design

Pergola Roof and Shade Options: How Much Shade You Get in Utah

How much shade a pergola gives is geometry, not opinion. Member depth divided by gap sets the angle each layer blocks, and Utah's afternoon sun decides the rest.

Updated September 1, 2026

A 12 by 16 pergola in an ebony black stain over a flagstone patio in bright early-afternoon sun, its two-layer slat canopy throwing a crisp grid of shadow across the stone with bright sun between the shadow bars
Direct answer

An open pergola puts somewhere between 45 and 100 percent of the patio beneath it out of direct sun across a summer day, and where you land in that range comes down to three things you can measure: how deep its members are, how wide the gaps between them are, and where the sun sits at the hour you actually sit outside. This guide gives those numbers for Utah.

The numbers below are computed for Provo's latitude from the sun's actual position and the shadow geometry of the two member layers a real pergola is built from, using Stillbury's own member sizes rather than a generic slat array.

Key takeaways

  • This guide covers: how much shade an open pergola really gives, hour by hour, at Utah's latitude; how member depth and gap control it; which way to run the rafters; and how the five roof options compare. For what a roof retrofit costs, see adding a roof to an existing pergola. For the permit rules a solid roof triggers, see the Utah permit guide. For choosing between structures, see pergola or pavilion.
  • One ratio explains almost everything: member depth divided by clear gap. That number sets the sun angle below which the roof blocks the direct beam completely.
  • A Stillbury pergola shades 45 to 100 percent of the patio through a July day in Provo and averages about 65 percent, with the worst hour, early afternoon, sitting near half.
  • The deep rafters do most of the work, not the shade planks. An 8-inch rafter casts a shadow more than five times longer than a 1.5-inch plank at the same sun angle, and low sun is when you need it.
  • Run the rafters north to south. It costs nothing and buys about seven points of average shade, and 18 points at six in the evening.
  • Nothing overhead fixes a 6 p.m. west sun. At 19 degrees of altitude the light arrives under the roof, not through it. That fix is vertical.
  • Shade is not sun protection. Measured protection factors under solid built shade at Denver's latitude averaged 7.4, and open sky between slats lets scattered ultraviolet through regardless of geometry.

Does a pergola actually provide shade?

Yes, partially, and the honest answer is a range that changes by the hour rather than a single percentage.

The objection deserves a straight concession first. "A pergola doesn't stop sun or rain, so why would anyone pay for one" is one of the most-asked questions in the category, and the honest answer is that an open pergola is a filter, not a lid. It will never be a roof, and a builder who implies otherwise is selling.

What it does instead is worth measuring, because a real pergola shades in two layers and almost every article on this subject only counts one of them.

Take the structure Stillbury actually builds. Shade planks are 2×4 dimensional lumber laid flat, so 1.5 inches deep, set at 11 to 12 inches on center with a 7 to 8 inch gap. Below them run interior rafters of 3 by 8, set on edge at 24 inches on center. The planks are the layer everyone photographs. The rafters, five times deeper, are the layer doing most of the work.

Here is what that assembly does on a July day in Provo, computed from the sun's position using the NOAA solar position algorithm and the shadow geometry of two crossed member layers. Dimensions throughout are actual, not nominal: a "2×4" is 1.5 by 3.5 inches under the American Softwood Lumber Standard.

Percent of the patio out of direct sun, Provo, July 21, Stillbury standard build (rafters north to south)
HourShade planks aloneRafters aloneBoth layers together
9:00 a.m.33%71%81%
11:00 a.m.35%37%59%
1:00 p.m.37%17%48%
3:00 p.m.36%25%53%
5:00 p.m.34%49%66%
6:00 p.m.33%69%79%
7:00 p.m.39%100%100%

Three things fall out of that table.

The floor is about 40 percent and the ceiling is the whole patio. Sixty percent of the sky is visible through this structure, so when the sun is directly overhead roughly 40 percent of the ground is shaded. Every hour the sun drops from vertical, the members cast longer shadows and the number climbs.

The deep members are carrying the day, not the pretty ones. At 9 a.m. and again at 6 p.m. the rafters alone are shading 70 percent of the patio while the planks contribute barely a third. That is the whole argument for depth. A 1.5-inch board can only ever cast a 1.5-inch-deep shadow; an 8-inch rafter casts a shadow more than five times as long at the same sun angle, and low sun is exactly when you need it.

