📐 Roof Pitch Calculator
Find your roof pitch, angle in degrees, slope factor, percentage grade, and rafter length. Enter rise and run, a pitch, or an angle — convert instantly between all of them. Free, no sign-up.
A roof pitch calculator finds how steep a roof is and converts between every way of expressing it. Roof pitch is the vertical rise over a horizontal run, written as a ratio like 6/12. The calculator turns rise and run into an angle, a slope factor, a percentage grade, and a rafter length. The core formulas are:
How to find roof pitch in 3 steps:
- Pick an input method — rise and run, a pitch in X/12 form, or an angle in degrees.
- Enter your figures and the building span so the rafter length can be worked out.
- Click Calculate Pitch to see the pitch, angle, slope factor, grade, total rise, and rafter length.
For example, a 6/12 pitch rises 6 inches per 12 inches of run — an angle of 26.57°, a 50% grade, and a slope factor of 1.118. On a 24-foot-wide building each rafter runs 12 feet and measures about 13.4 feet.
Roof Pitch Calculator
Enter rise and run, a pitch, or an angle — get pitch, degrees, slope factor and rafter length.
Know Your Roof Pitch Exactly –
as a Ratio, an Angle, and a Rafter Length
Roof pitch is written as a ratio, but plans, calculators, and tools each speak a different dialect — X/12, degrees, or percentage grade. This free calculator converts between all of them and works out the rafter length, so the numbers line up before you cut.
⚡ Try the Calculator NowRoof Pitch: The Number That Defines a Roof
Every roof has a steepness, and that steepness — the pitch — drives almost everything about it: how it sheds water and snow, what roofing material it can take, how much surface it has, and how long the rafters need to be. Get the pitch right and the rest of the roof falls into place. Get it wrong and the errors multiply down the whole build.
The trouble is that pitch is described in several different languages. A builder writes it as a ratio — 6/12. A plan might give it in degrees. A surveyor's tool reads percentage grade. They all describe the same slope, but switching between them by hand means trigonometry, and a small slip there becomes a rafter cut several inches off.
This free Roof Pitch Calculator speaks all three. Enter rise and run, a pitch in X/12 form, or an angle in degrees, and it instantly returns the pitch ratio, the angle, the percentage grade, the slope factor, and the rafter length for your building span. One set of numbers, every form.
How the Roof Pitch Calculator Works
Pick how you want to enter the slope, add the building span, and click once. The calculator returns the pitch in every form plus the rafter length. Here is what each field does.
Pick an Input Method
Choose Rise & Run if you measured the roof directly, Pitch X/12 if you know the ratio, or Angle if you have it in degrees. Each method reaches the same result.
Enter the Rise & Run
In Rise & Run mode, enter the vertical rise and the horizontal run in the same units — inches is standard, with a 12-inch run.
📐 A 6-inch rise over a 12-inch run is a 6/12 pitch.Or Enter a Pitch or Angle
In Pitch mode, enter just the first number of an X/12 ratio. In Angle mode, enter the roof angle in degrees. The calculator converts from there.
📊 A 45° roof and a 12/12 pitch are the same thing.Enter the Building Span
The span is the full width of the building. The calculator uses half of it as the horizontal run of each rafter to work out the rafter length.
Add Overhang & Rafter Count
In Advanced mode, add an eave overhang to extend each rafter, and a rafter count to total the linear feet of rafter stock for the whole roof.
Hit Calculate — Read Every Number
Instantly see the pitch ratio, the angle in degrees, the percentage grade, the slope factor, the total rise, the rafter length, and the rafter triangle.
✅ Angle = arctangent of rise ÷ runThe Roof Pitch Formulas, Explained
Roof pitch is a right triangle. Once you see the triangle, the rise, the run, and the rafter, every formula is just a side or an angle of it.
The pitch ratio: Pitch is rise divided by run — how far the roof climbs vertically for each unit it travels horizontally. By convention the run is fixed at 12 inches, so a roof that rises 6 inches over that 12-inch run is a 6/12 pitch. The ratio itself, 6 ÷ 12 = 0.5, is the foundation for everything else.
The angle: The roof angle is the arctangent of the pitch ratio. For a 6/12 pitch, that is arctan(0.5), which is about 26.57 degrees. A 12/12 pitch — where rise equals run — gives arctan(1), exactly 45 degrees. The angle and the ratio are two readings of the same slope.
