The immediate relationship
Ratio is rise divided by horizontal run. Rise per 12 scales that ratio to a 12-unit run. Angle is arctangent of the ratio. Percentage is the ratio multiplied by 100. Multiplier is √(1 + ratio²).
A 6/12 roof has ratio 0.5, angle about 26.57 degrees, percentage 50 and multiplier about 1.1180.
Why the distinction matters
A 50 percent slope is not a 50-degree roof. One is a ratio expressed per hundred; the other is an angle. Confusing them changes the geometry substantially.
Keep a record of the original measurements, unit system, selected mode and any adjustment. Recalculate independently before ordering material or making a construction decision.
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.
Detailed field guide
Regional language differs. US documents often use rise per 12, while degrees are common in specification and survey contexts. Percentage slope is common in civil and drainage contexts. Preserve the source label instead of assuming two numbers mean degrees.
A 3/12 pitch equals 14.036°, 25% and factor 1.030776. An 8/12 pitch equals 33.690°, 66.667% and factor 1.201850. Comparing all four forms exposes the common mistake of treating a percentage as an angle.
Shortcuts are safest after concepts are distinct. The ratio controls every conversion; the factor controls compatible length and area changes. Neither representation discovers a footprint, member size or roof junction.
Record the original value, its representation and the converted display. Re-entering a rounded conversion can drift, so calculations should retain the original or full-precision ratio.
Checks before using the result
- Preserve the original measurement, unit, endpoints and drawing revision.
- Keep different pitches and unsupported intersections separate.
- Compare one representative result with an independent calculation.
- Do not access a roof merely to obtain calculator inputs.
Start from the ratio
All common pitch forms begin with the same right triangle. Divide vertical rise by the matching horizontal run to obtain q. Rise per 12 is 12q, percentage is 100q, angle is atan(q), and the slope multiplier is √(1+q²). Keeping q at full precision makes each displayed form independently reproducible.
Recognise ambiguous notation
A note reading “6 in 12” is normally a rise-per-12 convention; “50%” is a ratio multiplied by 100; “26.565°” is an angle. A bare “6” is not enough. Record the symbol, label, drawing legend and endpoints before converting it, especially when information has crossed regional or trade contexts.
Check with a known run
Use a convenient horizontal run as a reasonableness check. At 6/12, a 12-unit run has 6 units of rise and a slope line of √180, about 13.416 units. At 30%, the same run rises only 3.6 units. This simple comparison quickly exposes degree-versus-percentage mistakes.
Report without false precision
Retain the source value and full-precision ratio in the calculation record, then round only the presentation. A converted 18.434949° may be displayed as 18.43°, but that display should not replace the original 4/12 input. Measurement uncertainty always limits the useful precision of every derived form.
Translate a pitch without changing its meaning
A roof can be described with a rise-over-run ratio, an angle, a percentage slope or a slope multiplier, but these are four views of the same right triangle. Start by reducing the measurements to a ratio using the same unit. A rise of 150 mm over a 600 mm horizontal run gives 0.25. That is 3/12, 25 percent and about 14.04 degrees. The multiplier is about 1.0308, meaning one unit of horizontal run corresponds to 1.0308 units along the slope. Keeping the underlying ratio visible makes it possible to check every representation without trusting a chart or a rounded label.
Do not compare unlike conventions as if their numbers were interchangeable. A 25 percent slope is not a 25-degree roof: 25 degrees corresponds to roughly 46.63 percent and about 5.60/12. Likewise, a printed 6:12 label describes six units of rise for twelve horizontal units, not twelve units measured along the roof. When a drawing, survey or product document uses unfamiliar terminology, identify its numerator, denominator and reference plane before entering anything. That short definition step prevents a plausible-looking conversion from attaching the right mathematics to the wrong measurement.
Choose the representation that fits the next task
Rise per 12 is convenient for communication in US roofing because common pitches can be compared quickly. Degrees suit instruments and drawings that report angular inclination. Percentage slope is common in drainage, civil and specification contexts, while the multiplier is useful for converting a supported horizontal run or plan projection into its sloping counterpart. None is inherently more accurate. Accuracy comes from the source measurement, the definition of run and the precision retained during conversion. Record the original form as well as the converted display so a later reviewer can distinguish measured evidence from a derived convenience value.
For repeated calculations, derive every output from the original ratio rather than chaining rounded displays. If 26.57 degrees is converted to a percentage and that rounded percentage is then converted to a multiplier, small errors accumulate. RoofFigured retains a full-precision ratio internally and rounds only for presentation. A manual check can use angle = atan(rise/run), percentage = 100 × rise/run and multiplier = √(1 + ratio²). Agreement at the shown precision is normally sufficient; an unexplained difference should trigger a review of units and definitions before anyone changes the formula.
Read pitch information critically
A pitch value alone does not define a complete roof. It does not state the building span, eaves position, ridge thickness, overhang, plane outline or whether different parts use different slopes. Treat it as one property of one identified plane. On a multi-plane project, label values such as “main east plane—6/12” and “rear addition—3/12” rather than placing an unqualified pitch in a general note. The label connects the number to a boundary and reduces the chance that a correct conversion is reused on the wrong section.
Use the converter as a communication and checking tool, not as structural or construction approval. A matching angle does not establish member size, drainage performance, weathering detail or code compliance. When pitch affects a product or design decision, consult the controlling drawing, manufacturer information and competent professional responsible for that decision. RoofFigured’s role ends after it shows the mathematical equivalence, its rounding and the inputs from which it was derived.
Worked comparison: why the notation matters
Suppose one note says 4/12, another says 33.33 percent and a third says 18.43 degrees. Dividing 4 by 12 gives one third; multiplying by 100 gives 33.333 percent, and atan(1/3) gives about 18.435 degrees. These values describe the same plane within display rounding. Its multiplier is √(1 + 1/9), about 1.054093. A 5 m horizontal run would therefore correspond to about 5.270 m of ideal slope line. Writing this short chain beside the source note provides a stronger check than accepting three labels because they look typical.
Now compare 4 degrees. Its tangent is about 0.0699, equivalent to roughly 0.839/12 and 6.99 percent—not 4/12. The distinction matters because each representation uses a different scale. When copying values between drawings, estimating software and product documents, include the symbol or words that identify the convention. If the convention is absent, ask for clarification or preserve the value as unresolved; do not let the interface’s available choices turn an ambiguous number into a false certainty.
Final verification before use
Before leaving the guide, test one value through every form. At 9/12 the ratio is 0.75, the percentage is 75, the angle is about 36.87 degrees and the multiplier is 1.25. A 2 m horizontal run therefore gives a 2.5 m ideal slope line. If a tool or document reports a materially different equivalent, verify the convention before using it.
Keep the original notation and its source beside every conversion. State whether the value belongs to the whole roof or one named plane, and record the rounding used for display. When passing the result to an area or rafter calculation, use the stored full-precision ratio rather than a value transcribed from a chart. This preserves a clear line from supplied evidence to derived result and prevents several individually small rounding steps from becoming a larger project discrepancy.