Do I need a building permit for roof repairs or replacement?

Most US jurisdictions require a permit for structural roof work — including rafter replacement, major repairs, or changes to roof framing. Re-roofing (replacing shingles only) may not require a permit in some areas. Always check with your local building department. Working without a required permit can result in fines, required demolition, and insurance complications.

How accurate is this rafter calculator?

This calculator uses the standard Pythagorean theorem for common rafter length calculation and industry-standard formulas for board feet and rafter count. It is accurate for gable roof common rafters. For hip roofs, valley roofs, or complex geometries, consult a licensed contractor or structural engineer.

Rafter Calculator 2026 | Calculate Rafter Length, Pitch & Lumber Needed

Q: How do you calculate rafter length?

Rafter length is calculated using the Pythagorean theorem: Rafter Length = √(Rise² + Run²). The rise equals the run × pitch (rise per 12 inches ÷ 12). Add the overhang length to get the total rafter cut length from ridge to tail. Example: 15-foot run, 6/12 pitch — Rise = 15 × (6/12) = 7.5 ft. Rafter = √(15² + 7.5²) = √(225 + 56.25) = √281.25 = 16.77 ft.

Q: What is roof pitch and how do I measure it?

Roof pitch describes how steep a roof is — expressed as rise over a 12-inch run (e.g., 6/12 = 6 inches rise per 12 inches horizontal). To measure an existing roof pitch, place a 12-inch level horizontally on the roof surface, hold it level, and measure the vertical distance from the level's end to the roof surface. That measurement is your rise.

Q: What is the most common roof pitch in the US?

The most common residential roof pitches in the United States are 4/12 and 6/12. A 4/12 pitch is considered a low-slope roof and is common in warmer, drier climates. A 6/12 pitch is the most popular across the country — balanced between water runoff efficiency and rafter lumber cost. Steeper pitches (8/12–12/12) are common in high-snow regions like New England, Colorado, and the Pacific Northwest.

Q: How many rafters do I need?

For 16-inch on-center spacing: Number of rafters per side = (Building length in inches ÷ 16) + 1. For 24-inch spacing: (Building length in inches ÷ 24) + 1. Double the count for both sides of the roof. Add 2 for gable end rafters. Always round up and add 10% for waste and cuts.

Q: What size lumber should I use for rafters?

Rafter sizing depends on span, spacing, species, and load. Common guidelines for 16-inch spacing (Southern Yellow Pine): 2×6 up to 14-foot span, 2×8 up to 18-foot span, 2×10 up to 22-foot span, 2×12 up to 26-foot span. Always consult your local building code and a structural engineer for snow-load regions or unusual spans.

Q: What is a ridge board and how long should it be?

The ridge board runs horizontally at the peak of the roof, connecting the tops of opposing rafters. Its length equals the building length minus twice the thickness of the gable end rafters. For most gable roofs, the ridge board is the same length as the building. It should be one size larger than the rafter lumber (e.g., if rafters are 2×8, use a 2×10 or 2×12 ridge board).

Q: What is the difference between common, hip, valley, and jack rafters?

Common rafters run perpendicular from the wall plate to the ridge board. Hip rafters run diagonally from a corner to the ridge on a hip roof. Valley rafters run diagonally in the interior angle where two roof sections meet. Jack rafters are shorter rafters that run from the wall plate to a hip or valley rafter. This calculator focuses on common rafter calculations for gable roofs.

Reviewed by the AmericaCalculator.com editorial team 🕐 Last Updated: August 2026

Calculate the exact rafter length, ridge board length, number of rafters needed, board feet of lumber, and estimated material cost for any gable roof. Enter your run, pitch, spacing, and overhang — and get instant results. Based on the standard Pythagorean theorem formula used by professional framers across the US.

Run — Feet

Run — Inches

Run = half the building width (span ÷ 2). For a 30-ft wide building, run = 15 ft.

Roof Pitch (rise per 12" run)

Overhang (inches)

Eave overhang past wall plate

Spacing (inches O.C.)

