Roof Pitch to Degrees: Converting Both Ways, With the Full Chart

Roofing math · Pitch and degrees · Updated 2026-09-27

A 6/12 roof is 26.57 degrees, and a 26.57 degree roof is 6/12. The bridge between them is the arctangent, not a scale factor, because x/12 is a ratio of two lengths and degrees are an angle. Those are different kinds of number, and they do not move in step. Doubling the pitch does not double the angle, and that one fact is behind almost every bad conversion written on an estimate.

This guide gives the formula in both directions, a worked example each way, a full table from 1/12 to 24/12 in degrees and percent grade, and the handling for a real measured pitch that comes back at 5.7/12 instead of something tidy. It also sorts out pitch, slope and grade, which are three names for the same steepness in three different units, and the specific wrong answers that show up again and again.

Pitch is a ratio, degrees are an angle

x/12 is a ratio. It says the roof rises x inches for every 12 in you travel horizontally. A 6/12 roof rises 6 in over 12 in of run, so the ratio is 0.5. Degrees are an angle, measured between the roof plane and level, from 0 degrees for a dead flat deck to 90 degrees for a wall. The two describe the same steepness, but they are not the same species of number, and what connects them is a trigonometric function rather than a multiplier.

That function is the tangent. The tangent of the roof angle is exactly rise over run, so the angle is the arctangent of x/12 and the pitch is twelve times the tangent of the angle. Because the tangent curve bends, equal steps in pitch are not equal steps in angle. Going from 1/12 to 2/12 adds 4.70 degrees; going from 11/12 to 12/12 adds only 2.49. The steeper the roof, the less each extra inch of rise buys in angle.

None of it is proportional. 6/12 is 26.57 degrees, but doubling the pitch to 12/12 does not give 53.13 degrees; it gives 45.00 degrees, because a 12 in rise over 12 in of run is a square corner cut in half. Halving 6/12 to 3/12 does not give 13.28 degrees either; it gives 14.04. Multiply or divide an angle to move around a pitch chart and you will be wrong, in a direction that depends on where you started.

The two formulas, and the check that closes them

• Pitch to degrees: angle = arctan(x / 12). Divide the rise by 12, then take the inverse tangent.
• Degrees to pitch: x = 12 tan(angle), twelve times the tangent of the angle. The answer is the rise in inches per 12 in of run.
• Either one to percent grade: grade = 100 tan(angle), the same as 100 times rise over run. From x/12 it is 100 times x divided by 12, with no trigonometry at all.
• The round trip check: tan(26.57 degrees) = 0.5001, and 0.5001 times 12 = 6.00. Convert forward, convert back, and see whether you land where you started. If it does not close, one step used the wrong function or angle mode.

Worked example: 7/12 into degrees

1. Write the pitch as a plain decimal: 7/12 means 7 in of rise for every 12 in of run. As a decimal that is 7 divided by 12, or 0.5833.
2. Take the arctangent: arctan(7 / 12) = 30.2564, so 7/12 is 30.26 degrees. On a handheld this is the inverse tangent key, printed as tan with a small minus one above it. Set the calculator to degrees, not radians, or you get 0.5281 with no warning.
3. Pick up percent grade: 100 times 7 divided by 12 = 58.33 percent. Percent grade is the easy one of the three, because it is the same ratio rescaled and needs no trigonometry.
4. Check it backwards: tan(30.26 degrees) = 0.5834, and 0.5834 times 12 = 7.00. The round trip closes to two decimals, so the conversion is sound.

Worked example: 32 degrees into x/12

1. Start from the measured angle: A digital level on a rafter, an inclinometer against a rake board or a phone gauge on the deck reads 32.0 degrees.
2. Take the tangent: tan(32 degrees) = 0.6249. Degrees mode again. A spreadsheet needs the angle in radians first, because its trig functions take radians whatever the cell is formatted as.
3. Multiply by twelve: 0.6249 times 12 = 7.4988, so the pitch is 7.50/12, written on a cut list as 7-1/2 over 12. The grade is 62.49 percent.
4. Decide what to do with the decimal: 7.50/12 falls exactly between two standard pitches, which makes rounding a real decision rather than a formality. Keep the decimal for anything you cut.

Roof pitch to degrees and percent grade: the full table

Every degree figure below is arctan(x / 12) rounded to two decimals, and every percent grade is 100 times x divided by 12 on the same row. The list skips odd steep pitches like 17/12 and 19/12 because they are almost never specified, though the formula handles them identically. If a number you have been handed disagrees with this table, doubt the number you have been handed.

