📚 What's in This Guide
A roof pitch calculator turns two measurements, the rise and the run, into everything you need to describe how steep a roof is: the pitch in x:12 form, the angle in degrees, the percent slope, the pitch multiplier, and the rafter length. It is built for homeowners comparing roofing quotes, builders framing a gable, shed or lean-to roof, and anyone who has a pitch in one format and needs it in another. Pitch matters because it decides which roofing materials are allowed, how much roof area you must cover, how long each rafter has to be, and how safely anyone can work on the roof. Enter your measurements in the calculator above, or start from a known pitch or angle if that is all you have.
Many roof slope calculators stop at converting rise and run. This one also solves for a missing rise or run, handles feet, inches, feet and inches, millimeters and meters, deducts the ridge board, adds the eave overhang, and converts the pitch multiplier into a sloped roof area, so one pass gives you both the geometry and the quantities.
Roof pitch = rise ÷ run × 12. A roof that rises 6 units for every 12 units of run has a 6:12 pitch, which is 26.57°, a 50% slope, and a pitch multiplier of 1.118. To convert any x:12 pitch to degrees, take arctan(x ÷ 12).
1. How the Roof Pitch Calculator Works
You choose what you already know. With Rise + Run, the calculator divides the rise by the run to get the slope, then converts that slope into the three ways pitch is written. With Pitch + Run or Pitch + Rise, you enter a pitch as x:12, degrees or percent, plus one dimension, and it solves for the other one. With Pitch only, it converts one pitch format into the others, which is how you turn a contractor's 7:12 into degrees or a 30° angle into a ratio.
Behind every mode is one number, the slope, which is rise divided by run. The pitch, the angle and the percentage are the same slope written three ways. The calculator then adds the pitch multiplier, which scales a flat measurement into a sloped one, and uses it to find the rafter line length. If you enter an overhang or a ridge board thickness, it adjusts the rafter length, and if you enter a plan area, it converts it to sloped roof area.
The calculator treats the roof as a simple right triangle: a straight common rafter rising at a constant pitch. For a gable roof it assumes both sides have the same pitch, and for area it assumes every roof plane has the same pitch. It does not size rafters, check spans or loads, or lay out a birdsmouth. Lengths are shown to the nearest 1/16 inch in feet-and-inches mode. Real roofs have framing details, so treat the numbers as planning figures and cut one test rafter before you cut the rest.
2. How to Use the Roof Pitch Calculator
- Choose what you know: rise and run, pitch and run, pitch and rise, or a pitch only.
- Pick your units: inches, feet, feet and inches, millimeters or meters. Your entries convert automatically if you change units later.
- Enter the rise and run, or enter the pitch as x:12, degrees or percent. The quick pitch buttons fill in common pitches from 2:12 to 12:12.
- Optionally add the eave overhang and ridge board thickness to get a total rafter length and the minimum standard lumber length it fits in.
- Optionally enter the plan area under the roof and a waste percentage to get sloped roof area and roofing squares.
- Read the pitch, angle, percent slope, multiplier, rafter length and the step-by-step math, then copy, share or download the result.
The pitch can be up to 130:12, 85° or 1,000%, and lengths can be up to 1,000 feet. If a value is outside the allowed range, the calculator tells you and uses the nearest allowed value instead of changing it silently. You do not need an app: the calculator runs in any phone or computer browser.
3. Roof Pitch Formulas
Here is how to calculate roof pitch by hand, including the roof pitch in degrees:
Pitch (x:12) = Rise ÷ Run × 12
Angle (°) = arctan(Rise ÷ Run)
Percent slope = Rise ÷ Run × 100
Rise and run must be in the same unit. The ratio itself has no unit, which is why 6:12 describes the same roof whether you measure in inches, feet or millimeters.