The worst hour is the early afternoon, and it is about half. One o'clock in July is the hardest moment for any open structure, because the sun is close to straight down and every member is casting its shortest shadow.

"Out of direct sun" is not the same as cool. Open sky between the members still delivers scattered daylight and heat even when no direct beam reaches the ground, and the share of open sky is a fixed property of the design rather than something that changes by the hour.

A pergola does not make shade the way a roof does. It makes shade the way a stand of trees does, moving and partial and different at four o'clock than at noon. Whether that is what you want is a real design question and it is worth answering before you pick a structure. If you want the number past 80 percent at every hour, no arrangement of open members gets you there. That is a roof, and the honest paths to one are adding a panel roof to the pergola or building a pavilion instead.

How far apart should pergola slats be for shade?

There is no correct spacing. There is a ratio, and it is member depth divided by clear gap.

That ratio sets the angle. A slat array blocks the direct beam completely once the sun's angle across the members falls below the arctangent of depth divided by gap. Above that angle, sunlight threads between the members and you get stripes.

This is where the most-repeated rule in the topic goes wrong. Search the question and you will be told, over and over, to use a 1:1 ratio: make the gap equal to the depth of the board. The advice is attributed vaguely to home-improvement magazines, and the AI answer engines now repeat it as though it were a standard. Run the arithmetic and a 1:1 array blocks the direct beam only above 45 degrees. In Provo on July 21, with the members running north to south, that array is in full shade until about 10:20 in the morning and again from about 4:50 in the afternoon. In between, for six and a half hours, it is striped. The rule everyone repeats fails during the middle of the day and works during the hours you were already comfortable.

What each layer blocks
MembersDepth ÷ clear gapBlocks the beam belowOpen sky through that layer
Big-box kit lattice: 2×4 flat, 6" gap0.2514°63%
Stillbury shade planks: 2×4 flat, 7.5" gap, 11" o.c.0.2011°68%
Stillbury interior rafters: 3×8 on edge, 21" gap, 24" o.c.0.3821°88%
2×6 on edge, 6" gap0.9243°80%
2×8 on edge, 4" gap1.8161°73%
2×8 on edge, 2" gap3.6275°57%

No single layer of an open pergola blocks much on its own. Stillbury's shade planks stop the direct beam only below 11 degrees, which is nearly sunset. Read in isolation that looks like a failure, and it is exactly how most articles on this subject read the question. It is the wrong reading, because a pergola is not one layer. Cross those planks over rafters that stop the beam below 21 degrees and the assembly shades 45 to 100 percent through the day and averages about 65 percent from nine in the morning to eight at night.

The rafters are where the depth is, and depth is what buys low-sun shade. An 8-inch rafter is more than five times deeper than a 1.5-inch plank, so it casts a shadow more than five times as long at any given sun angle. Members that deep need beams and posts sized to carry them, which is why they show up on an engineered heavy-timber frame and not on a bolted kit. Stillbury's numbers around them are 4 by 10 beams, 4 by 8 end rafters, 3 by 6 knee braces, and 6 by 6 or 8 by 8 posts, sized per span and load. The shade you get is a downstream consequence of that structure.

Hours of complete shade, Provo, July 21
ConfigurationFull shade untilFull shade resumesPartial-shade window
Big-box kit lattice aloneneverneverall day
Stillbury build, rafters north–south8:15 a.m.6:55 p.m.10 hr 40 min at 45–80%
Stillbury build, rafters east–west7:20 a.m.7:50 p.m.12 hr 30 min at 49–70%
2×6 on edge, 6" gap, single layer10:10 a.m.5:00 p.m.6 hr 50 min
2×8 on edge, 2" gap, single layer12:35 p.m.2:35 p.m.2 hr 0 min

Nobody publishes this table, which is why the question gets answered with adjectives. Read the bottom two rows honestly: you can chase complete shade by closing the top down to a 2-inch gap, and it works. What you spend is the open sky. That configuration leaves 57 percent of the sky visible where Stillbury's leaves 60, and it starts behaving like a solid surface in a snowstorm without being engineered as one. Past a certain point, closing the gaps is just building a roof badly. If complete shade is the goal, build it as a roof or build a pavilion.

Nominal numbers will mislead you. People compute the ratio from the name on the board. A 2×4 is not 4 inches of anything, it is 1.5 by 3.5, and laid flat it gives you the 1.5. The ratio you actually get is smaller than the one you calculated.

