Free Roof Pitch Calculator: Slope, Angle and Rise

A free roof pitch calculator works out a roof’s slope from its rise and horizontal run, then gives the pitch, angle, and related measurements. Enter the rise and run in the same units; the calculator below returns pitch as rise per 12 units of run, the angle in degrees, and the slope as a percentage.

Formula

Let r be the vertical rise and u the horizontal run, measured in matching units. Pitch in inches per 12 inches of run is 12 × r ÷ u. Roof angle is arctan(r ÷ u), converted to degrees. Slope percentage is 100 × r ÷ u. The rise and run units cancel in the ratios, so inches, feet, millimeters, or meters work as long as both measurements use the same unit.

Worked Example

Using the calculator’s defaults, the roof rises 6 inches over a 12-inch horizontal run:

• Pitch = 12 × 6 ÷ 12 = 6 in/12, commonly written 6:12.
• Angle = arctan(6 ÷ 12) = arctan(0.5) = 26.57°.
• Slope = 100 × 6 ÷ 12 = 50%.

These values describe the same slope in three different ways. The pitch is 6 inches of vertical rise for every 12 inches of horizontal run.

What Roof Pitch Means

Roof pitch describes how steep a roof is. In common North American usage, a pitch such as 6:12 means six units of rise for every 12 units of horizontal run. It is a ratio, not an angle: a 6:12 roof has an angle of about 26.57°, not 6° or 12°.

Roofing references may use “pitch” more loosely to mean steepness, while building geometry distinguishes pitch from slope. In geometry, slope is rise divided by run; pitch is often expressed as a rise-to-span ratio. This calculator uses the widely used rise-per-12 convention and labels the result explicitly to avoid that ambiguity.

The run is horizontal distance, not the length measured up the sloping roof surface. If the roof rises 6 inches across a horizontal run of 12 inches, its sloping length is about 13.42 inches. Substituting that sloping length as the run would produce the wrong pitch.

How to Measure Rise and Run

For an existing roof, a level and measuring tool can help establish a horizontal reference. Measure the vertical change over a known horizontal distance, without relying on the sloped surface as the run. For a small section, a 12-inch horizontal run makes the pitch easy to interpret: the measured vertical rise is the pitch in inches per 12.

For example, if a roof rises 8 inches over 12 inches of horizontal run, it is an 8:12 roof. If the available measurement is 24 inches of run and 16 inches of rise, the same ratio is 8:12 because 12 × 16 ÷ 24 = 8. The calculator accepts any positive run, so measurements do not have to be taken over exactly 12 inches.

• Use horizontal run, not the rafter or roof-surface length.
• Measure rise and run in the same units. Do not enter a rise in inches and a run in feet without converting one.
• Use a longer measured span when practical if it improves measurement resolution, then enter the actual rise and run.
• For a gable roof, do not confuse the horizontal run from the outside wall to the ridge with the full building width. The relevant run is normally half the span for a symmetrical roof.

Reading and Using the Results

Pitch, angle, and percentage are interchangeable descriptions of the same straight-line slope. Pitch is often convenient for discussing roof geometry; angle is useful for trigonometry; percentage is common in general slope calculations. A 3:12 roof, for instance, has a 25% slope and an angle of about 14.04°. A 12:12 roof has a 100% slope and a 45° angle.

The calculator reports the geometric slope, not the roof’s surface area, rafter length, or material quantity. Those require additional dimensions and, for material estimates, information about overhangs, roof shape, openings, and product-specific coverage. For a simple right-triangle section, the sloped length can be found from the Pythagorean theorem: √(rise² + run²). Keep the rise and run in the same units to get the length in that unit.

Pitch can help compare designs or check a measurement, but it does not by itself determine whether a particular roofing material is suitable. Requirements depend on the product, installation details, climate, and applicable building rules. Check the relevant manufacturer instructions and local requirements rather than treating a calculator result as approval.

Common Measurement Problems and Limits

A frequent mistake is mixing units. A rise of 1 foot over a run of 12 inches is not a 1:12 slope: convert the rise to 12 inches first, which makes it a 12:12 slope. The same rule applies in metric measurements; 150 mm over 1,000 mm is a 1.5:10 ratio, equivalent to 1.8:12.

Small measurement errors can noticeably affect results, especially over a short run. The calculator rounds pitch, angle, and slope for display, so use unrounded measurements for further calculations when possible. The displayed values are estimates based on the numbers entered, not a survey of a roof that may be uneven or have changing slopes.

This tool assumes one consistent slope represented by a straight cross-section. It does not account for hips, valleys, dormers, sagging, curved roofs, or changes in pitch. A complex roof may have several distinct planes, each requiring its own measurements. Do not climb onto a roof simply to obtain a measurement; use a safe method from the ground or consult a qualified professional when access is risky.

Frequently Asked Questions

How do I calculate roof pitch?
Divide vertical rise by horizontal run, then multiply by 12 to express the result as rise per 12 units of run. For example, 9 inches of rise over 12 inches of run is 9:12.

Is roof pitch the same as roof angle?
No. Pitch is usually a rise-to-run ratio, while angle is measured in degrees. Convert the ratio to an angle with arctan(rise ÷ run); a 6:12 pitch is about 26.57°.

What does a 4:12 roof pitch mean?
It means the roof rises 4 units vertically for every 12 units of horizontal run. The units can be inches, centimeters, or another consistent measurement.

Can I calculate pitch from rafter length?
Not from rafter length alone. You also need the horizontal run or another independent measurement. Rafter length is the hypotenuse of the roof section, not its horizontal run.

Can I use this calculator for metric measurements?
Yes. Enter rise and run in millimeters or meters, using the same unit for both. The ratios and angle remain the same; the pitch output is expressed as the entered unit per 12 of that same unit.

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in rise | Roof rise | in | 6 | 0
in run | Horizontal run | in | 12 | 0
out pitch | Pitch (rise per 12) | in/12 | rise * 12 / run | 2
out angle | Roof angle | degrees | atand(rise / run) | 2
out slope | Slope | % | rise / run * 100 | 2