To go the other way, from an angle or a percentage back to a pitch, reverse the steps:
Pitch (x:12) = 12 × tan(angle)
Pitch (x:12) = Percent slope × 0.12
The rafter length comes from the Pythagorean theorem, and the pitch multiplier is the same calculation for a run of 1:
Rafter line length = √(Rise² + Run²) = Run × Multiplier
Pitch multiplier = √(1 + (Rise ÷ Run)²)
Hip / valley multiplier = √(2 + (Rise ÷ Run)²)
Total rafter = (Run + Overhang − Ridge thickness ÷ 2) × Multiplier
The run in these formulas is the horizontal distance, and the overhang is also measured horizontally. Multiplying by the pitch multiplier converts each horizontal distance into a length along the slope.
4. Worked Example
A gable roof sits on a building 28 feet wide. Each rafter runs from the outside of the wall to the ridge, so the run is half the width: 14 feet, or 168 inches. The ridge sits 5 feet 3 inches (63 inches) above the top of the wall plate. The rafters overhang the wall by 1 foot, and the rafters meet a 1½ inch ridge board.
| Step | Calculation | Result |
|---|---|---|
| Slope | 63 ÷ 168 | 0.375 |
| Pitch | 0.375 × 12 | 4.5:12 |
| Angle | arctan(0.375) | 20.56° |
| Percent slope | 0.375 × 100 | 37.5% |
| Multiplier | √(1 + 0.375²) = √1.140625 | 1.0680 |
| Rafter line length | 168 × 1.0680 | 179.42 in = 14'-11 7/16" |
| Overhang tail | 12 × 1.0680 | 12.82 in = 1'-0 13/16" |
| Ridge deduction | (1.5 ÷ 2) × 1.0680 | 0.80 in = 13/16" |
| Total rafter length | 179.42 + 12.82 − 0.80 | 191.44 in = 15'-11 7/16" |
The pitch is 4.5:12, in the conventional range for houses. The total rafter length of just under 16 feet means 16 foot boards fit with almost no spare length, so a framer might buy 18 footers if the stock allows and trim to fit.
Converting a pitch works the same way. For a 30° roof, 12 × tan(30°) = 6.93, so a 30° angle is a 6.93:12 pitch, or a 57.7% slope. For a 4/12 roof, arctan(4 ÷ 12) = 18.43°.
5. How to Measure Roof Pitch
The safest place to measure is usually the attic, not the roof. Hold a 12 inch level horizontally against the underside of a rafter, with one end touching the rafter. Measure straight down from the 12 inch mark on the level to the rafter. That vertical distance in inches is the rise per 12 inches of run, so 6 inches down means a 6:12 pitch. A large carpenter's square, a speed square or a digital angle finder gives the same answer.
If you have the plans or can measure the building, use dimensions instead. Measure the rise from the top of the wall plate to the ridge, and the run from the outside of the wall to the point under the ridge, then enter both in the calculator. For a standard symmetrical gable, the run is half the building width.
You can also measure an angle directly with a phone inclinometer app or a digital level, then enter it in degrees. Check the app against a known level surface first, since phone sensors can be a degree or two off. Avoid climbing onto steep, wet, icy or fragile roofs just to measure them. Measuring from the eave with a ladder, from the attic, or from drawings is usually enough.
6. Understanding Your Result
The result is a description of steepness, and the same pitch can be written three ways. Contractors in North America usually say x:12, such as 6:12. Many tools and plans outside North America use degrees, and drainage and low-slope roofing often use a percentage. The calculator shows all three so you can match whatever your plans, supplier or installer uses.
| Pitch range | Common name | What it usually means |
|---|---|---|
| Under 2:12 (below 9.5°) | Flat or very low slope | Needs a low-slope membrane or built-up system. Asphalt shingles are not permitted. |
| 2:12 to under 4:12 (9.5° to 18.4°) | Low slope | Shingles allowed only with double underlayment. Metal and membrane roofs are common. |
| 4:12 to 9:12 (18.4° to 36.9°) | Conventional | The usual range for houses. Works with most roofing materials. |
| Over 9:12 (above 36.9°) | Steep | Sheds water and snow quickly but is harder and costlier to build and roof. |
The minimum slope for a roofing material comes from building codes and manufacturers. For example, a county building department summary of IRC section R905 states that asphalt shingles may be used only on slopes of 2:12 or greater, and that slopes from 2:12 up to 4:12 need double underlayment. Local codes and individual shingle makers can be stricter, so confirm both before you buy.
