gizmobench

Roof Pitch Calculator

Type a roof pitch like 6:12 and read its angle in degrees, its slope and its percent grade, or type the angle and get the pitch back as rise per 12. The stage draws the pitch triangle at true scale, and the rows give the slope, the angle, the grade, the length along the slope for the rise and run typed, and the line's equation, each with a copy button. This is the geometry of the pitch only: it does not size rafters or pick materials.

run 12rise 6
Roof pitch · rise per 12 of run6:1226.57° · slope 0.5 · 50% grade
Mode
Given
Pitch (rise:run)

A pitch is the rise per 12 of run: 6:12 climbs 6 for every 12 across. Type it as 6:12, 6/12 or just 6, or give the angle instead.

  • Pitchrise per 12 of run
    6:12
  • Angledegrees above horizontal, arctan of the slope
    26.5650511771°
  • Sloperise / run
    0.5
  • Percent gradeslope × 100
    50%
  • Distancealong the slope, for the rise and run given
    13.416407865
  • Equationy = mx + b, to four places
    y = 0.5x + 0
One line, six readings. Slope is rise divided by run. The angle is the arctangent of the slope, in degrees above horizontal, so 45 degrees is a slope of 1. Percent grade is the slope times 100, the number a road sign uses. Distance is the straight length between the two points, from Pythagoras. The equation is the slope-intercept form y = mx + b, with b where the line crosses the y axis. And a roof pitch is the same slope written as the rise per 12 of run, so 6:12 is a slope of 0.5, a 50% grade and an angle of 26.57 degrees. A vertical line has no slope at all: the run is 0, and the tool says so instead of printing infinity.

Common questions

What does a pitch like 6:12 mean?
The rise for every 12 of run. A 6:12 roof climbs 6 inches for every 12 inches it goes across, and it is the same roof whether you measure in inches, centimetres or feet, since the pitch is a ratio. Written as a slope it is 6 divided by 12, or 0.5; as a grade it is 50%; as an angle it is 26.57 degrees. Type it as 6:12, 6/12, 6 in 12, or just 6, and the tool reads all four the same way.
How do I convert a roof pitch to degrees?
The angle is the arctangent of the rise over the run. For 6:12 that is arctan(6 / 12) = 26.57 degrees; for 4:12 it is 18.43, for 8:12 it is 33.69, for 12:12 it is exactly 45. The tool does the arctangent for you: switch Given to Pitch, type the pitch, and read the Angle row. Pitch and angle are not proportional, so doubling the pitch does not double the angle; 12:12 is 45 degrees but 24:12 is 63.43, not 90.
How do I get the pitch from an angle?
Switch Given to Angle and type the degrees. The rise per 12 is 12 times the tangent of the angle, so 30 degrees is 12 × tan(30°) = 6.9282, which the tool writes as 6.9282:12. An angle of 90 is a vertical wall with no slope, and the tool says the slope is undefined rather than printing a pitch for it; anything past 90 either way is outside the range of a roof and is refused with the range named.
How do I measure the pitch of an existing roof?
With a level and a tape. Hold the level horizontal with one end touching the roof surface or a rafter, measure 12 inches along the level from that end, and measure straight down from that 12-inch mark to the roof. The distance down is the rise, and the pitch is that rise over 12. If you measure a different run, say 4 inches of rise over 18 inches of level, type 4:18 and the Pitch row rewrites it as 2.66667:12; the distance row keeps your 4 and 18.
Is a roof pitch the same as its slope?
They are the same tilt written two ways. Pitch is rise per 12 of run, so 6:12; slope is rise divided by run, so 0.5. Some trades also say pitch for the rise over the whole span rather than over the run, so a 6:12 roof on a 24-foot span may be called a quarter pitch: this tool always means rise over run. The percent grade is the slope times 100, and the angle is its arctangent; the tool prints all four so you can use whichever one the drawing or the ordinance asks for.

Slope, angle and distance are computed exactly from the numbers you give; the equation is shown to four decimal places. A roof pitch of 6:12 is the same as a 26.57 degree angle, and the tool says both.