The percentage grade: Multiply the pitch ratio by 100. A 6/12 pitch is a 50% grade, a 12/12 pitch is a 100% grade. Percentage grade is common in some regions and trades; it is the same steepness in a different costume.
The slope factor: Also called the rafter multiplier, the slope factor is the square root of one plus the ratio squared. For a 6/12 pitch that is the square root of 1.25, about 1.118. It converts any horizontal distance into the longer sloped distance above it — multiply the run by the slope factor to get the rafter.
The rafter length: A gable rafter spans from the wall to the ridge. Its horizontal run is half the building span. The rafter length is that run multiplied by the slope factor. A 24-foot building has a 12-foot run; at a 6/12 pitch, the rafter is 12 × 1.118, about 13.4 feet — before any eave overhang.
Pitch, Angle & Slope Factor Tables
These reference tables convert between the common pitches. The slope factor column is the one to keep handy — it turns a footprint into a rafter or a roof surface.
| Pitch | Angle | Grade | Slope Factor |
|---|---|---|---|
| 3/12 | 14.04° | 25% | 1.031 |
| 4/12 | 18.43° | 33% | 1.054 |
| 6/12 | 26.57° | 50% | 1.118 |
| 8/12 | 33.69° | 67% | 1.202 |
| 9/12 | 36.87° | 75% | 1.250 |
| 12/12 | 45.00° | 100% | 1.414 |
The formula in plain language: The angle is the arctangent of rise over run; the slope factor is the square root of one plus the ratio squared. A 6/12 pitch is a 26.57° angle and a 1.118 slope factor.
Roof Pitch Categories
| Category | Pitch Range | Notes |
|---|---|---|
| Flat | Below 2/12 | Needs membrane roofing, not shingles |
| Low-slope | 2/12 to 4/12 | Shingles allowed with extra underlayment |
| Conventional | 4/12 to 9/12 | The standard range for most houses |
| Steep-slope | 9/12 to 12/12 | Dramatic look, harder to work on |
| Very steep | Above 12/12 | Often needs roof jacks or staging |
Rafter Length Per Foot of Run
| Pitch | Rafter Per 1 ft of Run | For a 12 ft Run |
|---|---|---|
| 4/12 | 1.054 ft | 12.65 ft |
| 6/12 | 1.118 ft | 13.42 ft |
| 8/12 | 1.202 ft | 14.42 ft |
| 9/12 | 1.250 ft | 15.00 ft |
| 12/12 | 1.414 ft | 16.97 ft |
The rafter-per-foot figure is just the slope factor. Multiply it by the actual run — half the building span — to size each rafter.
Factors That Affect Roof Pitch
Pitch is not chosen at random. These factors push a roof steeper or shallower, and they shape what the right pitch is for a given building.
The Three Input Methods Compared
This calculator accepts roof slope in three forms. Pick whichever matches what you already have — they all converge on the same pitch.
| Method | Best When | You Enter | Notes |
|---|---|---|---|
| Rise & Run | You measured the roof yourself | Vertical rise and horizontal run | The most hands-on, on-site method |
| Pitch X/12 | You have the pitch from a plan | The first number of the ratio | The standard US builder notation |
| Angle | You have the slope in degrees | The roof angle in degrees | Common on metric and modern plans |
How to Measure a Roof Pitch: A Step-by-Step Roadmap
Measuring a roof's pitch takes a level, a tape, and a few minutes. Here are the four phases from no information to a confirmed pitch.
You need a level — ideally about 12 inches — and a tape measure. Decide where to measure: against a rafter in the attic is safest, or against the roof surface itself if you can reach it safely.
Rest one end of the level against the roof or rafter, bring it to level using the bubble, and mark the 12-inch point. That horizontal 12 inches is the run — the fixed bottom of the pitch triangle.
From the 12-inch mark on the level, measure vertically down to the roof or rafter surface. That distance is the rise. A 6-inch drop means a 6/12 pitch; a 4-inch drop means 4/12.
Enter the rise and run here to get the pitch, angle, slope factor, and rafter length. Measure in a second spot to confirm — a consistent reading tells you the roof is a true, even plane.
How Pitch Drives Roofing Cost
Two houses with the same footprint can have very different roofing bills, and pitch is the reason. A steeper roof costs more in two distinct ways.
