Two separate things decide whether you are in shade
The first is how much sun the canopy blocks, which is a property of the slats. The second is where that blocked light lands, which is a property of the sun angle and how high the canopy is. Get the first right and the second wrong and you have built a very good shade structure for a patch of lawn six feet to the east.
Blocking is easy once you notice that a slat is not flat. Seen from straight overhead, a 1-1/2 inch slat on 3 inch centres blocks half the light. But that slat is also 3-1/2 inches deep, and when the sun comes in at an angle the slat presents its depth as well as its width. The shadow it throws on the ground is its own width plus its depth divided by the tangent of the sun altitude. At 60 degrees that adds two inches, so the same slats block 116 percent of the spacing, which is to say all of it. Low sun makes a slatted canopy far more opaque than it looks.
Then the pattern moves. A canopy eight feet up throws its shadow sideways by eight feet divided by the same tangent. At 60 degrees that is 4.6 feet, so on a 12 foot deep pergola about 62 percent of the footprint is still under shadow. At 25 degrees the offset is 17 feet, which is more than the pergola is deep, and the shaded fraction of the floor is zero even though the canopy is blocking every ray that hits it.
The numbers, at one canopy across the day
| Sun altitude | Canopy blocks | Shadow offset, 8 ft canopy | Floor shaded, 12 ft deep |
|---|---|---|---|
| 80 deg, high summer noon | 70% | 1.4 ft | 62% |
| 60 deg, mid morning | 100% | 4.6 ft | 62% |
| 45 deg | 100% | 8.0 ft | 33% |
| 30 deg, late afternoon | 100% | 13.9 ft | 0% |
| 20 deg, near sunset | 100% | 22.0 ft | 0% |
Read the last column rather than the second. Blocking goes up as the sun drops, which feels like good news, and the useful shade goes to nothing at the same time. This is why people who have lived with a pergola end up hanging something on one side of it, and why a pergola on the west side of a house disappoints in a way a pergola on the south side does not.
Choosing a slat spacing that means something
Decide which hours you actually want shade in, look up the sun altitude for those hours at your latitude, and set the spacing for that angle. A structure tuned for midday can be quite open, because the slat depth is doing nothing at high sun and the width has to carry the whole job. A structure tuned for mid morning or mid afternoon can be much more open than people expect, because the depth is contributing heavily.
Depth is the underused lever. Turning a slat on edge changes nothing at noon and changes everything at 40 degrees, at the cost of weight and lumber. Running the slats in the other direction changes which hours they work in, since the geometry here assumes the sun crosses square to the member run and a canopy whose slats run parallel to the low sun does very little. The solar panel tilt angle calculator is a convenient place to get sun altitude figures for a latitude, since it is the same astronomy pointed at a different problem.
If the goal is shade at a specific hour rather than an average, do not average. Run the calculation at that hour, and accept that the structure will be too open at some other time and too dark at another.
What the lumber list here covers and what it leaves out
Rafters are counted across the length at the spacing you give, with the count one more than the number of spaces, and each one is the width plus the overhang at both ends. Slats are counted the same way across the width. Beams are counted as two runs of the full length, without plies, because whether a beam is one member or three is a sizing decision this page does not make. Posts are whatever you enter.
None of it is a structural design. Rafter span, beam span, post size, the connections between them and the anchorage at the bottom are the actual engineering, and on a pergola the governing load is usually wind rather than weight. A flat lattice on four legs is a very effective sail with a lot of uplift, and the failure mode is the whole structure leaving. Many jurisdictions require a permit for one, and footings for the posts put you in the same territory as the deck footing load calculator and the concrete footing calculator. Call 811 or your local equivalent before digging any of them.
If the pergola is going on top of an existing deck rather than its own footings, the posts land on the deck frame and their load has to go somewhere. That is a question for whoever sized the deck, and the deck framing calculator will show you what is under the spot you were planning to stand a post on.
Questions people ask
What slat spacing gives good shade?
It depends entirely on the hour you care about, which is why the calculator asks for a sun altitude rather than assuming one. As orientation: with 1-1/2 inch slats laid on edge, 3 inch centres block roughly half the sun at high noon and effectively all of it once the sun drops below about 65 degrees. Open that to 6 inch centres and midday blocking falls to a quarter while the mid afternoon figure stays high. If you want a single number to start from, pick the spacing that gives the midday shade you want, then check what it does at the angle you actually sit outside at, because that is usually the disappointing one.
Why does the shaded area drop to zero when the canopy is blocking everything?
Because blocking and covering are different. The canopy intercepts light in a plane eight or so feet above your head, and the shadow of that plane lands on the ground displaced horizontally by the canopy height divided by the tangent of the sun altitude. At 30 degrees that displacement is about 1.7 times the height, so an eight foot canopy throws its shade nearly fourteen feet to the side. If the pergola is only twelve feet deep, the shade has cleared the far edge and there is nothing under the structure at all. The canopy is working perfectly. It is just shading somewhere else.
Does it matter which way the slats run?
Considerably, and this calculator assumes the simple case where the sun crosses square to the members. Slats running parallel to the direction the low sun is coming from present only their width, not their depth, and shade far less at that hour. Slats running across it present the full depth and shade heavily. Since the sun sweeps through most of a half circle over a day, no orientation is right for all of it. Pick the hours that matter, work out roughly where the sun is then, and run the slats across that direction.
Will it be dark under a pergola that shades 60 percent?
No, and the figure is more optimistic than it sounds in one direction and less in another. This model handles direct beam sunlight only. On a clear day a substantial share of daylight arrives as diffuse light from the whole sky and as bounce off walls and paving, and none of that is blocked by a lattice with gaps in it. The practical effect is that a pergola cuts glare and the heat you feel on your skin much more than it cuts the general brightness, which is usually what people want from one. It also means the difference between 60 and 75 percent blocking is felt less than the arithmetic suggests.
Do I need a permit for a pergola?
Very often yes, and the answer varies by jurisdiction, by size, by whether it is attached to the house and by whether it sits on footings. Ask the building department before you order material rather than after. Two things drive the requirement: it is a structure with footings, and it is a large flat surface on legs, which makes wind uplift the governing load in most climates. Anchorage and the connection between posts, beams and rafters are where these structures fail, and those details are not something a quantity calculator supplies.