How to Calculate Roof Pitch in Degrees (Step by Step)

If you already know your pitch as a ratio and just want the number, drop it into the Roof Pitch Calculator and read the degrees straight off. But understanding the conversion is worth a few minutes, because it lets you check the calculator, work on paper when you have no signal on a roof, and reason about why a 12/12 pitch is exactly 45 degrees while a 6/12 is only 26.57.

Why you would convert pitch to degrees

Roof pitch is normally written as rise over a 12 inch run, such as 6/12, because that ratio maps directly onto the framing square and the way carpenters lay out rafters. It is an excellent working language, but it is not universal. Three groups routinely need the angle instead. Solar designers model panel tilt, sun path, and shading in degrees, so a roof described as 6/12 has to become 26.57 degrees before it enters their software. Anyone cutting rafters, fascia, or trim with a miter saw or bevel gauge sets those tools in degrees. And plans drawn outside the United States often give slope in degrees or as a percentage rather than in twelfths.

In each case you are not changing the roof, only translating its steepness into a different unit. The pitch, the angle, and the slope percentage are three descriptions of one physical thing, and being fluent in all three keeps you from ordering, cutting, or specifying the wrong slope. If you are still nailing down the pitch itself, start with how to calculate roof pitch, then come back here to turn that ratio into an angle.

It also pays to understand the conversion rather than treating the calculator as a black box, because a degree value that is off by even a couple of degrees can misalign a solar array or produce a rafter cut that does not seat cleanly. When you know where the number comes from, you can sanity-check it and catch an input error before it reaches the saw.

The arctangent formula

The whole conversion rests on one relationship from right-triangle trigonometry. Picture the roof as a right triangle: the run is the horizontal leg, the rise is the vertical leg, and the roof surface is the sloping hypotenuse. The tangent of the roof angle equals the opposite side over the adjacent side, which is the rise over the run. To get the angle from the rise and run, you reverse the tangent using its inverse, the arctangent.

That is the entire method. Every value in a pitch-to-degrees chart, and every angle the calculator reports, is this one formula applied to a different rise. Because the run is fixed at 12, you are always taking the arctangent of your pitch number divided by 12, which is what makes the conversion so quick once your calculator is in degree mode.

One setting trips people up: scientific calculators can work in degrees or radians, and the arctangent will return radians if the calculator is in radian mode, giving a nonsense-looking small number. Make sure the mode is set to degrees (often shown as DEG on the display) before you start, or convert radians to degrees by multiplying by 180 and dividing by pi.

Calculating pitch in degrees step by step

Here is the process from a measured pitch to a finished angle, laid out so you can follow it with any scientific calculator or the calculator app on a phone.

That is all there is to it. The same five steps convert any pitch, from a shallow 2/12 (9.46 degrees) to a vertical-feeling 18/12 (56.31 degrees). The only thing that changes is the rise you divide by 12. Practise on a pitch you already know the answer to, such as 12/12 giving exactly 45 degrees, to confirm your calculator is set up correctly.

Worked examples

Numbers make the method stick. Here are four conversions worked from the ratio to the finished angle.

The 12/12 example is the one to memorise, because it exposes the logic. When the rise equals the run, the ratio is 1, and the arctangent of 1 is exactly 45 degrees, the angle at which a roof rises as fast as it runs. Every pitch below 12/12 is under 45 degrees, and every pitch above it is over 45. That single anchor point lets you sanity-check any conversion: if you calculate an 8/12 roof and get something above 45 degrees, you know an input went wrong, because 8/12 is less than 12/12 and must be under 45.

Pitch to degrees quick table

For the common pitches, here are the angles ready to use without touching a calculator. For the complete range from 1/12 to 24/12, see the full roof pitch angle chart.

Doing it without a scientific calculator

You will not always have a trig calculator to hand, especially standing on a roof. There are three practical fallbacks. The first and easiest is to memorise or carry the quick table above, since roofs are built to whole pitches and those twelve values cover almost everything you will meet. The second is to use the table to interpolate: a 4.5/12 pitch sits about halfway between 4/12 (18.43) and 5/12 (22.62), so roughly 20.5 degrees, which is close enough for estimating.