Pitch also affects safety. As a rule of thumb, a dry roof at 6:12 or less is generally walkable, 7:12 to 9:12 calls for extra caution and often roof jacks or a harness, and anything steeper is not safely walkable without fall protection. Fall-protection rules depend on working height and local regulations as well as pitch, so use the rule of thumb as a warning, not a permission.
The pitch is exact for the numbers you enter, but your measurements are not. A quarter inch of error in a 12 inch level reading changes the pitch by about a quarter of a unit, so check your measurement twice before you round the pitch.
7. Roof Pitch Chart and Roof Slope Chart
The chart below lists every whole pitch from 1:12 to 12:12 with its angle, percent slope and multiplier. The typical roof pitch for houses in the United States falls roughly between 4:12 and 9:12, which is about 18° to 37°. Common pitches such as 4/12, 6/12 and 12/12 are 18.43°, 26.57° and 45°.
| Pitch (x:12) | Angle | Percent slope | Multiplier |
|---|---|---|---|
| 1:12 | 4.76° | 8.3% | 1.0035 |
| 2:12 | 9.46° | 16.7% | 1.0138 |
| 3:12 | 14.04° | 25.0% | 1.0308 |
| 4:12 | 18.43° | 33.3% | 1.0541 |
| 5:12 | 22.62° | 41.7% | 1.0833 |
| 6:12 | 26.57° | 50.0% | 1.1180 |
| 7:12 | 30.26° | 58.3% | 1.1577 |
| 8:12 | 33.69° | 66.7% | 1.2019 |
| 9:12 | 36.87° | 75.0% | 1.2500 |
| 10:12 | 39.81° | 83.3% | 1.3017 |
| 11:12 | 42.51° | 91.7% | 1.3566 |
| 12:12 | 45.00° | 100.0% | 1.4142 |
If you know the angle instead, use this degrees-to-pitch chart for common angles:
| Angle | Pitch (x:12) | Percent slope | Multiplier |
|---|---|---|---|
| 5° | 1.05:12 | 8.7% | 1.0038 |
| 10° | 2.12:12 | 17.6% | 1.0154 |
| 15° | 3.22:12 | 26.8% | 1.0353 |
| 20° | 4.37:12 | 36.4% | 1.0642 |
| 22.5° | 4.97:12 | 41.4% | 1.0824 |
| 25° | 5.60:12 | 46.6% | 1.1034 |
| 30° | 6.93:12 | 57.7% | 1.1547 |
| 35° | 8.40:12 | 70.0% | 1.2208 |
| 40° | 10.07:12 | 83.9% | 1.3054 |
| 45° | 12.00:12 | 100.0% | 1.4142 |
8. Roof Pitch Angles, Cuts, Hips and Valleys
Figuring roof angles matters when your tools are calibrated in degrees. On a miter saw, set the roof angle for the plumb cut, which is the vertical cut at the top of a rafter, and set 90° minus the roof angle for the level seat cut. For a 6:12 roof, that is 26.57° for the plumb cut and 63.43° for the seat cut. The calculator shows both when it has a pitch. On a framing square, put the rise number on the tongue and 12 on the blade, and the square gives you the same lines. On a speed square, the common rafter scale reads the pitch directly.
