How do you calculate rafter length?

Rafter length is calculated using the Pythagorean theorem. The run (horizontal distance from the wall to the ridge) and the rise (vertical distance from the wall plate to the ridge) form two sides of a right triangle. The rafter is the hypotenuse: length = square root of (run squared + rise squared). A quicker method uses the length factor for each pitch - multiply the run in feet by the factor. For a 4/12 pitch, the factor is 1.0541, so a 10-foot run gives a 10.54-foot rafter. Add overhang length separately.

What is a birdsmouth cut?

A birdsmouth is a notch cut into the rafter where it sits on the wall plate (top plate of the wall). It consists of two cuts: a seat cut (horizontal, rests flat on the plate) and a plumb cut (vertical, sits against the outside of the wall). The birdsmouth allows the rafter to bear weight evenly on the wall while maintaining the correct roof angle. Depth is typically equal to the wall plate width, usually 3.5 inches for a 2x4 wall.

What is roof pitch and how is it expressed?

Roof pitch describes the steepness of a roof as a ratio of rise to run. It is written as X/12, meaning the roof rises X inches for every 12 inches of horizontal run. A 4/12 pitch rises 4 inches per foot of run (about 18.4 degrees). A 12/12 pitch is a 45-degree angle. Low-slope roofs (under 3/12) need special waterproofing. Most residential roofs range from 4/12 to 9/12.

How do I determine the number of rafters I need?

Divide the building length by the rafter spacing and add 1. For a 24-foot building with 16-inch on-center spacing: 24 feet = 288 inches, 288 / 16 = 18, plus 1 = 19 rafters per side. A gable roof has two sides, so 38 rafters total. This is for common rafters only - hip roofs, dormers, and valleys require additional jack rafters and hip/valley rafters.

What size lumber should I use for rafters?

Rafter size depends on the span (run), spacing, species of wood, and expected loads (snow, wind). As a rough guide for SPF (Spruce-Pine-Fir) lumber at 16 inches on center: 2x6 handles up to about 9.5 feet of run, 2x8 up to 12.5 feet, 2x10 up to 16 feet, and 2x12 up to 19 feet. Always check your local building code span tables because allowable spans vary by lumber grade, species, and load requirements.

What is the overhang (eave) and how does it affect rafter length?

The overhang is the portion of the rafter that extends beyond the exterior wall. It protects the siding and foundation from rain and provides shade. Common overhangs range from 6 to 24 inches. The overhang adds to the total rafter length on the slope - for a 12-inch horizontal overhang at 4/12 pitch, the sloped overhang length is about 12.6 inches. Our calculator adds this automatically to the total rafter length.

What is the difference between a gable roof and a shed roof?

A gable roof has two sloping sides that meet at a ridge in the middle. Each rafter runs from the ridge down to one wall, and the run equals half the building span. A shed roof (lean-to) has a single sloping plane from a high wall to a low wall. The run equals the full distance between the two walls. Shed roofs are simpler to frame but limited in span. Our calculator supports both types.

How do I calculate the ridge height?

Ridge height above the wall plate equals the run multiplied by the pitch ratio. For a gable roof with a 24-foot span (12-foot run) at 6/12 pitch: ridge height = 12 feet × (6/12) = 6 feet above the wall plate. Add the wall height to get the total ridge height from the ground. For shed roofs, the rise is calculated the same way but using the full run distance.

Free Rafter Calculator

Rafter Calculator

Plug in your building span and roof pitch to get rafter length, rise, run, birdsmouth dimensions, cut angles, lumber size recommendation, and a full material count. Works for gable and shed roofs.

Roof Type

Symmetrical roof with two equal sloping sides

Dimensions

Building Span (wall to wall)

feet

inches

Roof Pitch

Overhang / Eave (inches)

Rafter Spacing

Ridge Board Thickness (in)

Birdsmouth Depth (in)

Rafter Dimensions

Enter span and pitch to calculate

Roof Pitch Quick Reference

Common roof pitches, their angle in degrees, rafter length factor, and typical applications.

PitchAngleLength FactorTypical Use

2/129.5°1.0138Low-slope commercial, covered patios

4/1218.4°1.0541Standard residential minimum

6/1226.6°1.1180Common residential, good drainage

8/1233.7°1.2019Steep residential, snow shedding

10/1239.8°1.3017Very steep, cathedral ceilings

12/1245.0°1.4142A-frame, chalet style

How to Use the Rafter Calculator

Select Roof Type

Choose gable (two sloped sides meeting at a ridge) or shed (single slope). For gable roofs, the calculator automatically halves the span to find the run. For shed roofs, the span you enter is the full run.

Enter Span and Pitch

Type in the building span in feet and inches. Then select the roof pitch from the dropdown - all common pitches from 1/12 to 16/12 are listed with their degree equivalent. The calculator instantly computes run, rise, and rafter length.

Set Overhang and Spacing

Enter the eave overhang in inches (12 inches is a common default). Pick rafter spacing: 16 inches on center is standard for most residential construction, 24 inches for lighter loads. The results panel updates with total rafter length including overhang and the number of rafters needed.

Review Cuts and Material

The results show plumb cut and seat cut angles for your birdsmouth, a suggested lumber size based on the run and spacing, and the total linear feet of rafter material. Export the full report or share the summary.