The first is surface area. A roof's sloped surface is always larger than the flat footprint beneath it, and the slope factor measures exactly how much larger. A 6/12 roof has a slope factor of 1.118, so its surface is about 12% bigger than the footprint — and that is 12% more shingles, underlayment, and decking. A 12/12 roof's surface is roughly 41% larger.
The second is labor. A roof steep enough to be unwalkable needs roof jacks, staging, or harnesses, and the work goes slower and more carefully. That added difficulty raises the labor rate, on top of the extra area to cover.
| Pitch | Slope Factor | Surface vs Footprint | Roofing Difficulty |
|---|---|---|---|
| 2/12 | 1.014 | +1.4% | Easy — but needs membrane roofing |
| 4/12 | 1.054 | +5.4% | Easy — comfortably walkable |
| 6/12 | 1.118 | +11.8% | Manageable — the common limit to walk |
| 8/12 | 1.202 | +20.2% | Harder — many crews use roof jacks |
| 12/12 | 1.414 | +41.4% | Steep — staging or harnesses needed |
Example Roof Pitch Calculations
Three roofs, three input methods — all worked through with verified math so you can sanity-check your own results.
Getting the Most From a Roof Pitch Figure
A correct pitch is the start of an accurate roof. These six habits turn that number into reliable material orders and clean cuts.
The most useful habit is treating the slope factor as your conversion key. Any flat measurement off a plan — footprint area, building span, a horizontal run — becomes its sloped equivalent when multiplied by the slope factor. Roof surface for shingles, rafter length for framing: both come straight from that single number.
The second habit is measuring the pitch in more than one place. A roof that reads 6/12 at one spot and 5/12 at another is either out of plane or being measured carelessly. A consistent reading across several points is your confirmation that the pitch — and every figure built on it — is sound.
Six Practical Habits
When This Calculator Is the Wrong Tool
The trigonometry here is exact, but a real roof has details a calculator cannot account for. Here is where the output needs care.
1. The rafter is the structural length only. The calculator gives run times slope factor, plus any overhang you add. A buildable rafter also needs allowances subtracted for the ridge board and cut for the bird's-mouth notch. Use this figure to order stock; mark the real cuts from a framing plan.
2. It assumes a simple gable. The rafter calculation treats the run as half the building span — correct for a symmetrical gable roof. Hip roofs, valleys, dormers, and uneven roofs have rafters of several different lengths that this single calculation does not resolve.
3. It does not check code or material limits. The calculator will report a pitch of 1/12 or 20/12 without comment. Whether that pitch is allowed, and whether your roofing material is rated for it, is a question for local building codes and the manufacturer — not this tool.
4. Real roofs are rarely perfect. An older roof can sag, twist, or settle out of its original plane. A calculated pitch assumes a true, even slope; measuring an irregular roof gives a figure that varies depending on where you measure.
Where to go instead: For the flat area of a roof footprint or any surface, a square footage calculator is the right tool — then multiply by the slope factor here. For framing-lumber volume, a board foot calculator handles the wood. This tool's job is the geometry: pitch, angle, slope, and rafter length.
Roofing Terms You'll See On This Page
Quick reference for the roofing and geometry terms used throughout this calculator.
- Roof Pitch
- The steepness of a roof, given as the vertical rise over a horizontal run — usually a 12-inch run, written as a ratio like 6/12.
- Rise
- The vertical height a roof gains over a given horizontal run. The "up" side of the pitch triangle.
- Run
- The horizontal distance over which the rise is measured. Conventionally fixed at 12 inches for stating pitch.
- Span
- The full width of the building. On a gable roof, each rafter's run is half the span.
- Slope Factor
- The rafter multiplier — the square root of one plus the pitch ratio squared. It converts a horizontal distance into the sloped distance above it.
- Rafter
- The sloped structural beam running from the wall to the ridge. Its length is the run times the slope factor.
- Ridge
- The horizontal line at the very top of the roof where the two slopes meet.
- Eave
- The lower edge of the roof, often extended past the wall as an overhang.
- Overhang
- The part of the roof that projects beyond the building wall at the eave. It is added to the structural rafter length.
- Bird's-Mouth
- A notch cut into a rafter where it sits on the top of the wall, letting the rafter seat flat and securely.
- Grade
- The pitch expressed as a percentage — rise divided by run, times 100. A 6/12 pitch is a 50% grade.
- Gable Roof
- A simple roof with two slopes meeting at a central ridge, forming a triangle at each end.
