Calcady™
Home / Trade / Construction / Roof Pitch & Rafter Length

Roof Pitch & Rafter Length

Calculate the exact rafter length and roof rise based on your building span and roof pitch. Perfect for framing contractors and DIY builders.

Roof Pitch & Rafter Length Calculator

Roof framing geometry uses the Pythagorean theorem — the rafter is the hypotenuse of a right triangle formed by the run (horizontal) and rise (vertical). The pitch ratio P/12 defines the rise per foot of run. Total rafter length adds the overhang (eave) beyond the wall plate.

Common Roof Pitches

Outside of wall plate to outside

Rise (in) per 12 in of run

Beyond the wall plate (typ. 1.5ft)

Run = W / 2 = 24 / 2 = 12.0000 ft
Rise = Run × (P/12) = 12.0000 × (6/12) = 6.0000 ft
Base Rafter = √(Run² + Rise²) = √(144.0000 + 36.0000) = 13.4164 ft
Total Rafter = Base + Overhang = 13.4164 + 1.5 = 14.9164 ft
Pitch Angle = arctan(6.000/12.000) = 26.57°
Rise (H)
6.000
ft
Base Rafter
13.416
ft (wall to ridge)
Total Rafter
14.916
ft (incl. 1.5 ft overhang)
Pitch Angle
26.6°
Moderate — common residential
Rise in feet-inches
6′ 0″
Base Rafter in feet-inches
13′ 4″ 16/16″
Total Rafter in feet-inches
14′ 10″ 16/16″
Total Rafter Length by Span (P=6/12, Overhang=1.5 ft)
16 ft
10.444 ft
20 ft
12.680 ft
24 ft
14.916 ft
28 ft
17.152 ft
32 ft
19.389 ft
40 ft
23.861 ft

Practical Example

A contractor frames a 24-foot wide garage with a 6/12 pitch and 1.5-ft eave overhang.

Run = 24 / 2 = 12 ft
Rise = 12 × (6/12) = 6 ft
Base Rafter = √(12² + 6²) = √(144 + 36) = √180 = 13.416 ft
Total Rafter = 13.416 + 1.5 = 14.916 ft (14′ 11″)

The contractor orders 16-foot lumber (next standard length above 14.916), giving 1.1 ft of cutting waste per rafter. This calculation also tells them the ridge board will sit exactly 6 ft above the wall plate.

💡 Field Notes

  • Measuring Run precisely: The run must be measured from the outside edge of the top plate to the centerline of the ridge board — NOT the centerline of the building. Subtract half the ridge board thickness (typically ¾" for LVL or 1½" for dimensional lumber) from the calculated run before ordering lumber. Ignoring this causes an imperfect fit where both rafters meet at the ridge.
  • Rafter tables vs. calculator: Traditional framing squares have rafter length tables printed on them in inches per foot of run. A 6/12 pitch = 13.416 inches per foot of run. Multiply by run in feet to get base rafter in inches. This calculator matches that table exactly. For complex hip and valley rafters, the unit run increases to 17 (the diagonal of a 12×12 square).
  • Pitch and snow/wind loads: The pitch angle directly affects how the roof handles snow and wind. Pitches below 4/12 require special low-slope roofing membranes (not standard shingles) per most building codes. Pitches above 8/12 shed snow quickly but create serious fall hazards — OSHA requires roof brackets or safety harnesses above 6:12 for workers.
Email LinkText/SMSWhatsApp

What is Roof Framing Geometry and Trigonometry?

Roof framing is applied trigonometry — the rafter is the hypotenuse of the right triangle formed by the horizontal run and the vertical rise. The pitch notation P/12 (e.g., 6/12) means the roof rises P inches for every 12 inches of horizontal run. Getting this geometry correct determines lumber lengths, ridge board height, and the structural load path to the walls.

Mathematical Foundation

Roof Run
Run=W/2\text{Run} = W / 2
WW= Total building span from outside wall plate to outside wall plate.
Run\text{Run}= Half the span — the base of the roof triangle from wall plate to ridge centerline.
Roof Rise
H=Run×(P/12)H = \text{Run} \times (P / 12)
HH= Vertical height from the wall plate to the ridge (total rise).
P/12P/12= Pitch ratio. A 6/12 pitch rises 6 inches for every 12 inches of horizontal run.
Rafter Length (Pythagorean Theorem)
L=Run2+H2+OL = \sqrt{\text{Run}^2 + H^2} + O
LL= Total rafter length including overhang — the lumber length to purchase.
OO= Eave overhang projection beyond the wall plate (typically 1 to 2 feet residential).

Laws & Principles

  • Ridge Deduction: The run is NOT half the building width. It is half the building span minus half the ridge board thickness. A standard 2x ridge board is 1.5 inches thick, so each rafter must be shortened by 3/4 inch from the calculated run. Skipping this causes the ridge board to buckle outward.
  • OSHA Fall Protection: OSHA 29 CFR 1926.502 requires fall protection for workers on roofs steeper than 4/12 (18.4 degrees). At 6/12 (26.6 degrees), roof jacks are strongly recommended. At 10/12 and above, fall arrest systems or scaffolding are required.
  • Lumber Ordering Rule: Always round the total rafter length UP to the next standard lumber length (8, 10, 12, 14, 16, 18, 20 feet). A 14.92-ft rafter requires 16-ft stock.