Ask for the clear gap and the member depth, not the on-center spacing. "Twenty-four inches on center" tells you nothing about shade until you know what is 24 inches apart and how deep it is. Stillbury's rafters at 24 inches on center behave completely differently from a kit's slats at 24 inches on center, because one of them is 8 inches deep and the other is an inch and a half.

We are not going to tell you we have shaded a hundred Utah patios, because we have not. Stillbury is new. What we can show you is the arithmetic above, the sources under it, our actual member sizes rather than a vague promise of quality, and a drawing of your own yard before you have paid anything. If you are comparing against a kit, the kit guide covers what actually arrives on the pallet. The Rustic and Modern pergola styles differ in brace shape, not in what the roof can carry.

Which direction should pergola rafters run for the most shade?

North to south, and on a two-layer pergola the direction that matters is the rafters, not the boards you can see from the patio.

The published advice on this contradicts itself, and if you have researched it you have already run into that. One set of sources says to run the members north to south so their shadows sweep across the space as the sun travels. Another says to run them east to west to block the high midday sun. Both are describing something real. They are describing different hours, and neither notices that a real pergola has two layers running at right angles, so the question is which layer you are talking about.

The deep layer wins the argument, because the deep layer is what casts a long shadow when the sun is low. Here is Stillbury's standard build rotated 90 degrees, same structure, same day, nothing else changed.

Same pergola, two orientations (Provo, July 21)
HourRafters north–southRafters east–west
9:00 a.m.81%63%
11:00 a.m.59%54%
1:00 p.m.48%50%
3:00 p.m.53%52%
5:00 p.m.66%56%
6:00 p.m.79%61%
7:00 p.m.100%79%
Daily mean, 9 a.m. to 8 p.m.65%58%

Running the rafters north to south costs nothing, changes no material, and buys about seven points of average shade. In the evening it buys far more than that: 18 points at six o'clock, and complete shade arriving at 6:55 p.m. instead of 7:50. The east–west arrangement wins exactly one hour of the day, one o'clock, and it wins it by two points.

So the tiebreaker is not physics. It is a question about your life: when do you actually use the patio? In most Utah backyards the answer is dinner and the hours after it, which is the window north–south rafters own outright. If your case is genuinely different, a poolside deck used at midday or a lunch patio at a workplace, the two arrangements are within a couple of points of each other at that hour and you should let the site decide instead.

There is a constraint worth naming. Rafters usually want to span the short direction between beams, so the orientation that shades best is not always the orientation that frames most simply, and on an attached pergola the house often settles it. That trade is a design conversation, not a rule, which is the honest reason Stillbury's pergola process starts by mapping the shade rather than by picking a style. The patio, the sun path, the elevation of the house, and how people move through the yard get looked at before anyone recommends a layout, because those four things decide whether the structure shades you at the hour you care about. The pergola service page walks through the rest of that sequence.

What are the roof options for a pergola?

Five, and the first choice is not the material. It is what you want stopped: sun only, sun and rain, or sun and rain and snow. Every option answers exactly one of those, and the tiers step up sharply in cost, weight, and what your city calls the structure.

Pergola roof options compared
OptionWhat it stopsWhat it does to lightUtah winterWhat it changes structurallyRelative cost
Fabric canopy, sail, or retractableMost direct sun while deployedSoft, even, dimmerMust come down before the first stormNothing, but the hardware carries wind loadLowest
Fixed slats or raftersSome direct sun, by geometryBright, striped, movingSnow falls through wide gaps; bridges on tight onesNothing, if the frame was drawn for the member sizeLow, and it is already in the structure
Translucent panel (multiwall polycarbonate)Sun, rain, and snowFiltered daylight, no stripesStays up; sheds snow if pitched and supportedReal snow load on the frameModerate
Solid roof (metal or shingle)EverythingDark underneathHandles snow like a roof, because it is oneBecomes a different structureHigh
Adjustable louversSun on demand; rain when closedFully variableManufacturer winter protocol; moving parts in the coldA mechanical system with a maintenance lifeHighest, by a wide margin

The cost column is deliberately ordinal rather than in dollars, because the spread inside each tier is wider than the gap between tiers and a single number would mislead you. What holds steady is the order: fabric is the cheapest real shade, deeper fixed members are close to free because they are already part of the frame, panels sit in the middle, a solid roof prices like construction, and louvers cost more than everything above them combined. Actual numbers are covered elsewhere. Retrofit pricing for panel roofs, including per-size kit numbers and the support-spacing tables that decide whether your frame qualifies, lives in adding a roof to an existing pergola. Whole-structure pricing lives in what a custom pergola costs in Utah.