Why Use This Rafter Calculator

Instant Rafter Length

Type the span and pitch and the rafter length appears immediately. No need to look up multiplier tables or do Pythagorean math by hand. The overhang is added automatically.

Birdsmouth Dimensions

Get the seat cut depth and plumb cut height for your birdsmouth based on the pitch angle and wall plate width. Saves layout time on the job site.

Visual Roof Diagram

A cross-section diagram updates in real time as you change inputs. See the rafter, walls, ridge, and overhang proportionally. Helpful for visualizing the finished roof before cutting a single board.

Lumber Recommendation

The calculator suggests a nominal lumber size (2x6, 2x8, etc.) based on the rafter run and your selected spacing. A starting point for checking against local code span tables.

Material Count

Get the total number of rafters for both sides of a gable roof and the total linear feet of material. Walk into the lumber yard with a number, not a guess.

Export Full Report

Download a text file with every input, measurement, cut angle, and material count. Hand it to your framing crew or keep it in your permit file.

The Complete Guide to Roof Rafters

Understanding Roof Framing Basics

A rafter is a sloped structural member that runs from the ridge of the roof down to the eave. Together with the ridge board at the top and the wall plates at the bottom, rafters form the skeleton of a stick-framed roof. Each rafter carries the weight of the sheathing, roofing material, snow loads, and wind loads down to the walls and ultimately to the foundation.

In a gable roof, rafters come in pairs that lean against each other at the ridge. Ceiling joists or collar ties connect the pairs to prevent the walls from spreading outward under load. In a shed roof, rafters run as single members from a tall wall (or ledger board) down to a lower wall. The geometry is simpler, but the structural demands are similar.

The Math Behind Rafter Length

Every rafter calculation boils down to a right triangle. The horizontal leg is the run - half the building span for a gable, full span for a shed, minus half the ridge board thickness. The vertical leg is the rise, determined by multiplying the run by the pitch ratio (rise per 12 inches). The rafter length is the hypotenuse.

Carpenters have used a shortcut for generations: the unit length factor. For any pitch, you calculate √(1 + (pitch/12)²) once and then multiply it by the run in feet to get the rafter length in feet. At 6/12 pitch, the factor is 1.1180 - a 14-foot run gives a 15.65-foot rafter. Our calculator displays this factor so you can use it for quick estimates on related parts of the roof.

The overhang adds length at the bottom of the rafter, past the wall. Because the rafter slopes, the overhang measured on the slope is longer than the horizontal overhang you specify. A 12-inch horizontal overhang at 6/12 pitch becomes 13.4 inches on the board. Always account for this when ordering lumber.

Birdsmouth Cuts Explained

The birdsmouth is arguably the most critical cut on a rafter. It is the notch that locks the rafter onto the wall plate. Two cuts define it: the seat cut (horizontal, parallel to the ground) and the plumb cut (vertical, perpendicular to the ground). The depth of the seat cut is typically equal to the width of the wall plate - 3.5 inches for a 2×4 wall, 5.5 inches for a 2×6 wall.

Building codes generally require that the birdsmouth does not cut more than one-third of the rafter depth. On a 2×6 rafter (5.5 inches deep), the maximum seat cut depth is about 1.83 inches. For standard 2×4 walls, a 3.5-inch seat cut works on 2×8 and larger rafters. If your rafter is too shallow for the required birdsmouth, you either need to upsize the rafter or use a different connection method like a metal connector.

The plumb cut angle on the birdsmouth matches the pitch angle. At 6/12, the plumb cut is 26.6 degrees from vertical. The ridge-end plumb cut uses the same angle. Mark these cuts with a framing square or speed square set to the pitch.

Choosing Roof Pitch

Pitch affects drainage, snow shedding, wind resistance, usable attic space, and aesthetics. Low pitches (2/12 to 4/12) are economical on material and labor but require waterproof underlayment because water moves slowly. Medium pitches (5/12 to 8/12) are the residential sweet spot - good drainage, moderate material use, and enough attic space for storage or HVAC equipment. Steep pitches (9/12 and above) shed snow aggressively and create dramatic interiors but cost more in material and labor, and catch more wind.

Local climate often dictates the minimum. Snowy regions favor steeper pitches to prevent dangerous snow buildup. Arid climates can get away with nearly flat roofs. Wind-prone coastal areas sometimes specify lower pitches to reduce uplift forces. Always check your local building code for minimum and maximum pitch requirements.

From Calculator to Job Site

Once the calculator gives you the rafter length, cut angles, and material count, the next step is layout and cutting. Use a framing square or speed square to mark the plumb cut at the ridge end, then measure along the top edge of the rafter to mark the birdsmouth location (run distance from the ridge cut). Cut the birdsmouth and the tail, and you have a pattern rafter.

Test-fit the pattern rafter on the building before cutting the rest. Set it in place with the birdsmouth on the wall plate and the ridge end against a temporary brace or the ridge board. Check that the overhang looks right and the ridge height matches your plan. If everything lines up, use the pattern to mark and cut all remaining rafters. Label each cut clearly - a single mislabeled angle can waste an entire board.

For material ordering, round up to the next standard lumber length. If your total rafter length is 13 feet 8 inches, order 14-foot or 16-foot boards. Buying boards that are slightly long is far cheaper than splicing short pieces together. Factor in 5 to 10 percent waste for knots, splits, and cutting errors.