Roof Pitch Calculator
Rise over run into angle, grade, multiplier and rafter length — one law, four ways to say it.
Roof Pitch Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Straight gable geometry — hips and valleys multiply runs their own way.
- No birdsmouth depth or stock-length selection.
- Overhang assumed on the same plane.
In short: A 6/12 roof: 26.565°, 50% grade, multiplier 1.118034. Half-width 12 ft with a 1.5-ft overhang: 15.093459 ft of common rafter; ridge 6 ft above the plates.
Formula
pitch x/12 = (rise ÷ run) × 12
angle = arctan(slope); grade = slope × 100%
multiplier = √(1 + slope²) = sec θ
rafter = (half-width + overhang) × multiplier
[('x/12', 'inches of rise per foot of run'), ('sec θ', 'the multiplier — plan to slope area'), ('overhang', 'rides the slope: add before multiplying'), ('drop ÷ 2', 'the 24-in level’s field answer')]
Worked Example
- Slope the rise over the run.
- Name it: x/12, degrees, grade percent.
- Multiply: √(1+slope²) for area work.
- Rafter: run plus overhang, times the multiplier.
- Ridge height from the rise per foot of run.
The 6/12 roof: 26.565°, 50% grade, multiplier 1.118034. Half-width 12 ft + 1.5-ft overhang: rafter 15.093459 ft; ridge 6.00 ft above the plates. The 24-in level reads it in the field: 12-in drop = 6/12.
Strengths & Limits Of This Model
Where this engine is strong
- Four languages of one slope, agreeing
- Multiplier shared to 6 decimals with the Roofing page
- The level trick as a field card
Where it stops
- Gable-only geometry
- No cut-sheet detail
Practical Use Cases
Material orders
The multiplier the roofing page consumes.
Rafter cuts
Angle and length per stick.
Existing roofs
Level trick to x/12 in the field.
Truss orders
Degrees the plant actually wants.
Dormer planning
Tie-ins at matching pitch.
Methodology & Editorial Standards
One slope, four expressions: x/12 normalized from any rise/run, arctan degrees, grade percent, and the secant multiplier √(1+slope²). Rafters multiply (half-width + overhang) — the overhang rides the slope, not a flat addition. Ridge height is rise/run × half-width. Zero run or negative rise is refused.
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Roof Pitch Calculator — 10 Expert FAQs
10 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
What does 6/12 pitch mean?
Six inches of rise for every twelve inches of run — a 26.565° slope, 50% grade, area multiplier 1.118034. The steepest pitch most homeowners can walk safely without staging.
How do I measure pitch on an existing roof?
Hold a 24-in level against the rafter or roof plane, measure straight down from the level’s far end, divide by two — 12 in of drop over 24 in is 6/12. The level doubles the run; halve the drop.
How do I convert pitch to degrees?
Arctan of rise over run: 4/12 is 18.435°, 6/12 is 26.565°, 8/12 is 33.690°, 12/12 is exactly 45°. The angle is what the saw and the truss order want.
What is the pitch multiplier?
√(1+slope²) — the number that turns floor footprint into roof surface. Multiply the plan by 1.054 at 4/12, 1.202 at 8/12, 1.414 at 12/12 before ordering anything measured in area.
How long is the rafter?
Horizontal run (half the building width) plus overhang, times the multiplier — 12 ft plus 1.5 at 6/12 is 15.093459 ft. Then the birdsmouth and ridge cuts take their inches; order the longer stick.
How high is the ridge?
Rise per run × half-width: at 6/12 across a 24-ft building, the ridge stands 6 ft above the plates. It is the fastest sanity check on a framing plan.
What is grade versus pitch?
Same ratio, different tribe: grade is slope × 100 (50% at 6/12) and rules civil site plans; pitch is x/12 and rules roofs. Neither changes the geometry.
How flat can a shingle roof be?
Shingles want 2/12 minimum with double underlayment below 4/12 — below that, membranes and metal own the roof. The multiplier law does not care; the warranty does.
Does overhang change the multiplier?
No — the multiplier is the slope’s own property. The overhang adds RUN, so it rides the multiplier: add it to the half-width before multiplying, exactly as the rafter card shows.
Why does 12/12 show 1.414?
A 45-degree slope’s hypotenuse is √2 × the run — every foot of plan becomes 1.414214 ft of roof. Steep roofs wear their slope in material; that is the multiplier talking.