Step-by-Step Example Walkthrough

" A framing contractor builds a 24-foot wide garage with a 6/12 pitch roof and 1.5-foot eave overhang. "

  1. 1. Run = 24 / 2 = 12 ft.
  2. 2. Rise = 12 x (6/12) = 6 ft.
  3. 3. Base rafter = sqrt(144 + 36) = sqrt(180) = 13.416 ft.
  4. 4. Add overhang: 13.416 + 1.5 = 14.916 ft total rafter.
  5. 5. Order lumber: next standard above 14.916 = 16-ft 2x8 or 2x10.
Final Result: Total rafter = 14.916 ft (14 ft 11 in). Order 16-ft lumber. Ridge sits 6 ft above the wall plate.

Quick Answer: How do you calculate rafter length from roof pitch?

Divide the building span by 2 to get the run. Multiply the run by the pitch ratio (pitch ÷ 12) to get the rise. Then apply the Pythagorean theorem: Rafter = √(run² + rise²). Add the eave overhang for the total lumber length. For a 24-ft span at 6/12 pitch with 1.5-ft overhang, the rafter is 14 ft 11 in — order 16-ft stock.

Rafter Length Equations

Run = Building Span ÷ 2

Rise = Run × (Pitch ÷ 12)

Rafter = √(Run² + Rise²) + Overhang

Ridge deduction: Subtract half the ridge board thickness (typically 3/4 inch for a 2x ridge) from the run before calculating the rafter length. This ensures the rafter bears flat against the ridge board.

Rafter Multiplier by Pitch

Roof Pitch Angle Multiplier per ft Run Rise per 12" Run
3/12 14.0° 1.031 3"
4/12 18.4° 1.054 4"
6/12 26.6° 1.118 6"
8/12 33.7° 1.202 8"
12/12 45.0° 1.414 12"

The multiplier is the rafter length per foot of horizontal run. For a 12-ft run at 6/12 pitch: 12 x 1.118 = 13.416 ft rafter length (before overhang). At 12/12 (45 degrees), the rafter is 41.4% longer than the run.

Rafter Calculation Mistakes

The Forgotten Ridge Deduction

A framer calculates rafters using the full run (half the span) without subtracting half the ridge board thickness. On a 30-ft span, each rafter is 3/4 inch too long. When both rafters meet at the ridge board, they push each other 3/4 inch past center on each side. The ridge board bows outward under the combined 1.5-inch excess, creating a visible hump in the ridge line visible from the street.

The Wrong Lumber Length

A contractor calculates a 14.9-ft rafter and orders 14-ft lumber to stay under budget. The lumber is 11 inches too short. The birdsmouth cut and tail cut cannot both fit on the same piece. 36 rafters worth of 14-ft stock become scrap. The project delays 3 days waiting for 16-ft lumber delivery, and the crew is paid to stand idle. Always round UP to the next standard length.

Rafter Framing Best Practices

Do This

  • ✓Cut and test a pattern rafter. Calculate, cut one rafter, and test-fit it against the ridge and wall plate before cutting the rest. Verify the birdsmouth seats flat on the plate and the plumb cut sits flush against the ridge board.
  • ✓Crown every rafter up. Sight down each piece of lumber and place the natural bow (crown) facing upward. Under roof load, the crown flattens. If placed crown-down, the rafter sags into a permanent dip.

Avoid This

  • ✗Don't confuse span with run. The span is the full wall-to-wall distance. The run is half the span. Using the full span in the formula doubles the calculated rafter length — a costly and dangerous mistake.
  • ✗Don't skip the overhang in your lumber order. The calculator gives the structural rafter length to the ridge. The overhang (typically 12 to 24 inches) must be added before ordering lumber. Forgetting it means every rafter is too short.

Frequently Asked Questions

What is the difference between span and run?

The span is the total horizontal distance between the outside faces of opposite wall plates. The run is half the span — the horizontal distance from one wall plate to the centerline of the ridge. For a symmetrical gable roof, run = span / 2. Using the full span instead of the run in the rafter formula will double your calculated rafter length.

What is a rafter multiplier?

The rafter multiplier is the rafter length per foot of horizontal run. It equals the square root of (1 + (pitch/12) squared). For a 6/12 pitch, the multiplier is sqrt(1 + 0.25) = 1.118. Multiply this by the run in feet to get the base rafter length before adding the overhang. This shortcut is printed on many framing squares.

How do I account for the ridge board thickness?

Subtract half the ridge board thickness from the run before calculating the rafter length. A standard 2x ridge is 1.5 inches thick, so deduct 0.75 inches (3/4 inch) from the run. For a ridge beam (such as a 4x or 6x), deduct half its actual thickness. This ensures the rafter plumb cut bears flat against the ridge face without the two opposing rafters pushing past each other.

What standard lumber lengths are available for rafters?

Standard lumber lengths are sold in 2-foot increments: 8, 10, 12, 14, 16, 18, and 20 feet. Lengths over 20 feet require special ordering (engineered lumber, LVLs, or finger-jointed stock). Always round your calculated total rafter length (including overhang) UP to the next standard length. The excess becomes cutting waste from the birdsmouth and tail cuts.

Related Calculators