Building Length (feet)

Lumber Size

Lumber Price ($/linear ft)

2026 avg: 2×8 ~$1.85/lf | 2×10 ~$2.20/lf | 2×12 ~$2.75/lf

Your Rafter Calculations

15 ft run, 4/12 pitch, 16" spacing, 40 ft building

Roof Cross-Section

15.62 ft Rafter Length (ridge to plate) + 12" overhang = 16.62 ft total cut

40 ft Ridge Board Length

62 Total Rafters (both sides)

820 Board Feet of Lumber

$1,516 Est. Lumber Cost

18.4° Rafter Angle (slope)

How to Use the Rafter Calculator

Enter the Run (half the building width) The "run" is the horizontal distance from the wall plate to the center ridge. It equals exactly half your total building width (span). For a 28-foot wide house, the run is 14 feet.
Select your roof pitch Pitch is expressed as rise per 12-inch run. A 6/12 pitch rises 6 inches for every foot of horizontal run. Common residential pitches are 4/12 to 8/12. Select from the dropdown or use our pitch chart below.
Enter overhang, spacing, and building length Overhang is how far the rafter extends past the wall plate (typical: 12–24 inches). Spacing is 16" or 24" on center. Building length determines how many rafters you need per side.
Select lumber size and enter price Common rafter sizes are 2×6, 2×8, 2×10, and 2×12. Your local lumber yard can give you the current price per linear foot. The 2026 national average for 2×8 dimensional lumber is approximately $1.85/linear foot.
Click Calculate Instantly get rafter length, total cut length (with overhang), ridge board length, rafter count, board feet, estimated cost, and rafter angle — everything you need to order materials and start framing.

Rafter Length Formula — The Math Explained

Rafter length is calculated using the Pythagorean theorem. A rafter, the horizontal run, and the vertical rise form a right triangle — and you're solving for the hypotenuse (the rafter):

Rise = Run × (Pitch ÷ 12)
Rafter Length = √(Run² + Rise²)
Total Cut Length = Rafter Length + Overhang Length
Overhang Length = Overhang(in) ÷ 12 × √(1 + (Pitch/12)²)

Example: 15-foot run, 6/12 pitch, 12-inch overhang

Rise = 15 × (6 ÷ 12) = 7.5 feet
Rafter length = √(15² + 7.5²) = √(225 + 56.25) = √281.25 = 16.77 feet
Overhang run = 12 in = 1 ft | Overhang rise = 1 × 0.5 = 0.5 ft
Overhang segment = √(1² + 0.5²) = 1.12 feet
Total cut length = 16.77 + 1.12 = 17.89 feet

💡 Framing square shortcut: Professional framers use a framing square. For a 6/12 pitch, set the square's tongue at 6" and the blade at 12". The hypotenuse of each 12" step equals your rafter unit length (13.42" for 6/12).

Roof Pitch Chart & Common Uses

Pitch	Angle	Multiplier*	Best For	Common Regions
2/12	9.5°	1.014	Porch overhangs, sheds	Hot, dry climates (AZ, NV)
3/12	14.0°	1.031	Low-slope commercial	Southern US
4/12	18.4°	1.054	Ranch-style homes	Southeast, Southwest
6/12	26.6°	1.118	Most popular residential	Nationwide
8/12	33.7°	1.202	Traditional colonial homes	Northeast, Midwest
10/12	39.8°	1.302	Cape Cod, steep-slope areas	New England
12/12	45.0°	1.414	A-frames, steep snow-load roofs	Mountain regions (CO, WA, MT)

*Multiplier: multiply the run by this factor to get the rafter length (before overhang). E.g., 6/12 pitch × 15 ft run × 1.118 = 16.77 ft rafter.

How Many Rafters Do I Need?

The number of rafters per side is determined by your building length and rafter spacing. Here's the formula:

Rafters per side = ⌈(Building Length ÷ Spacing) + 1⌉ × 2 sides
Add 10% for waste, cuts, and extras

Building Length	16" Spacing (per side)	24" Spacing (per side)	Total @ 16" (both sides)
20 ft	16	11	32
30 ft	23	16	46
40 ft	31	21	62
50 ft	39	26	78
60 ft	46	31	92

Rafter Lumber Sizing Guide (2026)

Rafter size depends on span, spacing, wood species, and roof load. Use this quick reference:

Lumber Size	Max Span @ 16" Spacing	Max Span @ 24" Spacing	2026 Avg Price/LF
2×6	up to 13–14 ft	up to 11–12 ft	~$1.10“$1.40
2×8	up to 17–18 ft	up to 14–15 ft	~$1.70“$2.00
2×10	up to 21–22 ft	up to 18–19 ft	~$2.10“$2.40
2×12	up to 25–26 ft	up to 22–23 ft	~$2.60“$3.00

⚠️ Always check local building codes. Rafter span tables in IRC (International Residential Code) are the legal standard. Snow load zones, wind zones, and local amendments can require larger lumber than these general guidelines.

