Quick answer
Rafter length = run × √(1 + (rise ÷ 12)²). For a 12 ft run at 6:12 pitch the level-cut length is 13.4164 ft.
Enter the horizontal run and the pitch (rise per 12 inches). The calculator returns the rafter length.
Related tools: Gutter Length Calculator: Total gutter length and number of sections from your eave lengths. Roofing Calculator: Roof surface area and roofing squares from the footprint and pitch. Roof Pitch Calculator: Roof pitch as rise per 12 inches, angle, slope percent and rafter length factor.
How to use the Rafter Length Calculator
- Enter horizontal run (ft) (above 0).
- Enter pitch (rise per 12 in run) (between 0 and 24). It starts at 6.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Horizontal run | A number, in ft | > 0 |
| Pitch (rise per 12 in run) | A number | > 0, ≤ 24, starts at 6 |
Formula and method
Formula
length = run × √(1 + (rise ÷ 12)²)
IEEE-754 double precision; shown to at most 6 decimal places.
Hypotenuse of the run/rise triangle; add overhang and cut allowances separately.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Horizontal run = 12; Pitch (rise per 12 in run) = 6.
| Result | Value |
|---|---|
| Rafter length | 13.4164 ft |
Example 2
Inputs: Horizontal run = 10; Pitch (rise per 12 in run) = 12.
| Result | Value |
|---|---|
| Rafter length | 14.1421 ft |
The first line is the headline result (rafter length). IEEE-754 double precision; shown to at most 6 decimal places.
The pitch factor
At 6:12, rafter length per foot of run is √(1 + 0.25) = 1.118. Multiplying the 12 ft run gives 13.416 ft, about 13 ft 5 in.
Overhang and cuts
The result is the level-cut length along the slope from the ridge to the outside wall line. Add the eave overhang along the slope, and the ridge board thickness reduces the length by half its thickness. Check the span with a rafter table.
How the result changes with horizontal run
Holding every other input at the first worked example, this table changes only horizontal run. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Horizontal run | Rafter length |
|---|---|
| 6 | 6.7082 ft |
| 12 | 13.4164 ft |
| 24 | 26.8328 ft |
| 48 | 53.6656 ft |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Horizontal run: entering "0" shows "Horizontal run must be greater than 0." beside that field and no result.
Choosing between the Rafter Length Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Gutter Length Calculator](/construction/gutter-length-calculator/) | length of each eave and section length | Total gutter length |
| [Roofing Calculator](/construction/roofing-calculator/) | building length, building width and roof pitch | Roof area |
| [Roof Pitch Calculator](/construction/roof-pitch-calculator/) | i know the and value | Pitch |
| [Roof Shingles Calculator](/construction/roof-shingles-calculator/) | roof area, bundles per square and waste allowance | Bundles needed |
| [Metal Roofing Calculator](/construction/metal-roofing-material-calculator/) | roof width to cover, panel coverage width and panel length | Panels needed |
Background: construction estimates
Material quantities are geometry plus a margin. Calculate the exact volume or area, add an allowance for waste, spillage, cuts and uneven ground (calculator pages commonly mention 5 to 10 percent, a rule of thumb that varies by material and job) and round up to whole units. One cubic yard is exactly 27 cubic feet.
Suppliers often have minimum order sizes and may charge for small loads, so confirm quantities, product yields and local code with your supplier or a qualified estimator before ordering.
Assumptions and limitations
- Level-cut length
Quantities are estimates. Add allowances for waste and site conditions, and follow local codes and a qualified professional's instructions for structural or safety-critical work.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for horizontal run to confirm this.
Frequently asked questions
What is run?
The horizontal distance from the wall to the ridge.
Does the pitch change the length?
Yes, a steeper pitch makes rafters longer.
Does it include the overhang?
No, add it separately.
What does the Rafter Length Calculator calculate?
Common rafter length from run and pitch. It returns Rafter length.
What formula does the Rafter Length Calculator use?
length = run × √(1 + (rise ÷ 12)²). Hypotenuse of the run/rise triangle; add overhang and cut allowances separately.
What do I need to enter in the rafter Length Calculator?
You enter Horizontal run (ft) and Pitch (rise per 12 in run).
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Level-cut length.
What is an example of a rafter Length result?
With horizontal run 12 and pitch (rise per 12 in run) 6, the rafter length is 13.4164 ft.
Can I rely on this calculator for a decision?
Quantities are estimates. Add allowances for waste and site conditions, and follow local codes and a qualified professional's instructions for structural or safety-critical work. For this calculator in particular: Level-cut length.
Related calculators
- Gutter Length Calculator — Total gutter length and number of sections from your eave lengths.
- Roofing Calculator — Roof surface area and roofing squares from the footprint and pitch.
- Roof Pitch Calculator — Roof pitch as rise per 12 inches, angle, slope percent and rafter length factor.
- Roof Shingles Calculator — Squares and bundles of shingles for a roof area.
- Metal Roofing Calculator — Number of metal roofing panels across a roof width.
- Roof Sheathing Calculator — Sheets of plywood or OSB for a roof area.
Sources
- OpenStax, University Physics Volume 1 (Rice University): mechanics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.