Pergola shade calculator
A pergola with 2×6 rafters at 24 inches on centre covers 23% of the sky. Everyone who builds one is surprised by that number, because they were picturing dappled shade and got a grill.
Rafter layout
How this is calculated
- Cover at 90° = rafter width ÷ spacing. A 5.5″ rafter at 24″ centres covers 22.9%.
- Cover at angle θ = min(1, (width × csc θ) ÷ spacing), because a slanted sun projects a wider shadow than the board is wide. At 45° the shadow is 1.41× the board width.
- Gap = spacing − width.
- Shadow offset = 1 ÷ tan θ feet horizontally per foot of height, which is how far the shade moves as you go down.
Worked example
2×6 rafters at 24″ on centre, sun at 45°:
- Cover overhead = 5.5 ÷ 24 = 22.9%
- Cover at 45° = (5.5 × 1.414) ÷ 24 = 32.4%
- Gap = 18.5″; shadow offset = 1 ft per foot of height
So a pergola that looks solid in a plan drawing gives a third coverage at the hours people actually sit under it. The 22.9% figure is the one people quote; 32.4% is the one they experience.
How to get more shade without a roof
- Narrow the spacing. 5.5″ rafters at 12″ centres covers 46% overhead — double, for twice the rafters.
- Add a second layer of slats perpendicular to the first. Two layers at 24″ each cover about 40% before the angle effect.
- Widen the rafters. A 2×8 at 7.25″ on 24″ centres covers 30%, only a modest gain for a lot of extra material.
- Add a shade cloth or louvred panels in summer only, which is the cheapest way to get 80% where it is needed.
What a shade percentage is not
- It does not model the sun path. The angle changes through the day and by season; one number is a snapshot, not an average.
- It does not account for orientation. Rafters running east-west and north-south shade differently at different hours.
- It does not include the beams, which add a small amount of cover perpendicular to the rafters.
- It does not size the structure. Span and load are in the rafter calculator.
Questions people actually ask
How much shade does a pergola provide?
With 2×6 rafters at 24 inches on centre, about 23% coverage from directly overhead and roughly 32% at a 45-degree sun angle. Narrower spacing is the only way to increase it substantially.
What rafter spacing gives the most shade?
12 inches on centre with 5.5-inch rafters covers 46%. Going below 12 inches adds cost quickly for diminishing returns; a shade cloth is usually the better answer beyond that point.
Do pergola rafters run along or across the beams?
Across. Rafters sit on top of the beams, perpendicular to them, and the beams span between posts. Rafter direction determines which hours get shaded.
Is a pergola worth it if it only gives 25% shade?
For the structure and the vine support, often yes. If the goal is usable shade at midday, budget for a shade cloth or closer rafters from the start rather than discovering the coverage afterwards.