Use this rafter length calculator to find the length of a common roof rafter. Enter the rafter run and roof pitch, the building span and pitch, or the roof rise and run, and the calculator returns the rafter length along with the roof rise, pitch, roof angle and slope factor.
Rafter Length Calculator
Calculate common rafter length, roof rise, roof angle, slope factor, and rafter length including overhang.
Rafter Length
Span Calculation
Rafter Length Formula
When run and pitch are known, first calculate the roof rise:
Then calculate the common rafter length:
The slope factor is:
Therefore, the same rafter length can also be calculated as:
For an overhang, the calculator converts the horizontal overhang to its corresponding sloped length using the same slope factor.
Add a horizontal eave overhang and it is converted to its sloped length and included in the total rafter length. Span mode can also deduct for a ridge board. The calculator works in imperial (decimal feet, with the ridge board in inches) or metric (metres, with the ridge board in millimetres). Formulas, worked examples, a rafter length table by pitch and common mistakes are covered below.
What Is Rafter Length?
A common rafter runs at right angles to the wall plate, from the plate up to the ridge. Seen from the side, it forms the sloping side (the hypotenuse) of a right triangle: the horizontal run is the base and the roof rise is the height. Rafter length is the length of that sloping line.
The result is a geometric line length. The final cut length of a board also depends on the ridge, birdsmouth, tail and fascia details of your framing, which are covered in the accuracy section below.
How to Use the Rafter Length Calculator
- Choose units. Imperial uses decimal feet for dimensions and inches for the ridge board; metric uses metres and millimetres. Switching units converts any values already entered.
- Choose a method. Run + Pitch if you know the rafter run, Span + Pitch if you know the building width, or Rise + Run if you know the rise but not the pitch.
- Enter the required values. Pitch is entered as rise per 12 units of run, so a 6:12 roof is entered as 6.
- Add a horizontal overhang if the rafter extends past the wall. Enter 0 for none.
- Select Calculate Rafter Length. Open Advanced Rafter Calculations for the complementary angle, rise per 12 and length per run unit.
Rafter Length Formula
Roof Rise From Pitch
Rise = Run × (Pitch ÷ 12)
With a 12 ft run and a 6:12 pitch: Rise = 12 × (6 ÷ 12) = 6 ft.
Rafter Length From Run and Rise
Rafter Length = √(Run² + Rise²)
Continuing the example: √(12² + 6²) = √180 ≈ 13.416 ft. That is the rafter's line length before any overhang.
Slope Factor
Slope Factor = √[1 + (Pitch ÷ 12)²]
The slope factor is the sloped length per unit of horizontal run, so Rafter Length = Run × Slope Factor. For 6:12 the factor is about 1.118: every 1 ft of run needs about 1.118 ft of rafter. In the calculator it appears as both Slope Factor and Length per Run Unit.
Calculation Methods
Run + Pitch
Use this when you know the horizontal run of one common rafter and the pitch. The calculator finds the rise from the pitch, then the rafter length.
Span + Pitch
Use this for a symmetrical gable roof when you know the full building span. Each rafter covers half the span. If you enter a ridge board thickness, the calculator deducts half of it from the half-span, because the ridge is centred on the building and each rafter stops at its face:
Adjusted Run = (Span ÷ 2) − (Ridge Thickness ÷ 2)
For a 24 ft span, 6:12 pitch and 1.5 in ridge board: half span = 12 ft, ridge adjustment = 0.75 in = 0.0625 ft, adjusted run = 11.9375 ft, and rafter length = 11.9375 × 1.118 ≈ 13.347 ft. Without a ridge board the rafter would be 13.416 ft. The Span Calculation panel in the results shows each step.
This method assumes a symmetrical gable roof. It does not apply to an offset ridge, unequal pitches or other irregular framing.
Rise + Run
Use this when you have measured the rise and run but do not know the pitch. The calculator works out the pitch first:
Pitch = (Rise ÷ Run) × 12
A 6 ft rise over a 12 ft run gives (6 ÷ 12) × 12 = 6:12 and a rafter length of about 13.416 ft. A rise of 0 is accepted and gives a flat 0:12 result.
Rafter Length With Overhang
Enter the overhang as a horizontal distance measured out from the wall. Adding it to the rafter length directly would understate the length, because the rafter tail slopes too.
Sloped Overhang
Sloped Overhang = Horizontal Overhang × Slope Factor
Total Rafter Length
Total Rafter Length = Base Rafter Length + Sloped Overhang
For a 10 ft run, 4:12 pitch and 2 ft horizontal overhang: slope factor ≈ 1.0541, base length ≈ 10.541 ft, sloped overhang = 2 × 1.0541 ≈ 2.108 ft, so the total is about 12.649 ft.
