What the calculator solves
Roof pitch describes the relationship between vertical rise and horizontal run. A rise of 6 units over a run of 12 units is written 6/12 in common US practice. The same geometry is approximately 26.57 degrees, a 50 percent slope and a 1.1180 slope multiplier.
The unit cancels in the ratio, so 500 millimetres over 1 metre produces the same pitch as 6 inches over 12 inches after the measurements are expressed in one unit.
Worked examples
Imperial example: rise 6 in and run 12 in gives ratio 0.5, angle 26.565051 degrees, percentage 50 and multiplier 1.118033989 before display rounding.
Metric example: rise 0.5 m and run 1 m gives the identical pitch. A flat roof input of rise 0 and run 12 returns zero degrees and a multiplier of exactly 1.
Inputs, errors and limits
Run must be greater than zero. Rise can be zero but cannot be negative. Blank, non-finite and unsupported values produce an error rather than NaN or Infinity.
These calculations describe geometry only. They do not size rafters or trusses, assess loads, approve a design, interpret building codes, specify cuts or fasteners, or guarantee material quantities.
Roof work can cause serious injury. Do not climb onto a roof merely to collect inputs. Prefer drawings, ground-level measurements, accessible interior information or dimensions supplied by a competent professional.
Inputs, units and calculation stages
Rise is the vertical change and run is the matching horizontal change, measured between the same two stations. Feet, inches, metres and millimetres are accepted; changing the selector converts both numbers. Rise per 12 is a conventional US notation, while the underlying ratio has no unit.
Confirm the two endpoints, select the unit actually used, and enter rise and run. The engine validates the measurements, divides rise by run, then derives rise per 12, degrees, percentage and multiplier from that one ratio. Rounding is applied only to displayed figures.
Worked examples
A survey note gives 6 inches rise over 12 inches run. The ratio is 0.5, so the display reads 6/12, 26.565°, 50% and factor 1.118034. Changing to millimetres converts the inputs to 152.4 mm and 304.8 mm without changing the pitch.
A drawing gives 0.42 m rise over 2.80 m run. The ratio is 0.15, equivalent to 1.8/12, 8.531°, 15% and factor 1.011187. This demonstrates why measurement precision should be preserved before display rounding.
Errors, limits and responsible use
Zero rise is accepted as a geometric flat line; zero run is indeterminate and rejected. Negative, blank, infinite and ambiguous values produce an alert and no result. Very steep geometry close to vertical is outside the practical workbench range.
Check the source measurements, selected unit, representation and displayed assumptions before consequential use. RoofFigured explains geometry only; it does not provide structural design, code approval, installation instructions or a guaranteed material order.
Frequently asked questions
- Is 6/12 the same as 50 percent?
- Yes. Six divided by twelve is 0.5, or 50 percent. It is not 50 degrees.
- Does the selected length unit change pitch?
- No, provided rise and run use the same unit. The selector converts both values to keep their ratio unchanged.
- How accurate should my measurements be?
- Use the precision justified by the source. Extra decimal places in a result cannot repair uncertain measurements.
- Can rise be zero?
- Yes for geometric comparison, but the calculator does not assess drainage or code requirements.
- Can it calculate a vertical roof?
- No. A 90-degree line has zero horizontal run and therefore no finite roof-pitch ratio.
Continue the calculation
Terminology guide provides the next explanation; Safe measurement guide
Prepare a defensible rise-and-run input
Use two measurements that describe the same right triangle: vertical rise and horizontal run. They may be entered in feet, inches, metres or millimetres, but both must use the selected unit. The run is not the sloping roof surface and is not automatically half a building width unless a separate symmetric-gable assumption establishes that relationship. Record where both measurements came from and which roof plane they describe before relying on the converted pitch.
Longer measured baselines usually reduce the proportional effect of a small reading error. A 3 mm error across a 100 mm run changes a ratio more than the same error across 1,000 mm. Repeat or independently check consequential measurements and preserve the original values. The calculator’s precision describes its arithmetic; it does not upgrade the accuracy of a drawing, photograph or field observation.
Audit the four equivalent results
Divide rise by run to obtain the ratio. Multiply by 12 for rise per 12 and by 100 for percentage slope. Apply arctangent for the angle and √(1 + ratio²) for the multiplier. For rise 6 and run 12, the ratio is 0.5, so the results are 6/12, 50 percent, about 26.565 degrees and about 1.118034. These independent relationships make it possible to spot a unit or transcription error.
Use full precision for downstream line and area calculations rather than copying a rounded angle or factor from the display. A rounded value is intended for reading and communication. If a manual result differs beyond the shown rounding, check that the run is horizontal, the units match and the percentage has not been mistaken for degrees. RoofFigured rejects zero run, negative dimensions and non-numeric values rather than producing an apparently valid output.
Apply pitch only within its supported boundary
Pitch describes inclination; it does not establish span, plane outline, ridge position, overhang or structural design. Label the result by plane and pass it only to calculations whose horizontal boundary is known. Different additions may use different pitches even when they appear visually related. For a mixed roof, keep each plane separate in the workbench instead of applying one pitch to the entire footprint.
Before construction or ordering decisions, compare the result with reliable drawings and competent project information. RoofFigured does not size members, assess loads, interpret codes, prescribe cuts or confirm safe access. Do not climb onto a roof to obtain an input. Use accessible evidence or a competent professional, and retain the formula, units, date and source with the result.
Record the result for later checking
Save the source rise and run, selected unit, plane label, measurement reference, calculated ratio and review date. If a downstream calculation uses the multiplier, retain its full-precision value even when the visible record rounds it. This small audit trail lets another person reproduce the conversion and determine whether a later difference came from changed measurements, a different boundary or display rounding. A bare label such as “6/12 roof” is useful for conversation but insufficient as the sole evidence behind a consequential area or line calculation.