Hip and valley rafters run diagonally across the corner where two roof planes meet. When both planes have the same pitch and meet at a right angle, the diagonal run is the common run times √2. That makes the hip or valley less steep than the common rafter and longer: its length is the common run times the hip/valley multiplier, √(2 + slope²), and its own angle is arctan(slope ÷ √2). At 6:12 the multiplier is exactly 1.5, so a hip over a 12 foot common run is 18 feet long, and its angle is 19.47°, shallower than the 26.57° common rafter.
9. Roof Pitch Multiplier and Roof Area
The roof pitch multiplier, sometimes called the slope factor or pitch factor, is the number that turns a flat measurement into a sloped one. It is √(1 + slope²), and it grows as the roof gets steeper, from 1.0035 at 1:12 to 1.4142 at 12:12. Multiply the run by it to get the rafter length. Multiply the plan area under the roof by it to get the true roof surface area.
For example, a roof covering 1,600 square feet in plan at 6:12 has a multiplier of 1.1180, so the roof surface is 1,600 × 1.1180 = 1,788.9 square feet. That is 17.9 roofing squares, since one square covers 100 square feet, and about 19.7 squares with a 10% waste allowance. Enter the plan area in the calculator to get these numbers for your own roof. If you only know the building's dimensions, our Square Footage Calculator can find the footprint area, and you should include the eave overhangs in it.
This works when every roof plane has the same pitch, including hips and valleys. If a roof mixes pitches, such as a steep main roof with a low porch roof, calculate each section separately and add them. Roof area is also only the start of a materials estimate, because valleys, ridges, starter courses and the way your roofer cuts shingles all change what you buy.
10. Shed, Lean-To and Flat Roofs
A shed roof, also called a lean-to or single-slope roof, has one plane that slopes from a high wall to a low wall. The same triangle applies, but the run is the full horizontal width from the low wall to the high wall, not half of it. The rise is the height difference between the two wall tops. If you only know the pitch you want, use Pitch + Run to find the height the high wall needs.
Many shed roofs use low slopes, and the minimum slope you can use depends on the roofing. Metal panels, membranes and shingles each have their own manufacturer limits, so check the product data before you settle on a pitch. Flat roofs are rarely perfectly flat, because water has to drain. A fall of 1/4 inch per foot, written 0.25:12, is a slope of about 1.19° or 2.1%, and you can enter decimals like that in the pitch field.
11. Units and Terminology
- Rise: the vertical height of the roof, measured from the top of the wall plate to the top of the rafter line.
- Run: the horizontal distance from the outside of the wall to a point directly under the ridge. For a symmetrical gable it is half the span.
- Span: the total horizontal distance a roof covers between its two supporting walls.
- Pitch and slope: in everyday North American use, both mean rise per 12 of run, like 6:12. In some older carpentry texts, pitch means rise divided by the full span, so a 6:12 roof is a 1/4 pitch. This calculator uses the everyday meaning.
- Angle and gradient: the same steepness in degrees or as a percentage. Roof gradient usually means the percentage or ratio form.
- Rafter line length: the length along the slope from the bearing point to the ridge, with no overhang. Plumb cuts and the birdsmouth are marked from this line.
- Overhang: the part of the rafter that extends past the wall, measured horizontally in this calculator.
- Plumb cut and seat cut: the vertical cut at the top of a rafter and the level cut where it rests on the wall.
Pitch is unitless, so metric and imperial users get the same x:12, degrees and percent values. Only lengths change. One inch is exactly 25.4 millimeters and one foot is 304.8 millimeters, and the calculator converts for you when you switch units.
12. Practical Tips
- Measure rise and run from the same reference points on every rafter, and write them down before you enter them.
- Keep units consistent. Mixing feet for the run and inches for the rise gives a pitch that is wrong by a factor of 12.
- Use the attic level method when you can. It is safer than measuring on the roof and gives the pitch directly.
- Round the pitch last. Carry the exact slope through the calculation, then round the final rafter length up to a cuttable length.
- Account for the ridge board. If rafters meet at a ridge board instead of each other, the deduction shortens every rafter slightly.
