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