- Low-Slope Roof
- A roof with a pitch below about 3/12, requiring membrane or built-up roofing rather than standard shingles.
- Arctangent
- The inverse tangent function. Applied to the pitch ratio, it returns the roof angle in degrees.
Frequently Asked Questions
The most common questions about roof pitch, angle, and rafter length.
What is roof pitch?
Roof pitch is the steepness of a roof — how much it rises vertically for a given horizontal distance. In the US it is written as a ratio of rise to a 12-inch run, such as 6/12, meaning the roof rises 6 inches for every 12 inches travelled horizontally. A higher first number means a steeper roof.
How do I calculate roof pitch?
Measure the vertical rise over a fixed horizontal run, then express it as rise over run. Hold a level out from the roof, mark a 12-inch run, and measure straight down from the 12-inch mark to the roof surface — that drop is the rise. A 6-inch drop over a 12-inch run is a 6/12 pitch.
What is the most common roof pitch?
Most residential roofs fall between 4/12 and 9/12. Pitches in the 6/12 to 8/12 range are the most common for houses — steep enough to shed water and snow well, but still walkable for installation and repair. Anything below 3/12 is considered low-slope, and above 9/12 is considered steep.
How do I convert roof pitch to degrees?
Take the arctangent of the rise divided by the run. For a 6/12 pitch, that is the arctangent of 6 ÷ 12, or 0.5, which works out to about 26.57 degrees. A 12/12 pitch — equal rise and run — is exactly 45 degrees. This calculator does the conversion automatically.
What is the slope factor of a roof?
The slope factor, also called the rafter or roof multiplier, converts a horizontal distance into the longer distance measured along the slope. It equals the square root of one plus the pitch ratio squared. A 6/12 roof has a slope factor of about 1.118, so the sloped surface is 11.8% longer than the flat footprint beneath it.
How do I calculate rafter length from roof pitch?
Multiply the horizontal run of the rafter by the slope factor. For a gable roof, the run is half the building span. A 24-foot-wide building has a 12-foot run per rafter; at a 6/12 pitch with a slope factor of 1.118, each rafter is 12 × 1.118 ≈ 13.4 feet, before any eave overhang is added.
What is the difference between roof pitch and roof slope?
The terms are often used interchangeably, but strictly, pitch is the ratio of rise to the full span while slope is the ratio of rise to run. In everyday building use, both describe how steep a roof is, and pitch is usually given as rise over a 12-inch run. This calculator uses the common rise-over-run convention.
What roof pitch is 30 degrees?
A 30-degree roof angle is a pitch of about 6.93/12 — close to a 7/12 roof. Roof pitch in degrees does not land on neat whole numbers: a 7/12 pitch is about 30.26 degrees, and a 6/12 pitch is about 26.57 degrees, so a true 30-degree roof sits just between the two.
What is considered a low-slope or flat roof?
A roof with a pitch below 3/12 is generally classed as low-slope, and pitches at or near 2/12 and below are treated as flat for roofing purposes. Low-slope roofs cannot use standard shingles and need membrane or built-up roofing systems designed to handle standing water and shallow drainage.
How does roof pitch affect the cost of a roof?
A steeper roof costs more. It has more surface area than the footprint it covers — the slope factor shows how much more — so it needs more material. Steep roofs are also harder and slower to work on safely, which raises labor costs. A 12/12 roof has roughly 41% more surface than the flat area beneath it.
What is the percentage grade of a roof?
The percentage grade is the pitch ratio written as a percent: rise divided by run, multiplied by 100. A 6/12 pitch is a 50% grade, since 6 ÷ 12 is 0.5. A 12/12 pitch is a 100% grade. Percentage grade is used more in some regions and trades than the X/12 ratio, but it describes the same steepness.
Can I measure roof pitch from the attic?
Yes. Inside the attic you can measure the pitch off a rafter using a level and a tape. Hold a level against the underside of a rafter, mark 12 inches along it, and measure straight down to the rafter at that point. This is often safer and easier than measuring on the roof surface.
More Tools You'll Love
Roof pitch is one piece of a building project. These companion calculators handle the related measurements.
Find Your Roof Pitch
in 30 Seconds
Enter rise and run, a pitch, or an angle — get the pitch ratio, angle in degrees, slope factor, percentage grade, and rafter length. All free.
Calculate Pitch — Free Takes 30 seconds · No account needed · 3 input methods