What this calculator does
Roof pitch describes how steep a roof is, and the standard way of stating it is as rise over a run of 12, such as a "6 in 12" roof, meaning the roof rises 6 units for every 12 units it runs horizontally. This calculator turns any rise and run measurement into that ratio, the equivalent angle in degrees, and the slope as a percentage, so the same steepness can be compared across the different ways it gets described.
How to calculate pitch is the same idea whichever units you measure in: divide the rise by the run. Working in inches with a run of 12 gives the familiar "X in 12" roofing figure directly, but the same maths works for a rise and run measured in any consistent unit, such as metres.
The formula
Divide rise by run to get the pitch ratio, reduced to its simplest whole-number form. The angle from horizontal is the arctangent of rise over run, and the slope percentage is the same ratio expressed as rise over run times 100.
| Term | Meaning |
|---|---|
| Pitch | The rise:run ratio of a roof, most commonly expressed against a run of 12, such as "6:12" or "6 in 12". |
| Rise | The vertical height gained over the horizontal run being measured. |
| Run | The horizontal distance over which the rise is measured, conventionally 12 units in the standard roofing notation. |
| Slope percentage | Rise ÷ run × 100, the same steepness expressed the way a ramp or road grade normally is. |
The inputs explained
| Field | What to enter |
|---|---|
| Rise (vertical, over the run below) (in) | The vertical rise over the run below. In the standard "X in 12" notation, this is the X. |
| Run (horizontal, typically 12 for US roof pitch) (in) | The horizontal run the rise is measured over. Use 12 to get the standard US roofing pitch notation directly. |
When to use it
Reading a roof pitch off a plan
Building plans and roofing suppliers usually quote pitch in the "X in 12" form; entering the rise and a run of 12 confirms the angle and slope percentage that figure actually represents.
Choosing roofing material for a given steepness
Many roofing materials have a minimum recommended pitch before they are watertight, usually stated as a slope percentage or an angle, so converting a rise and run into both figures checks a roof design against that requirement.
Comparing a roof pitch to a ramp or stair angle
Because rise, run and angle are calculated the same way regardless of context, the same figures let you compare a roof's steepness against a ramp gradient or a staircase angle on a like-for-like basis.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What angle and slope does each common roof pitch represent?
A fixed run of 12, across the common range of roofing rises.
| Rise (X in 12) | Roof pitch | Angle from horizontal | Slope |
|---|---|---|---|
| 2 in 12 | 1.00:6.00 | 9.46° | 16.7% |
| 4 in 12 | 1.00:3.00 | 18.43° | 33.3% |
| 6 in 12 | 1.00:2.00 | 26.57° | 50.0% |
| 8 in 12 | 2.00:3.00 | 33.69° | 66.7% |
| 10 in 12 | 5.00:6.00 | 39.81° | 83.3% |
| 12 in 12 | 1.00:1.00 | 45.00° | 100.0% |
Questions
How to calculate pitch from rise and run?
Divide the rise by the run. Expressed against a run of 12, that gives the standard roofing "X in 12" figure directly; the same division also gives the angle (via the arctangent) and the slope percentage.
What is the difference between roof pitch and roof angle?
Pitch is the rise:run ratio, most often shown against a run of 12. Angle is the same steepness expressed in degrees from horizontal. They describe the same slope in different units, and this calculator converts between them.
What counts as a steep roof pitch?
There is no single cutoff, but pitches above about 9 in 12 (roughly 37°) are generally considered steep in residential roofing, often needing different safety and access arrangements to work on than a lower-pitched roof.
Is roof pitch the same calculation as a ramp gradient?
Yes, mechanically. Both are a rise divided by a run. Roofing conventionally states the result against a run of 12, while ramps and roads more often use a slope percentage or a ratio such as 1:12, but the underlying arithmetic is identical.
For the equivalent slope calculation on a wheelchair ramp, see the ramp slope and length calculator. For the geometry of a staircase rather than a roof, use the stair rise and run calculator.