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