The third fallback is a small-angle approximation for shallow roofs. For pitches up to about 4/12, the angle in degrees is very close to the slope percentage times 0.57, or you can simply accept that low pitches cluster in the single digits and teens of degrees. None of these hand methods matches the precision of the arctangent, so for anything you will cut or specify, confirm the value later in the calculator. Use the mental methods to keep moving in the field, and let the calculator finalise the number.

Going from degrees back to a pitch

Sometimes you have the angle and need the x/12 pitch, for example when a plan specifies 25 degrees but you frame in twelfths. Reverse the process using the tangent instead of the arctangent.

Because roofs are framed to whole or half pitches, you round the result to the nearest one your structure is built around. A 25 degree roof lands between 5/12 and 6/12, and which one you choose usually depends on the rest of the design. This reverse conversion is exactly what the questions “what pitch is 30 degrees” and “what pitch is 45 degrees” are asking, and the angle chart lists the nearest pitch for every angle so you can look it up rather than calculate.

Degrees versus slope percentage

People often confuse the angle in degrees with the slope percentage, because both describe steepness, but they are computed differently and only agree at low slopes. Slope percentage is rise divided by run times 100, with no trigonometry involved, so a 6/12 pitch is a 50 percent slope. The angle for that same 6/12 pitch is 26.57 degrees, not 50 degrees.

The gap between the two widens as the roof steepens. A 12/12 pitch is a 100 percent slope but only 45 degrees, because at 45 degrees the rise finally equals the run. Percentage slope is common in drainage, road grading, and some European roofing specs, while degrees rule solar and toolwork. Keep them straight by remembering that percentage is a plain ratio and degrees come from the arctangent of that ratio. The calculator shows both at once so you never substitute one for the other by accident.

Where the degree value is actually used

Converting is only worthwhile because the angle unlocks specific tasks. In solar, the roof angle is a direct input to tilt and yield calculations, and it decides whether panels lie flat on the roof or need tilt frames, a topic explored in best roof pitch for solar panels. In framing, the plumb cut at the ridge equals the roof angle and the seat cut at the wall is its complement, so a rafter for an 8/12 roof is cut at 33.69 and 56.31 degrees respectively. The full framing workflow is in rafter length explained.

The angle also communicates steepness clearly to people outside the trade. Telling a homeowner their roof is 45 degrees lands harder than saying 12/12, and it immediately signals that the roof is steep and not walkable, which links to the steep roof pitch and walkable roof pitch guides. For international quotes, giving the angle lets a supplier in any country understand your roof without knowing the twelfths system at all.

Mistakes to avoid

The conversion is short, so almost every error comes from one of these.

Avoid those and your conversions will be reliable. The fastest cross-check is to compare your hand result against the calculator or the quick table above, which will immediately flag a radian-mode or span-versus-run slip.

The trigonometry behind it, in plain English

You do not need to love math to use the arctangent, but understanding what it does removes the mystery and helps you catch errors. A right triangle has three sides and, aside from the right angle itself, two other angles. The three basic trig functions (sine, cosine, and tangent) each connect one of those angles to a pair of sides. Tangent is the one that matters for roofs because it links the roof angle to the two sides you can actually measure: the vertical rise and the horizontal run. Tangent of the angle equals rise over run, full stop.

The catch is that tangent takes an angle and gives you a ratio, but you have the ratio and want the angle, so you need to run the function backwards. That reverse is the arctangent, and every scientific calculator has it built in. Feeding your rise-over-run ratio into the arctangent hands back the exact angle that produces that slope. There is nothing approximate about it; the relationship is fixed by the geometry of the triangle, which is why the same 6/12 pitch is 26.57 degrees on every roof in the world. Once this clicks, the pitch-to-degrees conversion stops feeling like a formula to memorise and becomes something you can reason about.

It also explains why the numbers behave the way they do. As the rise grows toward the run, the ratio climbs toward 1 and the angle climbs toward 45 degrees. Push the rise past the run and the angle passes 45 on its way toward 90, which would be a vertical wall. That is the mental model to carry: the arctangent simply reads off how steep a triangle with your rise and run has to be.