Two honest words for the options Stillbury does not build. Fabric is the cheapest real shade available and it is not a compromise for a household that wants sun in April and shade in July. Louvered systems genuinely do something no fixed roof can do, and no amount of clever geometry substitutes for a roof that opens.

What do you call a pergola with a roof?

Once the roof is solid, most people call it a pavilion or a covered patio, and the naming matters less than the fact that your city calls it something different too.

Adding a solid roof can change how a structure is classified, which changes whether a permit is required and what has to be shown on the drawings. The rules, including the exemption thresholds and the trap where an attached structure reads as an addition, are set out in the Utah pergola and pavilion permit guide. Check them before you commit to a roof, not after.

A solid roof also means the frame carries snow for the first time. Design snow loads on the Wasatch Front vary sharply between the valley floor and the benches, and past a certain point an engineer signs the drawings. That is its own subject and it is worth reading properly before choosing a roof for a bench lot.

If you are still deciding between structures rather than roofs, pergola or pavilion is the better starting point, and the pavilion page shows what a solid roof actually looks like on a Utah house.

Do pergolas block UV rays?

Partly, and less than most people assume.

Three things are worth knowing, and none of them appear on the pages currently ranking for this question.

Elevation raises the dose. The EPA states that ultraviolet intensity increases about 6 percent per kilometre of elevation above sea level. Provo sits near 4,550 feet, about 1.4 kilometres, so ultraviolet runs roughly 8 percent above the sea-level baseline that national shade advice is written against. A mountain lot at 7,000 feet runs about 13 percent above it.

Shade does not stop scattered ultraviolet. The CDC puts it directly: shade "does not block all UV radiation if it does not block all of the sky, nor does it protect against scattered UV rays." That sentence is the open-sky column from the spacing table above, stated as a health fact. A design that leaves 57 to 80 percent of the sky visible is leaving that much sky free to scatter ultraviolet onto the patio.

Even solid shade measures lower than people expect. A randomised trial that installed built shade structures in public parks in Denver and Melbourne and then measured ultraviolet underneath found protection factors of 3 to 17, averaging 7.4. Denver sits at 39.7 degrees north at high elevation, which makes it close to a twin for Utah Valley. Those were solid shade sails and hip-and-ridge structures, not slats.

The verdict is unglamorous. Design a pergola for comfort, for glare, and for how the space feels. Do not design it as sun protection and do not let anyone sell it to you as sun protection. Shade you can see through is shade ultraviolet can get through.

Is a slatted pergola enough shade for a west-facing patio?

No, and neither is a solid one. This is the single most useful thing in this guide, and it argues against selling you a bigger roof.

The reason is geometry. In Provo in late July the sun sits at about 31 degrees of altitude at 6 p.m. and about 19 degrees at 7 p.m. Light arriving at 19 degrees above the horizon comes in from the side. It passes under the roof rather than through it, and it lands on the people sitting at the table. Every horizontal option in the table above fails this the same way. A tighter plank gap does not help. A polycarbonate panel does not help. A full metal roof does not help. The sun is not overhead, so an overhead solution has nothing to work with.

The fix is vertical, and it goes in this order.

  1. Placement first, and it is free. If the house, a mature tree, or an existing fence can take the western exposure, put the structure where that happens. This is the cheapest shade anyone will ever sell you, and it costs nothing but the conversation.
  2. A slat screen on the west side. Vertical members on the sunset side do to a low sun exactly what horizontal members do to a high one, and the same depth-over-gap ratio applies. Stillbury offers horizontal slat screens as a pergola add-on for precisely this, and they double as privacy.
  3. A roll-down or fixed side panel. More coverage, less transparency, and it can be deployed only when needed.
  4. Plantings on the west. The slowest option and the best one in ten years.

None of this is visible on a plan drawing, which is the honest limitation of a guide like this one. Ratios and tables tell you what a design blocks in the abstract. They cannot tell you where the shadow actually lands on your patio at five o'clock, because that depends on your house, your fence line, your grade, and your trees. That is what the free 3D design is for: your structure, drawn on your yard, before you have spent anything. If you are in Provo or anywhere else on the Wasatch Front, you can start one here.

