Rafter Dimensions Calculator

About the Rafter Dimensions Calculator

Every rafter in a traditional stick-framed roof has the same few cuts. At the top, a plumb cut lets it meet the ridge board. At the bottom, a notch called the birdsmouth lets it sit flat on the wall plate: a level seat cut that bears on the top of the wall, and a vertical heel cut that hooks over its outside edge. Get these right on the first rafter, use it as a pattern, and the rest of the roof goes together quickly and flat. Get them wrong and the roof plane wavers, or the rafter is weakened by too deep a notch.

This rafter dimensions calculator works out those cuts from the roof pitch and the rafter size. It gives the plumb and seat cut angles, the depth of the heel cut, a check against the one-third depth limit, the plumb depth of the rafter, the height above plate, and the line length from wall to ridge.

How to Use the Rafter Dimensions Calculator

Enter the roof pitch as inches of rise per 12 inches of run.

Choose the rafter size.

Enter the seat cut length, usually the width of the wall plate, and the rafter run in feet.

The Formulas

  roof angle    = atan(pitch ÷ 12)
  plumb cut     = roof angle from square
  seat cut      = 90° − roof angle
  heel depth    = seat length × tan(roof angle)
  limit         = rafter depth ÷ 3
  plumb depth   = rafter depth ÷ cos(roof angle)
  HAP           = plumb depth − heel depth
  line length   = run ÷ cos(roof angle)

Step-by-Step Example

A 6/12 roof with 2×8 rafters on a 2×4 wall, 12 ft run.

  angle         atan(6 ÷ 12) = 26.57°
  cuts          plumb 26.57°, seat 63.43°
  heel          3.5 × tan 26.57° = 1.75 in   (limit 7.25 ÷ 3 = 2.42 in)
  plumb depth   7.25 ÷ cos 26.57° = 8.11 in
  HAP           8.11 − 1.75 = 6.36 in
  line length   12 ÷ cos 26.57° = 13.42 ft ≈ 13 ft 5 in

Understanding the Birdsmouth

The birdsmouth is named for its shape, like an open beak. The seat cut must be level so the rafter bears its load straight down onto the wall, and long enough to bear on the full width of the plate where possible. The heel cut is plumb, so the rafter cannot slide off. Because the seat is level and the rafter slopes, the heel depth grows as the pitch steepens: at 12/12 a 3½-inch seat needs a 3½-inch heel, more than a third of a 2×8. In that case the seat is shortened, often to the minimum bearing allowed by code, so the rafter is not over-notched.

The One-Third Rule

Cutting a notch out of the bottom of a rafter removes wood exactly where it is most stressed near the support. A widely used rule, written into many codes and engineering guides, is that the notch must leave at least two-thirds of the rafter's depth intact above the seat, so the heel cut should be no deeper than a third of the depth measured square to the rafter's edge. The calculator compares the heel depth with this limit and warns when the seat should be shortened or a deeper rafter used.

Height Above Plate

Height above plate, or HAP, is the vertical distance from the top of the wall to the top edge of the rafter, directly above the outside of the wall. Framers set HAP once and use it to lay out every rafter, because if all rafters have the same HAP and the same line length, the roof plane will be flat and the ridge level. HAP also tells you where the roof sheathing will sit relative to the wall, which matters for fascia, soffit and insulation depth at the eaves.

Plumb Depth

A rafter measured square across its face is its nominal depth, 7¼ inches for a 2×8. Measured vertically, along a plumb line, it is deeper, because the board is tilted. The steeper the roof, the bigger the difference. Plumb depth is used for HAP and for working out the ridge board depth: the ridge should be at least as deep as the plumb cut on the rafters, so a 2×8 rafter at 6/12 usually needs a 2×10 ridge board.

Line Length and Rafter Length

The line length here runs along the rafter from the outside of the wall plate to the centre of the ridge. To get the board length, deduct half the ridge thickness at the top and add the overhang beyond the wall at the bottom, measured along the slope. The rafter length calculator on this site does those steps for you.

Making a Pattern Rafter

Mark the plumb cut at the top with a framing square or speed square set to the pitch, measure the line length along the rafter, and mark the birdsmouth with the seat and heel cuts. Cut one rafter, test it in place at both ends of the roof, and adjust if needed. Then use it to mark all the others.

Understanding Your Result

The headline gives the plumb and seat cut angles.

The birdsmouth line gives the seat and heel and checks the one-third limit.

The height above plate line gives the plumb depth and HAP.

The length line gives the line length and the total rise.

When Should You Use This Calculator?

Use it when cutting a pattern rafter.

Use it to check whether a birdsmouth notch is too deep for steep roofs.

Use it to set the ridge height and ridge board depth.

Common Mistakes

Cutting the birdsmouth too deep. Keep the heel within a third of the depth.

Using square depth for HAP. Use the plumb depth.

Forgetting the ridge deduction. Line length is to the ridge centre.

Varying HAP between rafters. It makes the roof wavy.