Calculated
Roof Pitch Calculator
Sign up to favourite this calculatorConvert between X:12 roof pitch, degrees and slope percentage and estimate common rafter length from the measurements you know. Pitch is vertical rise over horizontal run; rafter length is before cuts or deductions.
Check the highlighted field to calculate the roof pitch.
Based on rise/run geometry and assumptions entered. Rafter length is common-rafter geometric length before ridge, birdsmouth, plumb-cut or other framing deductions.
Roof pitch
Roof angle
Slope percentage
Common rafter length (no overhang)
| Measurement | Value |
|---|---|
| Rise | 1.5 m |
| Horizontal run | 3 m |
| Rise:run ratio | 0.5 1:2 |
| Pitch (X:12) | 6:12 |
| Angle | 26.565° |
| Slope percentage | 50% |
| Rafter multiplier | 1.118 |
| Common rafter length (no overhang) | 3.3541 m |
| Horizontal overhang | |
| Common rafter length (with overhang) |
Formula used
rafter multiplier = √(1 + slope²) = √(1 + 0.5²) = 1.118
rafter length = run × multiplier = 3 m × 1.118 = 3.3541 m
This calculator gives roof geometry only. It does not produce a structural design, roof layout, cutting list, wind/snow-load assessment, building-regulation check, material specification or installation instruction. A rafter figure here is geometric length before cuts or framing deductions — never a cut length or a timber length to buy.
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Assumptions and limits
- An estimate from the numbers you entered, for guidance only. It is not financial, tax or medical advice.
- Calculator version 1, last updated 25 October 2026.
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How to use this calculator
- Choose which measurements you know: rise and run, pitch ratio and run, angle and run, or building span and ridge rise.
- Choose Metric or Imperial units.
- Enter the measurements for the mode you picked.
- Optionally enter a horizontal overhang for an extended rafter length.
- Read the pitch, angle, slope percentage and common rafter length, which update as you type.
What do I need to enter to find roof pitch?
- What do you know? — Rise and run, Pitch ratio and run, Angle and run, or Building span and ridge rise. It decides which fields show.
- Measurement units — Metric (mm, cm, m) or Imperial (ft, in). Each length has its own unit dropdown.
- Rise and horizontal run — the vertical and horizontal distances, each above zero and no more than 100 m.
- Pitch — the X in X:12, above 0 and up to 100.
- Roof angle — degrees, above 0 and below 90.
- Total building span and ridge rise — for a symmetrical gable, the run is taken as half the span.
- Horizontal overhang (optional) — how far the rafter projects past the wall plate, measured horizontally. Leave at zero for none.
What do the results show?
- Roof pitch, roof angle and slope percentage — the same slope as X:12, degrees and a percentage.
- Common rafter length — the geometric length along the slope, with the overhang included when you enter one.
- Breakdown table — rise, run, the rise:run ratio, rafter multiplier and the rafter length without overhang, plus the overhang when set.
- Working — the formula steps with your numbers, and any warnings about unusual values.
How is roof pitch calculated from rise and run?
Roof pitch is the ratio of vertical rise to horizontal run. Dividing rise by run gives the slope ratio, which converts directly into every other way of describing the same slope: an X:12 pitch, an angle in degrees, and a slope percentage.
slope ratio = rise ÷ run
- pitch (X:12) = slope ratio × 12
- angle (degrees) = atan(slope ratio) × 180 ÷ π
- slope percentage = slope ratio × 100
- rafter multiplier = √(1 + slope ratio²)
- rafter length = run × rafter multiplier = √(rise² + run²)
Example: a 1.5 m rise over a 3 m run
- Slope ratio = 1.5 ÷ 3 = 0.5.
- Pitch = 0.5 × 12 = 6:12.
- Angle = atan(0.5) ≈ 26.57°.
- Slope percentage = 0.5 × 100 = 50%.
- Rafter multiplier = √(1 + 0.5²) ≈ 1.118.
- Rafter length = 3 × 1.118 ≈ 3.3541 m, the same as √(1.5² + 3²).
Are pitch, degrees and percentage the same slope?
Yes — X:12 pitch, degrees and slope percentage all describe the identical slope, just in different units. A 6:12 pitch is a slope ratio of 0.5, which is the same slope as an angle of 26.57° and a slope percentage of 50%. Converting between them never changes the roof's actual steepness, only how it is expressed. The rafter multiplier — √(1 + slope ratio²) — is what turns a horizontal run into a sloped rafter length for that same slope.
How is common rafter length calculated?