Are louvered pergolas worth it?

They do something no fixed roof can do, and they cost and maintain like the mechanical product they are.

Stillbury does not build or sell louvered systems. That is worth stating plainly so the rest of this reads as information rather than as a knock on a competitor's product.

The case for them is real. An adjustable roof gives you sun in April, shade in July, and a closed roof when it rains, from one structure. No arrangement of fixed members achieves that, because fixed members are a single compromise chosen once. If your yard has to serve genuinely opposite needs across the seasons, louvers solve the problem and nothing else does.

The case against them is equally real. A louvered roof adds a motor, a controller, seals, and moving parts that live outdoors through Utah winters, and most manufacturers publish a winter protocol you are expected to follow. A fixed structure has none of that. It also has nothing to fail in February.

One related disclosure while the subject is what a structure does and does not include. Stillbury does not run electrical through posts and does not install outlets or fans. When customers want light under a structure, it is string lights.

Can you put a shade sail or canopy on a pergola in Utah?

Yes, and take it down before the first storm.

Fabric over a frame is the cheapest genuine shade there is, and it is worth saying so. A canopy or a retractable panel dims a patio far more effectively per dollar than any change to the wood above it, and a retractable one gives you a version of the adjustability that louvers charge five figures for.

The Utah failure mode is specific. Wet snow loads a fabric panel that has no way to shed it. The fabric tears, and the tear usually takes tracks, grommets, or hardware with it, which is a bigger repair than the fabric. Anything stretched over the top of a structure comes off in the fall here. That is not a defect. It is the deal.

There is a corollary almost nobody writes down, and it changes how you should chase shade in this climate. The same logic applies to very tight slat spacing. Close the gaps far enough and snow stops falling through and starts bridging across the members, and the frame quietly begins carrying a load nobody drew it for. That is the real limit on solving shade with spacing alone in Utah, and it is why the better route here is deeper members rather than tighter gaps. Stillbury's 7 to 8 inch plank gap and 21-inch clear span between rafters are wide enough that snow falls through rather than bridging, and the shade comes from member depth instead.

If the structure is on a bench lot or up a canyon, the snow question stops being a rule of thumb and becomes an engineering one. Worth settling before the roof is chosen, not after.

How to choose a pergola roof: questions to ask any builder

Ask these of anyone quoting you, including us. Every one of them is checkable, and a company that cannot answer them on the spot has not designed your shade, it has priced a shape.

  1. What size are the members in both layers, on edge or flat, and what is the clear gap in each? Not the on-center spacing. Depth and clear gap are the two numbers that decide your shade, and a pergola has two layers of them. Stillbury's answer is 2×4 planks laid flat at a 7 to 8 inch gap over 3×8 rafters at 24 inches on center.
  2. Which way do the deep rafters run, and what hours does that orientation shade? If the answer is not in hours, it is not an answer.
  3. Show me the shade at five o'clock, not at noon. Noon flatters every design. The late afternoon is the test.
  4. If this roof becomes solid, who handles the permit and the engineering? A solid roof can reclassify the structure, and somebody has to own that. Stillbury checks requirements during design and prepares the submittal when one is needed.
  5. What is the workmanship warranty, in writing, and for how long? Stillbury's is three years.
  6. What happens to this roof in February? Fabric comes down. Louvers follow a protocol. Panels need pitch and support. Wide slats do nothing at all, which is the correct answer for a lot of Utah backyards.

A pergola roof is not one decision, it is three: what you want stopped, how deep and how far apart the members sit, and which way they run. Get those right and an open structure will shade the hours you actually use. Get them wrong and you will have bought a very expensive piece of geometry that works beautifully at noon on a day nobody is outside.

If you would like to see the answer for your own yard rather than in a table, a free 3D design and written quote shows your structure on your patio, with the members sized and spaced the way they would actually be built, before you spend anything.

Key questions

Quick answers

Does a pergola actually provide shade?

A pergola provides partial, moving shade that ranges from roughly 45 percent to 100 percent of the patio across a summer day, depending on the depth of the members, the gaps between them, and the sun's angle at that hour. A Stillbury pergola in Provo, built with 2×4 shade planks over 3×8 rafters, averages about 65 percent from nine in the morning to eight at night, with its worst hour near half in the early afternoon.

