How to Calculate Roof Pitch in Degrees

A roof can look gentle from the yard and suddenly feel much steeper when you stand near it with a ladder. That shift in feeling is what roof pitch in degrees puts into a number. Once you know the angle, the roof stops being a shape you guess at and starts being something you can measure.

This number comes in handy when you read plans, set roof brackets, size solar mounts, talk with a roofer, or compare one roof shape to another. It also helps when a pitch ratio like 6/12 does not mean much to you yet, but a degree number does. The math is not hard. In most cases, you only need the rise and the run.

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What Roof Pitch in Degrees Means

Roof pitch in degrees is simply the angle of the roof slope measured from a flat, level line. A perfectly flat surface is 0 degrees. As the roof rises, the angle gets larger. A steeper roof has a bigger degree number.

Many roofers talk about pitch as a ratio like 4/12, 6/12, or 8/12. That ratio means the roof rises a certain number of inches for every 12 inches of horizontal run. The degree number tells the same story in a different language. A 6/12 pitch is about 26.6 degrees. An 8/12 pitch is about 33.7 degrees.

Think of it like miles per hour and kilometers per hour. They both describe motion. They just use different numbers. Roof pitch ratio and roof pitch in degrees work the same way.

Rise and Run Come First

Before you can calculate roof pitch in degrees, you need two numbers. The first is the rise. That is how much the roof goes up. The second is the run. That is the flat horizontal distance.

The word horizontal matters. If you measure along the roof surface, you are measuring the slope length, not the run. That is one of the easiest ways to get a wrong answer. The run must be a level distance, not the slanted face of the roof.

On a standard gable roof, the run for one side is half the full width of the building. If the house is 24 feet wide from one outside wall to the other, the run for one side is 12 feet, not 24 feet. That small mistake can throw the whole angle off.

The Formula for Roof Pitch in Degrees

Here is the formula:

roof angle in degrees = arctan(rise ÷ run)

That is the clean answer. Divide the rise by the run. Then take the arctangent of that number. On many calculators, the arctangent button looks like tan-1 or atan.

If your roof pitch is already written as a ratio over 12, the formula becomes even easier:

roof angle in degrees = arctan(pitch ÷ 12)

So if the pitch is 6/12, you divide 6 by 12 and get 0.5. Then you take the arctangent of 0.5.

arctan(6 ÷ 12) = arctan(0.5) = 26.57°

That means a 6/12 roof pitch is about 26.6 degrees.

How to Convert Roof Pitch to Degrees

Let’s walk through it in plain steps. Say the roof pitch is 8/12.

8 ÷ 12 = 0.6667
arctan(0.6667) = 33.69°

So an 8/12 roof pitch is about 33.7 degrees.

Here is another one. Say the roof pitch is 4/12.

4 ÷ 12 = 0.3333
arctan(0.3333) = 18.43°

So a 4/12 roof pitch is about 18.4 degrees.

Once you do this two or three times, the pattern becomes easy to spot. Lower pitch ratio, lower angle. Higher pitch ratio, steeper angle.

How to Measure Roof Pitch Before Converting to Degrees

If you do not already know the pitch ratio, you can measure it yourself. One easy way is to use a level and a tape measure on the roof surface, but only if the roof is safe to access.

Place one end of the level against the roof. Hold the level until the bubble sits in the center. That gives you a flat line. From the end touching the roof, mark 12 inches along the level. At that mark, measure straight down to the roof surface.

The distance down to the roof is the rise over 12 inches of run. If that distance is 6 inches, the roof pitch is 6/12. If it is 9 inches, the roof pitch is 9/12. After that, you can convert the ratio to degrees with the arctangent formula.

How to Measure Roof Pitch From the Attic

If the roof is wet, high, or too steep to walk, the attic is often the better place to work. The underside of a rafter follows the same slope as the roof above it, so you can measure there instead.

Hold a level flat against the side or bottom of a rafter. Keep the level horizontal. Mark 12 inches on the level. At that mark, measure straight up from the level to the rafter.

If that gap is 7 inches, the roof pitch is 7/12. To convert that into degrees, divide 7 by 12 and then take the arctangent.

7 ÷ 12 = 0.5833
arctan(0.5833) = 30.26°

That roof angle is about 30.3 degrees.

How to Calculate Roof Pitch in Degrees From Building Width and Height

Sometimes you do not have easy access to the roof or attic, but you know the full width of the building and the height from the wall top to the ridge. You can still get the angle.