Rafter Length by Roof Pitch
The table shows the rise, slope factor and rafter line length for a 12 ft run at common pitches, with no overhang. For any other run, multiply the run by the slope factor.
| Pitch | Rise (12 ft run) | Slope factor | Rafter length | Roof angle |
|---|---|---|---|---|
| 3:12 | 3 ft | 1.0308 | 12.369 ft | 14.04° |
| 4:12 | 4 ft | 1.0541 | 12.649 ft | 18.43° |
| 5:12 | 5 ft | 1.0833 | 13.000 ft | 22.62° |
| 6:12 | 6 ft | 1.1180 | 13.416 ft | 26.57° |
| 7:12 | 7 ft | 1.1577 | 13.892 ft | 30.26° |
| 8:12 | 8 ft | 1.2019 | 14.422 ft | 33.69° |
| 9:12 | 9 ft | 1.2500 | 15.000 ft | 36.87° |
| 10:12 | 10 ft | 1.3017 | 15.620 ft | 39.81° |
| 12:12 | 12 ft | 1.4142 | 16.971 ft | 45.00° |
For the same run, a steeper pitch gives a longer rafter: 12.649 ft at 4:12, 13.416 ft at 6:12 and 14.422 ft at 8:12.
Roof Angle and Complementary Angle
Roof Angle
Roof Angle = arctan(Pitch ÷ 12)
This is the rafter's angle from level, shown as Roof Angle and as Rafter Angle From Level. A 6:12 roof is about 26.57°, so a 6:12 pitch is a ratio, not a 6° slope.
Complementary Angle
Complementary Angle = 90° − Roof Angle
This is the rafter's angle from vertical. It is 63.43° for a 6:12 roof. It is shown in the advanced results because some saw and layout setups reference angles from plumb rather than level.
What Does a 6:12 Roof Pitch Mean?
A 6:12 pitch rises 6 units for every 12 units of horizontal run: a 12 ft run rises 6 ft, and a 24 ft run rises 12 ft. The slope factor is about 1.118 and the roof angle about 26.57°.
Imperial and Metric Units
| Input or result | Imperial | Metric |
|---|---|---|
| Run, span, rise, overhang | Decimal feet (e.g. 12.5 ft) | Metres |
| Ridge board thickness | Inches | Millimetres |
| Pitch | Rise per 12 | Rise per 12 |
| Length results | Feet to 3 decimals | Metres to 3 decimals |
| Angles | Degrees | Degrees |
Imperial lengths are in decimal feet, so 12 ft 6 in is entered as 12.5. To read a result in inches, multiply the decimal part by 12: 13.416 ft is 13 ft 5 in (0.416 × 12 ≈ 4.99 in). Pitch stays as rise per 12 in both systems because it is a ratio.
Roof Span vs Rafter Run
The span is the full horizontal width across the building. The run is the horizontal distance one rafter covers. On a symmetrical gable roof, the run is half the span, less half the ridge thickness. Entering the full span as the run roughly doubles the result, so if you only know the building width, use Span + Pitch.
How Accurate Is a Rafter Length Calculator?
The result is mathematically exact for the geometry entered. The length you actually cut can still differ because of framing details the calculator does not model, including:
- The ridge-to-rafter connection, beyond the half-thickness deduction in Span mode
- Birdsmouth (seat cut) position and depth
- Tail length and the eave, fascia and subfascia details
- Plumb and seat cut allowances
- Material dimensions and the framing plans for the project
Treat the result as a dimensional planning figure, and check it against your drawings before cutting.
Common Mistakes When Calculating Rafter Length
- Using the full span as the run. A common rafter covers half the span on a symmetrical gable roof.
- Deducting the full ridge thickness. Each rafter loses only half the ridge thickness, not all of it.
- Adding the horizontal overhang directly. The overhang must be multiplied by the slope factor first.
- Entering feet and inches as a decimal. 12 ft 6 in is 12.5 ft, not 12.6 ft.
- Confusing pitch with angle. 6:12 is about 26.57°, not 6°.
Rafter Length Calculator FAQs
Formula Questions
What is the formula for rafter length?
Rafter Length = √(Run² + Rise²). If you know the pitch, find the rise first with Rise = Run × (Pitch ÷ 12), or use Rafter Length = Run × √[1 + (Pitch ÷ 12)²].
How long is a rafter on a 6:12 roof?
It depends on the run. Multiply the run by 1.118: a 12 ft run gives about 13.416 ft, and a 10 ft run about 11.180 ft, before any overhang.
How do I calculate rafter length from the span?
Halve the span, subtract half the ridge thickness if there is a ridge board, then multiply by the slope factor. The Span + Pitch mode does this automatically.
How much should I deduct for the ridge board?
Deduct half the ridge thickness from each rafter's run. For a 1.5 in ridge, that is 0.75 in (0.0625 ft) off the half-span.
Using the Calculator
Does the calculator include the overhang?
Yes. Enter the horizontal overhang and it is converted to a sloped length and added to the total rafter length. The base rafter length is shown separately.
Can I calculate rafter length in metres?
Yes. Select Metric and enter dimensions in metres and the ridge board in millimetres. Values already entered are converted when you switch.
Does the result include the birdsmouth cut?
No. The calculator gives the geometric line length. Birdsmouth, plumb cut and tail allowances depend on your framing design and are worked out separately.
Does this calculator size the rafter?
No. Rafter sizing depends on loads, lumber species and grade, spacing, span, deflection limits and the building requirements that apply to your project. This calculator only works out lengths and angles.