How much shade does a pergola give?

The shade a pergola gives is set by member depth divided by the clear gap, applied to each of its two layers. Stillbury's 2×4 shade planks laid flat at a 7.5-inch gap block direct sun below 11 degrees on their own, and the 3×8 rafters beneath them at 24 inches on center block below 21 degrees. Crossed at right angles the two layers shade 45 to 100 percent of the patio through the day.

How far apart should pergola slats be for shade?

There is no single correct pergola slat spacing, because shade depends on the ratio of member depth to clear gap rather than on the gap alone, and on both layers of the structure rather than the visible one. Stillbury sets 2×4 shade planks at 11 to 12 inches on center with a 7 to 8 inch gap, over 3×8 rafters at 24 inches on center. The widely repeated "1:1 ratio" rule blocks direct sun only above 45 degrees, so at Utah's latitude it leaves a striped patio through the middle of the day.

Which direction should pergola rafters run for the most shade?

Pergola rafters should run north to south in most Utah backyards, and it is the deep rafters rather than the shade planks above them that decide the answer. On a Stillbury build in Provo, north-to-south rafters average 65 percent shade from nine in the morning to eight at night against 58 percent east to west, and the gap widens to 18 points at six in the evening. East to west wins only the one o'clock hour, and only by two points.

What are the roof options for a pergola?

A pergola roof can be fixed slats, a fabric canopy or sail, translucent multiwall polycarbonate panels, adjustable louvers, or a solid metal or shingled roof. The right choice follows from what you want stopped: sun only, sun and rain, or sun and rain and snow. Each step up adds cost, weight, and structural consequence.

What do you call a pergola with a roof?

A pergola with a solid roof is usually called a pavilion or a covered patio, and Utah cities may classify it differently from an open pergola. That reclassification is what matters, because it can change whether a building permit is required and whether the structure needs engineered drawings for snow load.

Does a slatted pergola keep rain off?

A slatted pergola does not keep rain off, because the gaps that let light through also let water through. Keeping rain off requires a continuous surface: a fabric canopy, translucent polycarbonate panels, closed louvers, or a solid roof.

Do pergolas block UV rays?

Pergolas block some ultraviolet but should not be treated as sun protection. The CDC states that shade does not block all UV radiation if it does not block all of the sky and does not protect against scattered UV rays, and an open slat design deliberately leaves 57 to 80 percent of the sky visible. A randomised trial measuring built shade structures in Denver and Melbourne found protection factors of 3 to 17, averaging 7.4, even under solid shade.

Is a slatted pergola enough shade for a west-facing patio?

A slatted pergola is not enough shade for a west-facing patio in the evening, and neither is a solid one. At 7 p.m. in July the Utah sun sits around 19 degrees above the horizon, so light arrives from the side and passes beneath any horizontal roof. Shade for a western exposure has to be vertical: placement behind the house or a tree, a slat screen on the west side, or a roll-down panel.

Are louvered pergolas worth it?

Louvered pergolas are worth it for a yard that needs genuinely opposite things across the seasons, because an adjustable roof gives sun in spring, shade in summer, and rain cover when closed, which no fixed roof can do. The trade-off is a motor, seals, and moving parts that live outdoors through Utah winters, plus a manufacturer winter protocol. Stillbury does not build or sell louvered systems.

Can you put a shade sail or canopy on a pergola in Utah?

You can add a shade sail or canopy to a pergola in Utah, and it must come down before the first snow. Fabric has no way to shed wet snow, so a loaded panel tears and usually takes tracks or hardware with it. Fabric is the cheapest genuine shade available, and seasonal removal is the cost of using it here.

Does tighter slat spacing cause snow problems in Utah?

Tighter slat spacing can cause snow problems in Utah, because gaps narrow enough to stop snow falling through cause it to bridge across the members instead. The frame then carries a load it was not designed for. The safer route to more shade in a snow climate is deeper members rather than narrower gaps.

How do you get shade from a pergola in the late afternoon?

Late-afternoon shade from a pergola comes from vertical elements, not from the roof. In order of cost: place the structure so the house or an existing tree takes the western sun, add a vertical slat screen on the west side, add a roll-down or fixed side panel, or plant on the west. A low sun passes under any horizontal roof regardless of how its members are sized or spaced.

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