Percent grade, the third unit

Percent grade is the same ratio as pitch, expressed per hundred instead of per twelve. A 6/12 roof rises 6 in per 12 in, which is 50 in per 100 in, so it is a 50 percent grade. Move between the two by rescaling and nothing else: grade is 100 times x divided by 12, and x is 12 times grade divided by 100. Because there is no trigonometry in that leg, pitch and percent grade really are proportional to each other, even though neither is proportional to degrees. Halving a 50 percent grade does give 25 percent, which is 3/12.

Percent grade is the working unit in earthworks, drainage and road work, where surfaces are nearly flat and a percentage is easier to say than a fraction of an inch. It also turns up on installation literature written in metric countries, where a minimum slope may be given as a percentage rather than as x/12, and in gutter fall, usually quoted in percent or inches per foot. The thing to hold on to is that 100 percent grade is 45 degrees, not vertical. Grades pass 100 without trouble: a 24/12 roof is a 200 percent grade at 63.43 degrees.

Degrees to pitch, straight off a chart

Going the other direction, angle to x/12, is what you do after reading a digital level or scaling an angle off a drawing. The last column is there because material is ordered and rafters are cut in whole pitches far more often than in decimals. Note how unevenly whole pitches sit against round degree values: 45 degrees is exactly 12/12, and 30 and 40 degrees land within a tenth of an inch of 7/12 and 10/12, while 25 and 35 degrees sit about four tenths of an inch of rise away from any whole pitch.

All three units from one reading. Roof Pitch Gauge & Factor reads out degrees, x/12 pitch and percent grade together from a single measurement, so there is no conversion step left to get wrong. Lay the phone flat on the deck, run its long edge along a rafter or a rake board, or sight a gable from the driveway, and a stillness gate locks the median of a steady window instead of whatever your thumb happens to catch. It is coming soon for iPhone. Learn more about Roof Pitch Gauge & Factor.

Converting a decimal pitch, not a tidy one

Real roofs do not land on whole numbers. Decks settle, rafters crown, an old house has moved, and a careful reading comes back at 5.7/12 rather than 6/12. The formula does not mind. arctan(5.7 / 12) = 25.41 degrees, and the grade is 100 times 5.7 divided by 12 = 47.50 percent. Put the decimal straight into the arctangent. Forcing it to a whole pitch first is how the error gets in, because you then convert a number you chose rather than the one you measured.

The same holds in reverse: a measured 25.41 degrees gives 12 tan(25.41) = 5.70/12, and the trip closes. Half pitches convert no differently, and the very low ones matter most, because a quarter inch of rise can separate a membrane minimum from a panel minimum. Which minimum applies is set by the code adopted in your jurisdiction and by the manufacturer's own installation instructions, either of which can be stricter than the published minimums by covering. The roof pitch chart carries the halves and quarters alongside the whole numbers, and how to measure roof pitch covers getting a reading worth two decimals in the first place.

What rounding to the nearest standard pitch costs

Rounding a measured pitch to the nearest standard whole number is normal practice and usually right: material is sold, flashed and installed by standard pitch, and code minimums are written against standard pitches. It is still worth knowing what you give up. Calling that 5.7/12 a 6/12 moves the angle from 25.41 to 26.57 degrees and the slope factor from 1.1071 to 1.1180, about 1 percent more roof. On a 2,400 sq ft footprint that is roughly 26 sq ft, about a quarter of a roofing square. On a 14 ft run the common rafter grows about 1-7/8 in.

So rounding is cheap on area and can be dear on a cut. Round for ordering and for code; keep the measured decimal for anything you cut to length or lay out on a rafter square. Half a degree is the usual snapping window, worth about 0.13 in of rise at 6/12 and about 0.21 in at 12/12. Rounding is only defensible when the reading deserved it: a figure sighted from the ground is worth a couple of degrees at best, and rounding it to a hard number hides the uncertainty rather than resolving it.

Pitch, slope and grade: three names for one steepness

• Pitch, in the North American roofing trade, is rise in inches over 12 in of run, written 6/12. You will also see 6:12; same notation, same number.
• Slope is rise over run as well, and in current trade use the two words are interchangeable. Code language prefers slope; roofers and shingle wrappers say pitch.
• Strict traditional usage did separate them: pitch meant rise over the full span, slope rise over the run. On a 24 ft span a 6/12 slope rises 6 ft, so the old pitch was 6 over 24, a quarter pitch. You may still hear quarter pitch or third pitch, but no modern order form means it.
• Grade or gradient is the same ratio as a percentage, 100 times rise over run. It is standard in earthworks, drainage and road work rather than in roofing.
• Degrees is the angle itself, 0 to 90. It is what levels, inclinometers and phone motion sensors physically measure; x/12 and percent grade are derived from it afterward.
• Run is not span. Run is the horizontal distance from wall to ridge, half the span on a simple symmetrical gable. Substituting span for run is the most expensive arithmetic mistake in the subject, and the rafter length calculator guide works it through.

