Equivalent ways to describe one slope
Rise per 12 is common in US roofing. Degrees describe the angle above horizontal. Percentage slope is one hundred times rise divided by run. The multiplier is the ratio of sloping length to horizontal run.
Changing the representation does not change the roof geometry. Converting 45 degrees returns 12/12, 100 percent and a multiplier of about 1.4142.
Conversion and rounding
The converter retains full precision internally. A displayed number converted back may differ in its last shown decimal because the display is a readable summary, not the stored calculation value.
For checks, compare within the documented tolerance and avoid repeatedly retyping rounded display values when the original measurement is available.
Useful boundaries
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.
Keep a record of the original measurements, unit system, selected mode and any adjustment. Recalculate independently before ordering material or making a construction decision.
Inputs, units and calculation stages
Choose the representation already present in the drawing, survey or specification: rise per 12, degrees, percentage slope or multiplier. These are dimensionless descriptions, so the converter needs context rather than a length unit.
The selected value is normalised to a rise-to-run ratio. Every other form is then calculated directly from that full-precision ratio. Copy all values creates a labelled text record; it does not copy an unlabeled rounded number.
Worked examples
Entering 4/12 produces ratio 0.3333333333, angle 18.434949°, percentage 33.333333% and multiplier 1.054092553. Converting the unrounded ratio back produces the original pitch.
Entering 30° produces ratio 0.5773502692, rise 6.928203/12, percentage 57.735027% and multiplier 1.154700538. This is not the same as a 30 percent slope, which is about 16.699°.
Errors, limits and responsible use
Rise per 12 and percentage must be non-negative. Degrees must be from zero to below 90. A multiplier must be at least 1. Values producing a non-finite tangent are rejected. Copying displayed figures preserves labels but not hidden precision.
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
- Why do converted values not round-trip exactly?
- A displayed value is rounded for reading. Re-entering it discards digits retained by the original calculation.
- Is percentage the same as degrees?
- No. Percentage is rise divided by run times 100; degrees use the arctangent of that ratio.
- What does multiplier 1 mean?
- It is the geometric factor for zero rise: slope length equals horizontal run.
- Can I enter a ratio other than per 12?
- Scale it first or use the pitch calculator with the original rise and run.
- What should I copy into a record?
- Keep the source representation, converted values, rounding note and calculation version together.
Continue the calculation
Pitch terminology provides the next explanation; Validation register
Identify the source convention first
Choose the representation actually supplied by the drawing, instrument or specification. Rise per 12 means vertical rise for twelve horizontal units. Degrees measure angle above horizontal. Percentage is one hundred times rise divided by run. The multiplier compares sloping length with horizontal run. A number without its convention is incomplete: 30 percent, 30 degrees and 3/12 describe three different inclinations.
Retain the original form in the job record before converting it. If a drawing says 22.5 degrees, preserve that source value even if the next calculation uses the derived ratio. This makes later checking possible and prevents a rounded converted value from being mistaken for a measurement. Do not infer pitch from a roof-style name or a perspective photograph when reliable geometry is unavailable.
Check conversions with the underlying ratio
Every conversion passes through rise divided by horizontal run. For 6/12, the ratio is 0.5; percentage is 50, angle is atan(0.5), about 26.565 degrees, and multiplier is √1.25, about 1.118034. For 45 degrees, tangent gives ratio 1, producing 12/12, 100 percent and multiplier √2. Checking one ratio-based identity is more reliable than comparing two rounded chart entries.
Repeated conversions should begin from the stored full-precision value. Retyping 26.57 degrees and then converting that displayed result back to rise per 12 introduces a small difference from the original 6/12. RoofFigured rounds only the presentation. Use the original measurement or stored ratio for downstream work and treat the displayed digits as a readable summary.
Use the converted form for communication, not approval
Select the form that best fits the next task: degrees for an angular comparison, rise per 12 for common US communication, percentage for some specifications, or multiplier for supported line and area calculations. Converting the label does not add information about the plane boundary, measurement accuracy or building. Keep the plane name, source and date beside the value.
A converted pitch does not confirm product suitability, drainage, structural capacity or code compliance. Those decisions require their governing documents and competent review. If the source convention remains ambiguous, stop and resolve it rather than choosing the representation that gives the most plausible-looking roof. The calculator can translate known geometry but cannot determine what an undocumented number was intended to mean.