Roof Pitch Calculator: Find the Pitch, Angle and Rafter Length

How to use the roof pitch calculator

Five tabs, five different starting points. Pick whichever matches what you already have in front of you.

Rise and run. The one most people want. Measure 12 inches out along a level from the roof surface, measure straight down to the roof at that point, and you have a rise over a run of 12. Any matching pair works, so a rise of 6 feet over a run of 12 feet gives the same answer.

Pitch in x/12. If someone has already told you it is a 6/12, start here. Add a run and it works out the rise and the rafter length for you.

Percent grade. Civil drawings and metric plans often give the fall as a percentage rather than a fraction. A 25 percent roof slope is a 3/12, and this is the tab that tells you so.

Rafter and run. For an existing roof. Measure the rafter and the run and it works the pitch back out, which is often easier than getting a level up there.

Length and angle. For working backwards from a measured rafter and a reading off an angle finder or a phone level.

Under the fields of every tab there are three optional boxes. Fill them and you get more back. Ridge thickness and overhang turn the theoretical rafter into the length you actually cut. Footprint area turns the slope factor into a roof area and a count of squares. Leave them empty and the calculator behaves exactly as it did before.

What you get back

One measurement, every form of it a roofer, a framer or a supplier might ask for.

• Pitch as x/12, the number the trade actually speaks in.
• Angle in degrees, for setting a saw or a rafter square.
• Percent grade, with the ratio beside it.
• Rise and run, worked out from whichever pair you did not enter.
• Rafter length, the straight line from the ridge down to the wall plate.
• The slope as a tidy fraction where one exists, so a 6/12 also reads as 1/2.
• The traditional pitch over the span, which for that same 6/12 is 1/4. The next section but one explains why those are two different numbers for the same roof.
• The slope factor, the number that turns a floor area into a roof area.
• The rafter to cut, if you gave a ridge thickness or an overhang. Half the ridge off, the tail on, and the deduction taken in the right place, so it is a length you can mark rather than a theoretical one.
• Roof area and squares, if you gave a footprint. Roofers order in squares of 100 square feet.
• A verdict saying what that pitch means for the covering, the underlayment and getting up there safely.

The verdict is the part worth reading. A number on its own does not tell you whether you can shingle the roof, whether you can walk it, or whether the quote you are holding makes sense.

How precise the numbers are

Nothing rounds until it prints. Angles show three decimal places, the rafter length four.

For a single cut that is more precision than you need. A rafter length rounded to two decimals of a foot is out by about an eighth of an inch, which is inside a pencil line. It earns its keep in two places: when you are sitting on a threshold and need to know which side of 2/12 or 4/12 you are actually on, and when you convert between forms, because rounding at each step compounds in a way that rounding once does not. If you take our angle, convert it back by hand and land a digit away, ours is the value carried at full precision.

About units

Pick the unit from the dropdown. Feet, inches, metres, centimetres, millimetres and yards all work, and the rise and the run have to be in the same one, because a pitch is a ratio and a ratio only holds if both halves are measured the same way. The pitch in x/12 is unitless by definition, so it reads the same whatever you picked. Whatever unit you use, the run has to be the flat horizontal distance, not a measurement taken up the slope. That one rule decides roof pitches, and it decides whether a ramp meets the ADA limit for a ramp too.

The roof pitch formula

Pitch is the rise divided by the run, quoted against a run of 12. Six inches of rise for every twelve inches along is a 6/12.

The run is the flat horizontal distance from the outside wall to a point directly under the ridge, which on a symmetrical gable is half the span. The rise is the vertical height from the wall plate up to the ridge. The rafter is the straight line joining them, and its length is the square root of the rise squared plus the run squared.

Look at the last two boxes. The same roof is a 6/12 and a one quarter, because the first is measured against the run and the second against the span. That is not a rounding difference, it is two different words, and the next section is about why it catches people out.

How to calculate roof pitch by hand

Take a roof that rises 6 feet over a run of 12 feet.