The common wrong answers

• 45 degrees is 12/12, not 45/12. A 45 degree roof rises exactly as far as it runs, so the pitch is 12 in over 12 in. An actual 45/12, meaning 45 in of rise per 12 in of run, is 75.07 degrees, nearly a wall.
• A 12/12 roof is not a 100 percent pitch. It is a 100 percent grade, the percentage unit, and it is 45 degrees. Nothing in x/12 is written as a percentage, and 100 percent is no ceiling: 24/12 is a 200 percent grade.
• Do not copy a degree reading into the pitch box. A level set to degrees on a 30 degree roof is telling you 30 degrees, which is 6.93/12, effectively 7/12. Writing 30/12 turns an ordinary roof into a 68 degree one, and every derived figure with it.
• Do not scale angles. The reasoning that 6/12 is 26.57, so 12/12 must be about 53, is the most common error in the subject; the answer is 45.00. Ratios double, angles do not double with them.
• Do not interpolate across a gap. Between adjacent whole pitches, interpolation is accurate to hundredths of a degree. Between 12/12 and 24/12 it is 2 degrees out.
• Check degrees against radians. A calculator left in radians converts 7/12 to 0.5281 and reports no error. Spreadsheet trig takes radians whatever the cell formatting, so an arctangent needs a degrees conversion around it and a tangent a radians conversion inside it.

The next number an estimate needs is the multiplier that turns flat footprint into actual roof surface. That is the roof slope factor, one divided by the cosine of the angle, and it is what a job is priced from. For a full reference set to read on a phone at the eave, use the roof pitch chart; Roof Pitch Gauge shows degrees, pitch and grade side by side as you measure.

Frequently asked questions

What is 6/12 pitch in degrees?

6/12 pitch is 26.57 degrees. It comes from arctan(6 / 12), the inverse tangent of 0.5, which is 26.565 degrees before rounding. The same roof is a 50 percent grade, because it rises 6 in for every 12 in of run.

How do I convert roof pitch to degrees?

Divide the rise by 12 and take the inverse tangent of the result: angle = arctan(x / 12). For 8/12 that is arctan(0.6667) = 33.69 degrees. Make sure the calculator is in degrees mode rather than radians, because a radians answer looks like a plausible small number and carries no warning.

What roof pitch is 45 degrees?

45 degrees is 12/12, a rise of 12 in for every 12 in of run. It is also a 100 percent grade, since rise and run are equal. A 45/12 pitch is a different and much steeper roof at 75.07 degrees, so the two are easy to confuse and costly to swap.

What is 30 degrees in roof pitch?

30 degrees works out to 6.93/12, which for ordering and cutting is treated as 7/12. A true 7/12 is 30.26 degrees, so the gap is about a quarter of a degree and well inside a normal snapping window. The grade at 30 degrees is 57.74 percent.

Is a 12/12 roof a 100 percent pitch?

No. A 12/12 roof is a 100 percent grade, which is the percentage unit for the same steepness, and it measures 45 degrees. Pitch in the x/12 system is never written as a percentage, and 100 percent is not the maximum: a 24/12 roof is a 200 percent grade at 63.43 degrees.

How do I convert a decimal pitch like 5.7/12 to degrees?

Exactly the same way as a whole pitch: arctan(5.7 / 12) = 25.41 degrees, and the grade is 47.50 percent. Do not round the pitch to 6/12 before converting, because you would then be converting a number you chose rather than the one you measured. Round afterward, if at all, and keep the decimal for anything you are cutting.

Why does my pitch chart disagree with my calculator?

Usually one of three things. The chart rounded to whole or one-decimal degrees while the calculator did not, the value was interpolated across a gap in the chart rather than read from a row, or the calculator was left in radians. Work the round trip to settle it: convert your angle back to x/12 and see whether you land on the pitch you started from.

Keep reading

• Roof Pitch Chart: Degrees, Percent Grade, Slope Factor and Hip/Valley Factor
• How to Measure Roof Pitch: Every Method, and How Each One Goes Wrong
• Roof Slope Factor: What It Is, the Full Table, and How Estimators Use It