- Add waste for roof area. Ten percent is a common starting point, and a roof with many hips, valleys or dormers may need more.
- Cut one test rafter and check its fit before you use it as a pattern for the rest.
13. Common Mistakes
- Using the span instead of the run: entering the full building width with the rise of one side halves the pitch. For a gable, use half the width.
- Mixing units: rise in inches and run in feet, or the other way around, gives a wildly wrong pitch.
- Confusing pitch with slope in degrees: a 6:12 roof is 26.57°, not 6°, and the x in x:12 is not an angle.
- Treating a 45° roof as 45:12: 45° is a 12:12 pitch, because 12 × tan(45°) = 12.
- Using the plan area as the roof area: the surface of a sloped roof is larger than its footprint by the pitch multiplier.
- Forgetting the overhang: the rafter has to reach past the wall, so the tail adds length that the rafter line length alone does not include.
- Trusting a calculator over the plans: structural details, spans and uplift connections come from your plans and local code.
14. Related Calculations and Use Cases
This roof pitch calculator is useful for comparing roofing bids that quote pitch in different formats, checking a design before you order lumber, framing a garage, shed, porch or addition, working out the ridge height a given pitch produces, and giving a solar installer or insurer the angle in degrees. Pitch is often the first number in a longer roofing estimate, and once you have the pitch and sloped area you can move on to shingles, underlayment, flashing and ventilation. Because the calculator shows each step of the math, you can also use it to check a number someone else has given you.
15. Frequently Asked Questions
Divide the rise by the run and multiply by 12 to get the pitch in x:12 form. If a roof rises 6 feet over a run of 12 feet, 6 ÷ 12 × 12 gives a 6:12 pitch. For the angle, take the arctangent of rise ÷ run: arctan(0.5) is 26.57°. For percent slope, multiply rise ÷ run by 100, which gives 50%. Rise and run must be in the same unit, and the calculator above does all three conversions at once.
A 4/12 roof pitch is 18.43°, a 6/12 pitch is 26.57°, and a 12/12 pitch is exactly 45°. The formula is arctan(x ÷ 12), where x is the first number of the ratio. As percent slopes they are 33.3%, 50% and 100%. The pitch chart in this guide lists every whole pitch from 1/12 to 12/12.
Most houses in the United States have a pitch between about 4:12 and 9:12, which is roughly 18° to 37°. Low-slope roofs below 4:12 are common on ranch-style and modern homes, while steeper roofs are used on traditional, Victorian and snowy-climate designs. The right pitch for your roof depends on the design, climate, roofing material and local code, so check your plans.
The roof pitch multiplier, also called the slope factor, converts a flat measurement into a sloped one. It equals the square root of 1 plus the slope squared, where slope is rise ÷ run. Multiply the run by it to get the rafter length, or multiply the plan area under the roof by it to get the sloped roof area. A 6:12 roof has a multiplier of 1.1180, so a roof that covers 1,600 square feet in plan has about 1,789 square feet of roof surface.
The International Residential Code allows asphalt shingles only on roof slopes of 2:12 or greater, and it calls for double underlayment on slopes from 2:12 up to 4:12. Individual shingle manufacturers can set stricter limits, and local codes can differ, so check the shingle wrapper and your local building department before you choose a roofing material for a low-slope roof.
Conclusion
A roof pitch calculator takes the guesswork out of describing and framing a sloped roof. From a rise and a run, or from any known pitch, it gives you the x:12 pitch, the angle, the percent slope, the pitch multiplier and the rafter length in one pass. Accurate measurements matter most, because a small error in rise or run carries through every result. Use the roof pitch calculator above to plan your rafters and roof area, then confirm the numbers with your plans, your roofing manufacturer and your local building code before you cut or order anything.
This calculator is for planning purposes only. Rafter size, spans, roofing material limits and underlayment must follow your plans, the manufacturer's instructions and local building code. Confirm all quantities with your supplier before ordering.