Common roof angles and what they feel like

Degrees become intuitive once you attach them to how a roof looks and behaves. Anything under about 10 degrees (roughly a 2/12 pitch) reads as nearly flat from the street and behaves like a low-slope roof, needing sealed membranes rather than shingles. From 14 to 18 degrees (3/12 to 4/12) the slope is visible but gentle, the modern low-profile look, and 4/12 is where standard shingles usually become acceptable. The 18 to 27 degree band (4/12 to 6/12) is the everyday residential range most people picture as a normal roof.

Climb past 27 degrees and the roof starts to dominate the building. From 27 to 34 degrees (6/12 to 8/12) you get the traditional, weather-shedding look of older and colder-climate homes, still workable but demanding care. Above 34 degrees (8/12 and up) the roof is steep, no longer comfortably walkable, and needs roof jacks or staging to work on, as the steep-roof working guide covers. At 45 degrees (12/12) the two slopes are as steep as they are wide, the signature of A-frames and dramatic architectural roofs. Knowing roughly where an angle sits on this feel-scale lets you gut-check a conversion: if you calculate 40 degrees for a roof that looks like an ordinary suburban house, something is off.

Roof angle and the sun: solar tilt basics

The reason solar people insist on degrees is that the sun works in angles. A panel produces the most energy when it faces the sun as squarely as possible over the year, and the ideal fixed tilt is roughly equal to the site latitude. Since your roof angle sets the tilt of any panel laid flat against it, the pitch-in-degrees conversion is the first step in deciding whether a roof suits solar as-is or needs tilt frames to lift the panels to a better angle.

As a rough guide, a roof angle within about 15 degrees of your latitude captures most of the available energy, which is why so much of the residential United States, sitting around 30 to 45 degrees latitude, pairs well with common 4/12 to 9/12 roofs (18 to 37 degrees). A very shallow roof may need panels tilted up to perform, and a very steep roof may over-tilt them. This is exactly the analysis in best roof pitch for solar panels, and it all begins with converting the roof pitch to degrees, then comparing that angle to your latitude.

Setting a saw to the roof angle

For anyone framing rafters, the degree value is what you dial into the saw. A rafter has two defining cuts. The plumb cut, where the rafter meets the ridge, stands vertical when the rafter is in place, so its angle measured off the square equals the roof angle itself. The seat cut, or bird’s mouth, where the rafter rests on the top of the wall, is the complement of the roof angle, meaning 90 degrees minus it. For an 8/12 roof at 33.69 degrees, the plumb cut is 33.69 degrees and the seat cut is 56.31 degrees.

Getting these angles exactly right matters because the error repeats on every rafter and compounds across the roof. A plumb cut that is a degree off leaves gaps at the ridge, and a seat cut that is off will not let the rafter sit flat on the plate. This is why framers convert the pitch to degrees precisely rather than rounding, and why the rafter length guide pairs the angle with the length and the bird’s mouth position. If you are using a speed square instead of a saw protractor, the speed square guide shows how the tool reads pitch directly, sidestepping the degree conversion for layout.

International and metric slope conventions

The x/12 pitch is largely a North American convention. In the United Kingdom, Europe, Australia, and much of the rest of the world, roof slope is quoted in degrees or as a percentage, so a plan may simply say 30 degrees or 58 percent rather than 7/12. When you meet one of those, the arctangent relationship still bridges the gap: a percentage divided by 100 gives the rise-over-run ratio, and its arctangent gives the degrees, which you can then read back to the nearest x/12 pitch if you frame in twelfths.

Metric drawings sometimes express slope as rise in millimetres per metre of run. A 250 mm rise per 1000 mm run is a 25 percent slope, whose arctangent is about 14 degrees, close to a 3/12 pitch. The practical rule when the units look unfamiliar is to reduce everything to a plain rise-over-run ratio first, then apply the arctangent, then translate to whatever unit you build in. Because the underlying angle is universal, this always works, and the calculator will carry the conversion for you if you prefer not to do the arithmetic.

How the angle connects to material choice

Although manufacturers write their rules in x/12 pitch, the degree value is a useful lens on the same decision, because it maps cleanly onto how water behaves. Below about 9.5 degrees (a 2/12 pitch) water moves too slowly for overlapping shingles to stay watertight, which is why that angle is the practical floor for shingle and metal panel systems and why anything shallower is treated as a low-slope roof with a sealed membrane. The material thresholds gathered in what is the minimum roof pitch all correspond to angles, even when they are printed as ratios.