Types of Rafters

Common Rafter: Runs perpendicular from wall plate to ridge board. Most standard rafter in gable roof construction. This calculator focuses on common rafters.
Hip Rafter: Runs diagonally from a corner of the building to the ridge, forming the hip on a hip roof. Hip rafters are longer than common rafters at the same pitch and require compound-angle cuts.
Valley Rafter: Forms the internal angle where two roof sections meet. Found in L-shaped houses or any intersecting roof planes.
Jack Rafter: A shorter rafter that runs from the wall plate to a hip or valley rafter rather than to the ridge board. Used to fill in the triangular sections of hip or valley roofs.
Collar Tie: Not technically a rafter — a horizontal member connecting opposing rafters to prevent spreading. Required by code at or near the ridge.

Worked Example — 40-Foot Ranch Home, 6/12 Pitch

Let's work through a real project: a 40-foot wide, 60-foot long ranch home with a 6/12 pitch, 16-inch rafter spacing, and 18-inch overhang.

Calculation	Formula	Result
Run	40 ft ÷ 2	20 ft
Rise	20 × (6/12)	10 ft
Rafter length	√(20² + 10²) = √500	22.36 ft
Overhang length	1.5 ft × 1.118	1.68 ft
Total cut length	22.36 + 1.68	24.04 ft
Rafters per side	(60 ft × 12 ÷ 16) + 1	46
Total rafters	46 × 2 sides + 10% waste	102
Linear feet of lumber	102 × 24.04 ft	2,452 lf
Estimated cost (2×10 @ $2.20/lf)	2,452 × $2.20	$5,394

Frequently Asked Questions — Rafter Calculator

How do you calculate rafter length?

Use the Pythagorean theorem: Rafter Length = √(Run² + Rise²), where Rise = Run × (Pitch ÷ 12). Add the overhang length to get total cut length. Example: 15-ft run, 6/12 pitch → Rise = 7.5 ft → Rafter = √(225 + 56.25) = 16.77 ft.

What is roof pitch and how do I measure it?

Roof pitch is rise over run, expressed as X/12. Place a 12-inch level horizontally on the roof surface, hold it level, and measure the vertical distance from the level's end to the roof — that's your rise. A 6-inch rise = 6/12 pitch.

What is the most common roof pitch in the US?

6/12 pitch is the most popular across the country. 4/12 is common in warmer climates. Steeper pitches (8/12–12/12) are used in heavy-snow regions.

How many rafters do I need?

Per side: (Building length in inches ÷ spacing in inches) + 1, rounded up. Double it for both sides. Add 10% for waste. For a 40-ft building at 16" spacing: (480 ÷ 16) + 1 = 31 per side = 62 total × 1.1 = 68.

What size lumber should I use for rafters?

Quick reference: 2×6 up to 14-ft spans, 2×8 up to 18-ft spans, 2×10 up to 22-ft spans, 2×12 up to 26-ft spans (at 16" spacing, standard lumber grade). Always verify with IRC span tables for your specific load zone.

What is a ridge board and how long should it be?

The ridge board runs at the peak of the roof. Its length equals the building length (for a simple gable). It should be one size larger than the rafter lumber (e.g., 2×10 ridge for 2×8 rafters).

What is the difference between common, hip, valley, and jack rafters?

Common rafters go straight from wall to ridge. Hip rafters run diagonally to a corner on hip roofs. Valley rafters sit in the inside angle where two roof sections meet. Jack rafters are short rafters that connect to a hip or valley rafter instead of the ridge.

Do I need a building permit for roofing work?

Yes, for any structural roofing work (rafter replacement, new framing, additions) in most US jurisdictions. Shingle-only replacement may not require a permit everywhere. Check with your local building department before starting work.