Pergola span calculator
| Member | Size | Allowable span | Your span | Used | Limited by |
|---|---|---|---|---|---|
| Beam | doubled 2x12 | 13'-6-1/4" | 12'-0" | 79% | bending, snow case |
| Rafters | 2x6 | 12'-10-3/4" | 10'-0" | 60% | bending, snow case |
How the pergola span calculator works
A pergola roof is a ladder of boards. The rafters rest on the beams, and the beams rest on the posts. The pergola span calculator checks two spans: how far the beam goes between posts, and how far the rafters go between beams or from a beam to the house. For each one it shows the longest span the board can take, the share of that limit your span uses, and which check sets the limit.
Beam span and rafter span
The beam span is measured from the center of one post to the center of the next. The rafter span is measured from the center of one beam to the center of the other, or from the beam to the face of the ledger on an attached pergola. Spans are taken center to center, which is slightly longer than the clear gap and so errs on the safe side (our own conservative choice, not a code rule).
What the percent used means
At 100% a board is exactly at its limit. Under 100% it passes, over 100% it fails. In the default example, a double 2x10 beam over a 12'-0" span uses 110% and 2x8 rafters over a 10'-0" span use 38%.
The checks behind the answer
Bending
The board bends under load, and bending sets the span for most pergola rafters. Wet outdoor lumber is weaker than the dry values in the usual tables, so the calculator reduces the bending strength to 85% for wet service. A tall, narrow board can also twist sideways, which the calculator checks with the NDS beam stability factor. The top edge is held by the boards above it.
Deflection
A pergola can pass on strength and still sag. The calculator limits the sag to span over 180 under snow or live load and span over 120 under all loads together. Long beams in softer lumber are often limited by this, not by strength.
Shear and overhang
Shear is checked near the supports, where short, heavily loaded boards can split. Overhangs past the beam add bending and sag of their own, so the calculator checks them too. Keep an overhang under a quarter of the back span (25% rule, carried over from deck framing).
Choosing the boards
Rafters
Closer spacing lets a rafter go further. At 12 in on center a 2x8 spans 18'-5-3/4", at 16 in 16'-2-1/2" and at 24 in 13'-4-3/4", in Southern Pine under the default snow load. Rafters carry the slats too, but in a pergola the slats are light.
Beams
A double beam, one board on each side of the posts, is the strongest and the simplest to build. A beam sitting on top of the posts needs a post cap and two or three plies. If a beam fails by a small margin, one more post is usually cheaper than a deeper board: it cuts the span in half for the middle bay.
Posts
The posts are checked as columns in the designer and the pergola plan, not in this calculator. A 6x6 is the safer choice for any pergola taller than 8 ft or with a long beam.
What this calculator does not check
It does not check wind uplift, the footings, the post connections or the ledger on the house. The pergola designer checks all of them for the whole pergola and shows a pass or fail for each. Snow sliding off the house roof onto an attached pergola is not in the loads. Local rules and homeowner associations can set their own limits.
Building a patio cover instead? A pergola plan lists every board and fastener for a size you pick.
Where the numbers come from
More free calculators
Questions
Anything else? Write to us or see every calculator.
Questions people ask
It depends on the boards, the load and the number of plies. With a double beam in Southern Pine, 6x6 posts and 30 psf of ground snow, a pair of 2x8 boards spans 9'-8-1/2", a pair of 2x10 boards 11'-5-1/2" and a pair of 2x12 boards 13'-5", carrying 10 ft rafters. Enter your own spans above and the calculator checks them.
As a pergola rafter at 16 in on center, a 2x10 spans 19'-0-1/4" between beams in Southern Pine with 30 psf of ground snow. As a double beam carrying 10 ft rafters it spans 11'-5-1/2" between posts. The beam is the lower figure because it carries the rafters as well as the roof load.
Pergolas have no span table in the building code the way decks do, so we work each span out from the wood properties and the loads instead of reading a chart. The result is the same kind of answer: a rafter spans 12'-10-3/4" in 2x6, 16'-2-1/2" in 2x8, 19'-0-1/4" in 2x10 and 22'-2" in 2x12 at 16 in on center under the default snow load. The calculator shows yours.
A lot where it snows. A 2x8 rafter at 16 in on center spans 18'-6-1/2" with no snow load and 16'-2-1/2" with 30 psf of ground snow. Ask your building department for the ground snow load of your address and enter it.