What angle is a 6/12 roof pitch?

26.57°. Divide rise by run (6 ÷ 12 = 0.5) and take the inverse tangent: arctan(0.5) = 26.57°. It is not 22.5°, which would be half of 12/12.

How do you convert roof pitch to degrees?

Angle = arctan(rise ÷ run). For a 4/12 pitch, 4 ÷ 12 = 0.333, and arctan(0.333) = 18.43°. Use a calculator's tan⁻¹ key in degree mode.

What pitch is a 22.5 degree roof?

About 4.97/12. Convert with rise = 12 × tan(22.5°). The closest standard pitch is 5/12, which is 22.62°.

Why isn't roof pitch proportional to angle?

Pitch is a ratio of rise to run, and the angle is the arctangent of that ratio. Arctangent is a curve, not a straight line, so equal steps in pitch give smaller and smaller steps in angle as the roof gets steeper.

What is a 12/12 pitch in degrees?

45°. The rise equals the run, so the ratio is 1, and arctan(1) = 45°. It's the only pitch where the rise and the run make the same angle with the rafter.

MeasuringShop Math & AnglesPitch vs angle

Is a 6/12 roof pitch half as steep as a 12/12?

12/12 is 45°. Everybody knows that one. So 6/12 is half of that, 22.5°, and you set the brake, bend the flashing, carry it up the ladder, and it rocks on the roof like a seesaw. Adam Fleisch made a whole reel about this. Short answer: no.

⚡ Rule of thumb

No. Pitch (rise per run) and angle are not proportional. 12/12 is 45°, but 6/12 is 26.57°, not 22.5°. Always convert with angle = arctan(rise ÷ run) before you set a bevel, a brake, or a saw. Halving the pitch never halves the angle.

Starting point

3/12 = 14.04° · 4/12 = 18.43° · 5/12 = 22.62° · 6/12 = 26.57° · 8/12 = 33.69° · 9/12 = 36.87° · 12/12 = 45°

Measured

Pitch = rise per 12 in of run (or per 1,000 mm, or %); angle = degrees from horizontal

Confidence

Widely accepted

▶ Source video — Cutting the pitch in half doesn't cut the angle in half — Adam Fleischwatch on Facebook ↗

Applies to

Process: Sheet-metal and roofing layout, flashing and trim bends, rafter and stair work
Materials: Any. This is geometry
Setup: Calculator with tan⁻¹, square, protractor or bevel gauge
Orientation: Rise is vertical, run is horizontal, angle measured from level

Why it matters

Pitch is a ratio of two lengths. Angle is a rotation. They line up at 0 and at 12/12, and in between the angle grows slower than the pitch does. Halve the pitch and the angle drops by a lot less than half.

Get it wrong and the error is about 4° at 6/12. That's a flashing leg standing off the shingles, a gutter hanger that won't sit flat, a trim piece that gaps at one end.

The worst of it sits right in the middle of the range. Which is where most real roofs are.

What good looks like

Every angle you set comes from arctan(rise ÷ run), never from scaling another pitch
A trial bend or cut sits tight on the real slope with no gap at either end
Your numbers match the table: 4/12 = 18.43°, 6/12 = 26.57°, 8/12 = 33.69°

How to apply it

Get the rise and run. From a pitch, the run is 12 and the rise is the first number: 6/12 means rise 6, run 12.
Divide rise by run: 6 ÷ 12 = 0.5.
Take the inverse tangent: arctan(0.5) = 26.57°. That's the angle from horizontal.
Set the bevel, protractor or brake to that angle, not to a fraction of 45°.
Going the other way, degrees to pitch: rise = 12 × tan(angle). Half of 45°, 22.5°, works out to about 4.97/12. 30° is about 6.93/12.
Metric or percent works the same: 500 mm rise per 1,000 mm run is 50%, which is 6/12, which is 26.57°.

Test it on your setup

Draw it full size: a 12 in (305 mm) run, a 6 in (152 mm) rise, connect the ends. Put a protractor on it. It reads about 26.5°, not 22.5°.
Bend a short test piece of the actual flashing at your computed angle and set it on the roof before you bend the run.

Exceptions & tradeoffs

At very low pitches it almost is linear: 1/12 is 4.76°, 2/12 is 9.46°. That's why the shortcut feels right, and why it falls apart as the roof gets steeper.

Roofers often never need degrees at all. A speed square has a pitch scale, and plenty of saws and brakes are set by pitch directly. You only convert when a tool or drawing calls for degrees.

Mind you, some tools measure from vertical. The plumb-side angle is 90° minus the roof angle: 63.43° for a 6/12.

Common mistakes

Halving the angle because the pitch was halvedRecompute with arctan every time: 6/12 is 26.57°, not 22.5°
Measuring the angle from vertical instead of horizontalRoof angle is from level; the plumb-side angle is 90° minus it
Reading pitch as a percentage of 45°Pitch is rise ÷ run. 6/12 is a 50% slope, not 50% of 45°

Frequently asked questions

What angle is a 6/12 roof pitch?26.57°. Divide rise by run (6 ÷ 12 = 0.5) and take the inverse tangent: arctan(0.5) = 26.57°. It is not 22.5°, which would be half of 12/12.
How do you convert roof pitch to degrees?Angle = arctan(rise ÷ run). For a 4/12 pitch, 4 ÷ 12 = 0.333, and arctan(0.333) = 18.43°. Use a calculator's tan⁻¹ key in degree mode.
What pitch is a 22.5 degree roof?About 4.97/12. Convert with rise = 12 × tan(22.5°). The closest standard pitch is 5/12, which is 22.62°.
Why isn't roof pitch proportional to angle?Pitch is a ratio of rise to run, and the angle is the arctangent of that ratio. Arctangent is a curve, not a straight line, so equal steps in pitch give smaller and smaller steps in angle as the roof gets steeper.
What is a 12/12 pitch in degrees?45°. The rise equals the run, so the ratio is 1, and arctan(1) = 45°. It's the only pitch where the rise and the run make the same angle with the rafter.

Adam FleischSource & visual reference

12/12 = 45°, 6/12 = 26.565° on the calculator, and applying the converted angle to bent sheet-metal trim — Most people think cutting the pitch in half cuts the angle in half. It doesn't. ↗ at 0:36.

Summarized and independently edited by Start Here from Adam Fleisch's clip, read off the frames, burned-in captions and calculator readouts, no audio. The 45° layout, the 26.56505° readout and the bent-trim payoff are his. His calculator also shows 22.61986°, which is 5/12; I read that as him showing the pitch closest to a true 22.5°, but that's my inference from a frame, not his words. The pitch table, 4.97/12, the percent and metric versions, and the tests are mine.