inches, by default.

Example:
A roof labeled 6/12 means:

• It rises 6 inches
• For every 12 inches of horizontal distance

2. Formula to Calculate Roof Angle

The roof angle is based on trigonometry, specifically the arctangent function.

Roof Angle Formula

$\text{Angle (in degrees)}={tan}^{-1}\left(\frac{\text{Rise}}{\text{Run}}\right)$

This formula works for any pitch.

3. Step-by-Step Method (Easy Explanation)

1. Take the rise value.
2. Take the run value (usually 12).
3. Divide rise ÷ run.
4. Apply arctan (also called inverse tan).
5. The result is your roof angle in degrees.

That’s it.

Examples

Example 1: Roof pitch 4/12

Step 1: Rise = 4

$Run=12$

Step 2: Divide rise by run

$\frac{4}{12}=0.3333$

Step 3: Apply arctan

$\text{Angle}={tan}^{-1}\left(0.3333\right)$

Angle = 18.43° (approx)

Example 2: Roof pitch 6/12

Step 1:

Rise = 6
Run = 12

$\frac{6}{12}=0.5$

$\text{Angle}={tan}^{-1}\left(0.5\right)$

Angle = 26.57°

Example 3: Roof pitch 9/12

Step 1:

Rise = 9
Run = 12

$\frac{9}{12}=0.75$

$\text{Angle}={tan}^{-1}\left(0.75\right)$

Angle = 36.87°

Roof Pitch to Angle Quick Reference

How to Measure Rise and Run (if you're on-site)

If you're physically checking a roof:

Option 1: Use a level & tape measure

1. Hold a 2-foot or 4-foot level horizontally.
2. Measure straight down (vertical) from the end of the level to the roof surface.
3. This measurement is your rise.
4. Your level length becomes the run.

Example

If a 12-inch level shows a 5-inch drop:
→ Pitch is 5/12

Why Roof Angle Matters

• Solar panel tilt
• Rain and snow drainage
• Roofing material choice
• Attic space planning
• Construction safety

A well-calculated roof angle ensures better strength and longer life.

Conclusion

Calculating roof angle is simple once you understand the relationship between rise, run, and arctan.
Whether you're building a shed, renovating, or checking if solar panels will fit your roof, this method works every time.