The geometric line
With run 4 m and pitch 6/12, rise is 2 m and the diagonal is √(4² + 2²), or 4.472135955 m. The same answer is run multiplied by the 1.118033989 slope factor.
Ridge thickness and overhang may change the horizontal line used for a particular record. Keep them explicit and confirm the required endpoints.
Where the calculation stops
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.
Member size, species, grade, loads, connections, cuts and code compliance require competent design and project-specific information.
Roof work can cause serious injury. Do not climb onto a roof merely to collect inputs. Prefer drawings, ground-level measurements, accessible interior information or dimensions supplied by a competent professional.
Detailed field guide
The line derivation starts with run and rise. At 4 m run and 6/12, rise is 2 m; √(4² + 2²) is 4.472136 m. Multiplying run by factor 1.118033989 gives the same check.
A ridge deduction changes the horizontal endpoint before slope conversion. Horizontal eaves overhang extends it. Neither value represents a distance already measured along the rafter.
The ideal line omits timber depth, bearing seats, plumb and tail cuts, ridge connection, fascia treatment and fabrication tolerance. Adding an arbitrary allowance would hide these project-specific decisions.
Structural adequacy depends on loads, span, spacing, species, grade, section, restraint, connections and applicable rules. A geometric answer cannot approve any of them.
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.
Define the ideal line
The calculated slope line joins the selected horizontal endpoints of a right triangle. For run r and ratio q, rise is rq and the line is r√(1+q²). This is a geometric reference only; it is not automatically the top edge, centreline or purchasable length of a physical member.
Apply horizontal changes first
A ridge thickness entered in the calculator is treated as a horizontal thickness and half is deducted from each symmetric run. A horizontal eaves overhang is then added. The adjusted run is converted to a slope line once, avoiding the common error of mixing horizontal and along-slope allowances.
Keep fabrication outside the formula
Bearing seats, birdsmouths, plumb cuts, fascia details, member depth and saw tolerance depend on the actual assembly. Adding a generic number would conceal those decisions. Preserve the ideal line and let the competent designer or fabricator establish the project-specific stock and cut dimensions.
Do not infer structural adequacy
Two members with the same geometric length can have very different capacity because of loading, species, grade, section, spacing, restraint and connection details. RoofFigured performs no load path or code check. Structural selection belongs to the governing design process.
Define the geometric line before naming a member
The calculator’s common-rafter result is the hypotenuse of a right triangle whose base is the selected horizontal run and whose rise follows the selected pitch. It is an ideal reference line between stated endpoints. A physical rafter has depth, bearing, cuts and connections, so its required stock length and fabrication dimensions are not automatically equal to that ideal line. Write down the line’s endpoints before calculating—for example, “outside wall reference to near ridge face”—and keep that description with the result.
For a 4 m horizontal run at 6/12, rise is 2 m and the ideal line is √(4² + 2²), or about 4.472136 m. The equivalent calculation is run × √(1 + 0.5²). These two methods should agree before display rounding. If they do not, check whether the supplied pitch used horizontal run, whether the units match and whether an adjustment was included twice. Agreement validates the arithmetic model, not the field measurements or structural design.
Apply horizontal adjustments in a traceable order
Where the selected span is measured between outside wall faces, a centred ridge thickness may require half its horizontal thickness to be removed from each symmetric side. A horizontal eaves projection may then be added. Calculate the adjusted horizontal run first and apply the pitch factor once. Do not add an along-slope overhang to a field that expects a horizontal projection. At 6/12, 300 mm horizontally corresponds to about 335 mm along the slope, so confusing the two directions creates a material difference.
Not every drawing uses the same reference. A run dimension may already terminate at the ridge face or eaves edge, in which case another adjustment would be wrong. Keep the unadjusted measurement, each adjustment and the final run as separate lines in the job record. This makes it possible to remove or revise one assumption without reconstructing the entire calculation from a rounded final length.
Know what the right triangle cannot decide
Common-rafter geometry does not determine species, grade, section, spacing, restraint, loading, deflection, bearing or connection capacity. It also does not provide a birdsmouth, plumb cut, seat cut or fascia detail. Those decisions depend on the actual assembly and governing design process. Two roofs with identical span and pitch can require different members because their loads and supports differ. Do not describe a geometric result as a safe, compliant or ready-to-cut rafter length.
Use the result as one checked dimension within a larger professional record. Compare it with the controlling drawing, confirm the endpoint convention and keep the original run and pitch visible. If the roof is asymmetric, intersecting, curved or otherwise outside the supported simple triangle, stop rather than adapting the formula silently. A competent designer or fabricator should resolve the physical member and detail where the ideal line no longer represents the required work.
Worked line record with independent checks
Take a centred gable whose outside-wall span is 7.2 m and pitch is 5/12. The base run is 3.6 m and the rise over that run is 1.5 m. Pythagoras gives √(3.6² + 1.5²) = 3.9 m for the unadjusted ideal line. The factor method uses √(1 + (5/12)²) = 1.083333333 and also gives 3.9 m. This exact 5–12–13 relationship, scaled by 0.3, is a useful fixture for checking that span was halved once and pitch was interpreted as rise over horizontal run.
If the line should extend 0.24 m horizontally beyond the wall and terminate 0.015 m short of the ridge centreline, record adjusted run 3.825 m. At the same pitch, the ideal adjusted line is about 4.14375 m. Do not simply add 0.225 m to the original 3.9 m, because the adjustments were stated horizontally and must be transformed by the slope factor. Keep both line results: the first checks the base triangle, while the second documents the chosen endpoints. Neither number specifies cuts, bearing or stock length.
Final verification before use
For handover, retain the base horizontal run, pitch source, any ridge deduction, any horizontal overhang, adjusted run, unrounded factor and ideal line. Add an explicit statement that cuts, bearing and structural adequacy are excluded. A reviewer can then reproduce the geometry without mistaking it for a fabrication schedule. If a physical member length is required, route that decision to the responsible design or trade process.
Check the record by recalculating rise from adjusted run × ratio and applying Pythagoras to the resulting legs. Compare that line with adjusted run × factor. Use the same endpoints for both methods and avoid inserting physical allowances into only one path. If they agree, the arithmetic is consistent. The next review still needs to confirm that the endpoints, ridge convention and overhang direction match the project information.