The rise, run and sloped rafter form a right triangle, so the rafter length follows Pythagoras' theorem directly: rafter length = √(rise² + run²) — see the Pythagorean Theorem Calculator for the general case. This is the same as multiplying the run by the rafter multiplier. The result is the common-rafter geometric length from the wall plate to the ridge centreline — before ridge board thickness, birdsmouth, plumb or tail cuts, or any other framing deduction. If you enter a horizontal overhang, the calculator also shows this length extended by that horizontal projection past the wall plate.
Standard roof pitch reference table
Common X:12 roof pitches with their equivalent angle, slope percentage and rafter multiplier. This is a geometry reference only — it does not indicate which pitch suits a given material, climate or building type.
| Pitch (X:12) | Angle | Slope percentage | Rafter multiplier |
|---|---|---|---|
| 1:12 | 4.764° | 8.33% | 1.003 |
| 2:12 | 9.462° | 16.67% | 1.014 |
| 3:12 | 14.036° | 25% | 1.031 |
| 4:12 | 18.435° | 33.33% | 1.054 |
| 5:12 | 22.62° | 41.67% | 1.083 |
| 6:12 | 26.565° | 50% | 1.118 |
| 7:12 | 30.256° | 58.33% | 1.158 |
| 8:12 | 33.69° | 66.67% | 1.202 |
| 9:12 | 36.87° | 75% | 1.250 |
| 10:12 | 39.806° | 83.33% | 1.302 |
| 12:12 | 45° | 100% | 1.414 |
| 16:12 | 53.13° | 133.33% | 1.667 |
What this calculator does not cover
This calculator estimates roof geometry only, from the measurements and assumptions entered. It does not provide a structural design, roof layout, cutting list, wind or snow-load assessment, building-regulation check, material specification or installation instruction. The "building span and ridge rise" mode assumes a symmetrical, two-sided gable roof with the ridge centered over the span — for an offset ridge, a lean-to, a hip, a valley or an irregular roof, measure the rise and run for the individual rafter line instead. Check drawings, manufacturer guidance and local professional requirements before cutting or building.
Frequently asked questions
What does a 6:12 roof pitch mean?
A 6:12 pitch means the roof rises 6 units for every 12 units of horizontal run — a slope ratio of 0.5, an angle of about 26.57°, and a slope of 50%. The "12" is a US roofing convention based on one foot (12 inches) of run, but the ratio and the angle it describes are the same anywhere.
How do I calculate roof pitch in degrees?
Divide the rise by the run to get the slope ratio, then take the inverse tangent (arctan) of that ratio and convert from radians to degrees. For a 1.5 m rise over a 3 m run, the ratio is 0.5 and the angle is atan(0.5) ≈ 26.57°.
How do I calculate rafter length from roof pitch?
Find the rafter multiplier — the square root of (1 + slope ratio²) — then multiply it by the horizontal run. This is the same as using Pythagoras’ theorem directly on the rise and run: rafter length = √(rise² + run²). The result is the common-rafter geometric length from the wall plate to the ridge centreline, before any cuts or framing deductions.
What is the difference between roof pitch and roof angle?
Pitch (X:12) and angle (degrees) describe the same slope in different units. Pitch is a ratio of rise to a fixed 12 units of run, commonly used in US framing. Angle is measured directly from horizontal, in degrees. A 6:12 pitch and a 26.57° angle describe an identical slope.
What is the difference between roof pitch and slope percentage?
Slope percentage is the rise-to-run ratio multiplied by 100. A 6:12 pitch has a ratio of 0.5, so its slope percentage is 50%. Percentage grade is common in civil and drainage work; X:12 pitch and degrees are more common in roof framing.
Does the rafter length include the overhang?
Only if you enter one. The calculator always shows the common rafter length from the wall plate to the ridge centreline. If you enter a horizontal overhang, it also shows an extended rafter length that includes that horizontal projection past the wall plate — still a geometric length, not a cut length.
Can I use the total building width instead of one side’s run?
Yes — use the "Building span and ridge rise" mode. Enter the full building span and the ridge rise, and the calculator halves the span to get the run for a symmetrical, centered gable roof. For an offset ridge, a lean-to, a hip, a valley or an irregular roof, measure the rise and run for the individual rafter line instead.
Does this calculator size rafters or check building codes?
No. It calculates geometry only — pitch, angle, slope percentage and a geometric rafter length. It does not size lumber, check span tables, assess wind or snow loads, check building regulations, or account for birdsmouth, ridge, plumb or tail cuts. Check drawings, manufacturer span tables and local building requirements before cutting or building.
Why is my rafter length different from the actual timber I need to buy?
The rafter length here is the geometric distance from the wall plate to the ridge centreline (plus any overhang you enter), following the roof slope. Real timber lengths also depend on the ridge board thickness, birdsmouth and tail cuts, and standard timber lengths available — all of which reduce or round the geometric length differently. Use this figure as a starting geometry, not a cutting list.
Last updated 25 October 2026.