At the other extreme, very steep angles change the fastening rules rather than the waterproofing. Past roughly 60 degrees (a pitch above 20/12) some coverings need extra mechanical fixing so they do not sag or slide, and the wind loading climbs as the roof presents more face to the weather. Between those limits, the angle mostly influences how fast the roof sheds water and snow and how much surface area it carries, both of which feed into cost. Converting your pitch to degrees, then, is not just a paperwork exercise; it tells you at a glance which side of the material and fastening thresholds your roof sits on.

A note on precision and rounding

How many decimals you keep depends entirely on what the angle is for. If you are describing a roof to a homeowner or on a listing, rounding to the nearest whole degree is fine; a 6/12 roof is comfortably called a 27 degree roof in conversation. If you are setting a solar array or cutting rafters, keep the two-decimal value, because a fraction of a degree accumulates across a long panel row or a full roof of rafters into a visible misalignment. The difference between 26.57 and 27 degrees sounds trivial, but over a 30 foot run it shifts the ridge line by a noticeable amount.

The safest habit is to carry the full value through your calculations and round only at the very end, at the moment you actually mark or set something. Rounding early and then multiplying or adding compounds the error. When precision really counts, skip the mental math and read the exact figure from the calculator, which holds more decimal places than you will ever need and removes any rounding you might introduce by hand.

Five angle facts worth memorising

If you internalise a handful of reference points, most day-to-day conversions become instant recognition rather than calculation. First, 12/12 is exactly 45 degrees, the anchor for everything else. Second, 6/12 is 26.57 degrees, the default medium roof. Third, 4/12 is 18.43 degrees, the usual shingle minimum. Fourth, every pitch below 12/12 is under 45 degrees and every pitch above it is over 45, which lets you sanity-check any result. Fifth, the angle rises fast at first and then slows, so the jump from 2/12 to 4/12 adds about 9 degrees while the jump from 20/12 to 22/12 adds only about 2.

With those five facts you can place almost any roof without a calculator and immediately spot a conversion that has gone wrong. They also make you quicker on site, because you recognise a 6/12 as “about 27 degrees” without reaching for anything. For the values in between, lean on the quick table above or the full angle chart, and when you need an exact figure to cut or specify against, confirm it in the calculator. The math is fixed and the tools agree, so once you know these anchors you can move between pitch and degrees with real confidence.

A quick conversion checklist

Before you rely on any pitch-to-degrees conversion, run through a short mental checklist so the number you carry into cutting, ordering, or solar planning is sound. Confirm you are working from the true pitch of the plane you care about, not a hip rafter or a sagging section, using the measuring steps in how to calculate roof pitch. Confirm your calculator is in degree mode. Confirm you used the run of 12, or half the span if you started from whole-building dimensions. Then take the arctangent and round only at the end.

Those four checks catch the errors that account for nearly every wrong angle. When the result matches how the roof looks and lines up with the quick table, you can trust it. When it does not, one of the four checks will show you why. This discipline is what separates a reliable conversion from a guess, and it takes only a few seconds once it becomes habit. Pair it with a final look at the calculator for anything you will cut or specify, and your degree values will be right the first time, every time.

Let the calculator do the trig

Hand conversion is a good skill and a useful backup, but for day-to-day work the roof pitch calculator is faster and eliminates the radian-mode trap entirely. Enter the pitch and it returns the angle to full precision, plus the slope percentage and the rafter multiplier, so you can move straight into cutting or ordering. Enter an angle and it hands back the nearest pitch, covering the reverse conversion too.

From the angle you can flow into the connected tools without re-entering anything: pair it with roof area with pitch to size materials, or the rafter length guide to lay out framing at the right cut angles. You will find the roof pitch tool with the rest of the estimators in the construction calculators category, alongside site tools like the dirt calculator, and the full roofing library sits in the roof pitch blog reachable from the homepage. Whether you convert by hand or by calculator, the arctangent is the engine underneath, and knowing it means you can trust and verify every angle you use.

How to calculate roof pitch in degrees: frequently asked questions