1. Divide the rise by the run: 6 ÷ 12 = 0.5.
2. Multiply by 12 to get the pitch the trade uses: 0.5 × 12 = 6, so a 6/12.
3. As a percentage, multiply by 100: 50%.
4. For the angle, take the arctangent of 0.5: 26.565°.
5. For the rafter, √(6² + 12²) = √180 = 13.4164 ft.

Working the other way is the useful one on site. A 4/12 over a 15 foot run rises 4 ÷ 12 × 15, which is 5 feet.

The common ones, worked out

Six pitches cover most of what gets asked for. The calculator handles anything in between.

Pitch	Degrees	Percent	Slope factor	Over the span
2/12	9.46°	16.67%	1.01379	1/12
4/12	18.43°	33.33%	1.05409	1/6
6/12	26.57°	50.00%	1.11803	1/4
8/12	33.69°	66.67%	1.20185	1/3
10/12	39.81°	83.33%	1.30171	5/12
12/12	45.00°	100.00%	1.41421	1/2

Roof pitch and roof slope are not the same word

In everyday use they are treated as the same thing, and every calculator online, this one included, labels rise over run as the pitch. Strictly they are two different measurements.

• Slope is rise over run, written as x in 12. Our example is a 6 in 12.
• Pitch, in its traditional sense, is rise over span, written as a plain fraction. The same roof is a one quarter pitch, because 6 divided by the 24 foot span is a quarter.

Modern trade usage has collapsed the two, and a pitch gauge laid on a rafter reads x in 12 whatever the label on it says. So for almost every job the distinction does not matter, and you should not correct a supplier who says pitch when they mean slope.

It matters in one place. Older architectural drawings, heritage work and some truss schedules still specify pitch the old way, as a fraction like a third or a quarter. Read a one third pitch as a 3/12 and you are out by a mile, because a one third pitch is a 8/12. If a drawing gives you a plain fraction rather than something in 12, check which one it means before you cut anything.

What the rafter length does not include

The rafter length here, and on every other calculator, is the straight line from the centre of the ridge down to the outside face of the wall. It is not the board you cut. Two things have to happen to it first.

The rafter stops at the face of the ridge board rather than its centreline, so half the ridge thickness comes out, and the tail beyond the wall gets added. The part worth the read is where the ridge deduction happens: it is horizontal. Half the ridge comes off the run, and then you work out the length. It does not come off the finished rafter.

Those two are not the same number, and the gap grows as the roof gets steeper. Take a unit of run away and you take away more than a unit of rafter, because on a slope the rafter covers more distance than the run underneath it. How much more is exactly the slope factor, the same number the calculator already prints. So the honest deduction off a finished rafter length is half the ridge times the slope factor, and a flat half-ridge takes off too little. With a 1½ inch ridge, so ¾ of an inch:

Pitch	Slope factor	What the rafter really loses	What the ¾ in shortcut takes	Every rafter ends up long by
4/12	1.05409	0.791 in	0.750 in	0.041 in
6/12	1.11803	0.839 in	0.750 in	0.089 in
9/12	1.25000	0.938 in	0.750 in	0.188 in
12/12	1.41421	1.061 in	0.750 in	0.311 in, over 5/16

On a shallow roof it is inside the pencil line and nobody notices. On a 12/12 you are better than five sixteenths long on every single rafter, and once a few are up the ridge tells you. The fix costs nothing: take the deduction off the span before you halve it, or off the run before you square anything, and let the length fall out of the adjusted numbers. Or put the ridge thickness into the calculator above and let it hand you the length to cut.

The flat half-ridge shortcut is written up in plenty of places, including on pages that rank well for this. It is close enough to sound right, and it is wrong in the direction that leaves you trimming.

The roof slope factor, and what it multiplies

The slope factor is how you turn a flat area into a sloped one. It is the rafter length divided by the run, which is the same as the square root of the slope squared plus one. A 6/12 gives 1.11803.