Start with the full width of the building, also called the span. Divide that by 2 to get the run for one side of a standard gable roof. Then divide the rise by the run. After that, take the arctangent.

Let’s say a garage is 24 feet wide and the roof rises 6 feet from the top of the wall to the ridge.

span = 24 feet
run = 12 feet
rise = 6 feet
6 ÷ 12 = 0.5
arctan(0.5) = 26.57°

The roof pitch in degrees is about 26.6 degrees.

Common Roof Pitch to Degrees Chart

If you want a quick reference, this chart helps. These numbers are rounded to one decimal place.

A 12/12 roof lands at 45 degrees because the rise and the run are equal. That makes the roof form a neat right triangle where both legs match. It is one of the easiest angles to remember.

How to Use a Phone Calculator

You do not need a fancy construction calculator for this. A phone works fine. Just make sure it is set to degree mode, not radian mode. That detail matters. If the calculator is in radian mode, the answer will look wrong even if your math is right.

Here is the fast method. First, divide the rise by the run. Second, press the arctangent button. On some phones, you may need to turn the calculator sideways to see the scientific buttons. On others, the button may read tan-1, atan, or appear after you tap a function key.

For a 9/12 roof:

9 ÷ 12 = 0.75
arctan(0.75) = 36.87°

Round that to 36.9 degrees.

Roof Pitch in Degrees Versus Roof Pitch Ratio

Some people find the ratio easier. Some find the angle easier. Roofers often talk in 6/12, 8/12, or 10/12 because that language fits field measurements. Engineers, solar installers, and plan readers often like degree values because angle settings on gear are usually shown that way.

Neither method is better in every case. They are just two ways to name the same slope. If someone says a roof is 33.7 degrees, that matches an 8/12 pitch. If someone says a roof is 26.6 degrees, that matches a 6/12 pitch.

Once you know how to move from one form to the other, both numbers start to feel familiar.

Common Mistakes That Throw Off the Angle

The biggest mistake is measuring along the roof surface instead of using the horizontal run. The sloped face of the roof is not the run. It is longer than the run, so it gives you a bad angle.

Another mistake is using the full width of the house as the run on a standard gable roof. The full width is the span. The run for one side is half of that.

People also get tripped up by the calculator mode. If your calculator is in radians instead of degrees, the result will not match the roof angle chart you expect to see.

Rounding too early can also muddy the answer. If your rise is 5.75 inches over 12 inches of run, use 5.75 in the math before rounding the final degree number.

Why Roof Pitch in Degrees Matters

Knowing the angle helps in real jobs. It can help with roof brackets, flashing details, solar racking, attic framing checks, and the feel of the roof underfoot. A low-slope roof and a steep roof do not behave the same way in rain or snow. They do not feel the same to walk on either.

The degree number also helps when you compare roofs that look close at a glance. From the ground, a 6/12 roof and an 8/12 roof may not seem worlds apart. On paper, though, one is about 26.6 degrees and the other is about 33.7 degrees. That difference shows up fast when you stand on it or price materials for it.

A roof angle can also shape the look of a house. A lower angle can make a home look broader and calmer. A steeper angle can give it a sharper profile, almost like a hat pulled higher over the walls.

When Not to Measure From the Roof

If the roof is slick, storm-damaged, very steep, or simply too high to reach with good footing, skip the rooftop method. Use the attic method if you can. If there is no attic access, work from plans, take outside measurements from a safe spot, or bring in a roofer with the right gear.

No angle number is worth a fall. A roof may only ask for one clean measurement, but gravity does not cut deals.

The Fast Way to Remember It

If you want one line to keep in your head, use this:

roof angle in degrees = arctan(rise ÷ run)

If the pitch is already written as x/12, use this version:

roof angle in degrees = arctan(x ÷ 12)

That is the whole idea. Measure the rise. Measure the horizontal run. Divide one by the other. Then use arctangent to get the roof pitch in degrees.

Final Answer

To calculate roof pitch in degrees, divide the rise by the horizontal run and then take the arctangent of that number. If the roof pitch is written as 6/12, the math is arctan(6 ÷ 12), which gives about 26.6°. If the pitch is 8/12, the math is arctan(8 ÷ 12), which gives about 33.7°. Once you know that one formula, you can convert almost any standard roof pitch ratio into degrees without much fuss.