Multiply the footprint by it, meaning the area the roof covers when you look down at it from above, and you get the actual surface area you have to cover. A building 30 feet by 40 feet under a 6/12 roof has a 1,200 square foot footprint and 1,341.6 square feet of roof.

The trap is applying it to a number that already has the slope in it. If you measured up the slope with a tape, or took the area off a drawing that shows the roof surface rather than the plan, the factor has already been accounted for. Multiply again and you over-order by the same percentage a second time. On the 6/12 above that is another 12 percent of material sitting on the driveway.

The six most common pitches have their factors listed further up this page if you just want to read one off.

Minimum pitch by roofing material

A pitch is not just a number, it decides what you are allowed to put on the roof. The shingle limits below come from the IRC minimum slope for asphalt shingles, section R905.2.2, which says asphalt shingles are for slopes of 2:12 or greater, and requires a doubled underlayment from 2:12 up to 4:12. The calculator checks your answer against those two thresholds automatically.

The rest of the table is normal practice rather than code. Walkability, staging and waste are judgement calls that vary by crew, surface and weather, so treat those rows as a starting point and not a rule. Three things outrank this table every time: your local amendments, the covering manufacturer’s own written instructions, and your inspector. Manufacturers can and do set stricter limits than the code, and installing outside their instructions is the usual way a warranty gets voided.

Pitch	Angle	What it will take
Under 2/12	under 9.46°	No asphalt shingles. Options are a single-ply membrane, modified bitumen or a standing seam metal system, and each has its own minimum. See the note under the table
2/12 to under 4/12	9.46° to 18.43°	Shingles, but almost every manufacturer requires doubled underlayment. Check the warranty
4/12 to 7/12	18.43° to 30.26°	Conventional. Shingles, tile or metal, and normally walked with care when dry
7/12 to 9/12	30.26° to 36.87°	Takes any common covering, but walking depends on surface and weather. Many crews use roof jacks from about 7/12
9/12 to 12/12	36.87° to 45°	Roof jacks or staging needed. Labour goes up
Over 12/12	over 45°	Scaffolding, and more waste on every cut

Low slope does not mean anything goes. Each of those systems carries its own minimum in the IRC, and they are not the same. Built-up, modified bitumen and single-ply membranes such as TPO and EPDM all need at least 1/4 in 12, and so do sprayed foam and liquid applied systems. Coal-tar built-up roofing is the single exception in the whole chapter, allowed down to 1/8 in 12. A standing seam metal system also needs 1/4 in 12. Lapped, non-soldered metal panels, the corrugated sheets people reach for on outbuildings, need 1/2 in 12 with lap sealant and a full 3 in 12 without it, which is steeper than shingles rather than shallower. Metal is not automatically the low slope answer.

A shed or a lean to sitting at 1.5/12 is the one that catches people. It looks like a roof and it takes shingles physically, but it is below the rating, and a shingled low slope roof can start letting water back up under the tabs inside a single winter. Local code and the manufacturer’s own instructions both beat any general table, including this one.

Five reasons a roof pitch comes out wrong

The arithmetic is one division. Almost every wrong answer comes from what went into it.

1. The run was measured along the roof. The bottom of the sum is the flat horizontal distance. Run a tape up the slope and you have measured the rafter, which is always longer, so the pitch comes out shallower than it is.
2. The level was not level. Reading a rise off a level that is sitting on the shingles rather than held true is the most common measuring error there is. On a textured surface, rest it on a straight edge.
3. The span was used instead of the run. Halve the span first on a symmetrical gable. Use the full span and you have halved the pitch.
4. The ridge deduction went in the wrong place. Covered above. It comes off the run, not the rafter.
5. The roof has more than one pitch. Additions, dormers and lean to sections rarely match the main roof, and a valley between two different pitches is its own angle again. Measure each plane separately.

Frequently asked questions

How do you convert roof pitch to degrees?

Divide the pitch by 12, then take the arctangent. A 6/12 is 6 ÷ 12 = 0.5, and arctan 0.5 is 26.57 degrees. On a calculator that is the tan⁻¹ or atan key. The common ones are 4/12 at 18.43°, 6/12 at 26.57°, 8/12 at 33.69° and 12/12 at 45°. The calculator above does it in both directions.

Why isn’t a 6/12 pitch 22.5 degrees?

Because degrees and pitch do not run on the same scale. A 12/12 is 45 degrees, so it looks like half of that should be 22.5, but a 6/12 is 26.57. The relationship is a tangent curve, not a straight line, and it bends. The same trap runs the other way: doubling a pitch does not double the angle, and a 24/12 is 63.43 degrees rather than 90. Anything involving angles has to go through arctan, every time.

What is the minimum roof pitch for asphalt shingles?

2/12, which is 9.46 degrees. Below that, shingles are not rated and you need a membrane system instead. Between 2/12 and 4/12 they are allowed but nearly every manufacturer requires a doubled underlayment, and skipping it will usually void the warranty. Above 4/12 it is a standard single layer. Check the specific product instructions, since they beat the general figure.

What is a normal roof pitch?

Most houses land between 4/12 and 9/12. That range sheds water and snow properly and takes any common covering. Below 4/12 you start hitting underlayment rules. Walking gets awkward from about 7/12, and past 9/12 the labour cost climbs because nobody is up there unaided. Climate pushes it about: heavy snow areas go steeper, dry flat regions go shallower.

What is the difference between roof pitch and roof slope?

Slope is rise over run, written as x in 12. Pitch, strictly, is rise over the whole span, written as a plain fraction. A roof rising 6 feet over a 12 foot run on a 24 foot span is a 6 in 12 slope and a one quarter pitch. In everyday trade use the two words have merged and almost everyone says pitch for both, which is fine. It only bites on older drawings that give a bare fraction, where a one third pitch means an 8/12, not a 3/12.

How do you measure roof pitch without getting on the roof?

From inside the attic is the usual way. Hold a level horizontally against a rafter, mark 12 inches along it, then measure straight down from that mark to the underside of the rafter. That drop is your pitch in 12. From outside, hold a level against the gable end trim and do the same. A phone angle app against the gable board gets you close enough to identify the pitch, then round to the nearest whole number in 12, since roofs are framed in whole numbers.

What roof pitch is walkable?

Up to about 7/12 is generally walked with normal boots and care. Between 7/12 and 9/12 depends on the surface, the weather and the person. Past 9/12 almost nobody walks it unaided and you are into roof jacks or staging, which is why quotes jump at that point. Wet, mossy or frosted surfaces move the whole scale down, and a dry 8/12 can be safer than a damp 5/12.

Walkable is not the same as safe, and it is not the same as compliant. Pitch decides how hard a roof is to stand on. It does not decide what protection the work requires. Roofing work done by an employer is subject to OSHA 1926.501, which sets the duty at unprotected sides and edges six feet or more above a lower level. The trigger height is the same on every roof. What you are allowed to use is not: OSHA draws the line between a low slope roof and a steep one at 4:12, and a steep roof loses the warning line options a low slope roof has. Residential construction has a route of its own at 1926.501(b)(13). Look at where 4:12 sits on the chart above, because that pitch is the line the rule turns on. And look at who the rule is written for. 1926.501 sets requirements for employers, so a homeowner working alone on their own roof is not covered by it at all. The fall is the same height either way. A 4/12 you can walk comfortably is still six feet up at the eaves on most houses.

What is a roof pitch multiplier and when do you use it?

It is the same thing as the slope factor: the number that converts a flat footprint into actual roof area. A 6/12 is 1.11803, so a 1,200 square foot footprint is 1,341.6 square feet of roof. Use it when you are ordering material off a plan view. Do not use it on an area you measured up the slope, because that figure already includes it and multiplying twice over-orders by the same percentage again.