Pergola Louver Angle Calculator

How the calculator finds the angle

There are three steps, and none of them is a rule of thumb.

1. Where the sun is. The sun's height and compass direction come from the equations in the NOAA Global Monitoring Laboratory's solar calculator, including its correction for the bending of light in the atmosphere. The same code is tested against the U.S. Naval Observatory's tables. It uses the clock of the place you pick, daylight saving included.

2. The sun as the blades see it. Blades pivot on a line along their length, so only the sun's position in a cross-section across the blades matters. Its height in that section is the profile angle, β. If the sun is at height h and its direction makes an angle A with the line square to the blades, then tan β = tan h / cos A. When the sun is square on to the blades, β is simply its height; when it is in line with them, β is 90°, however low the sun is.

3. When the gap closes. Take blades of width w on a pitch s (centre to centre), tilted by θ from flat. Looking along a sun ray, each blade covers a width of w·|sin(θ − β)|, and the gap from one blade's centre to the next is s·sin β. The beam is stopped when the first is at least as big as the second:

w · |sin(θ − β)| ≥ s · sin β

So the sun gets through only while θ is within γ of β, where sin γ = s sin β / w. The two tilts at the edge of that window, β − γ and β + γ, are the most open settings that still stop the beam, and the calculator offers whichever lets in more sky light. If w is smaller than s sin β, no tilt can stop it: the best the blades can do, square on to the rays, leaves 1 − w / (s sin β) of the beam coming through.

The sky light figure is the share of a uniform sky, weighted as light falling on a level floor, that passes the same row of blades at that tilt. It is worked out by adding up the sky in small steps of height and direction, and checked in the test against rays traced through blades drawn as line segments.

A worked example

London, 21 June 2026, 1 pm British Summer Time. The sun is due south and 61.9° above the horizon. The blades run east-west and are 20 cm (7.9 in) wide on a pitch of 17.5 cm (6.9 in). Seen along the blades the sun is square on, so β = 61.9°.

sin γ = 17.5 × sin 61.9° / 20 = 0.772, so γ = 50.5°. The sun gets through for tilts from 61.9 − 50.5 = 11.4° up to 61.9 + 50.5 = 112.4°, which is 11° toward the sun, through upright, to 68° leaning away from it. The two settings that just stop it are therefore 11° toward the sun, which lets 5% of the sky light through, and 68° away from the sun, which lets 35%. Closed flat, these blades let none through, because they are wider than the pitch.

Now take narrower blades, 10 cm (3.9 in) wide on the same sort of 20 cm (7.9 in) pitch, at the same moment. 10 is less than 20 × sin 61.9° = 17.6, so no tilt stops the sun; with the blades square on to the rays, 43% of the beam still comes through. Blades narrower than their pitch cannot close the roof, and for them the calculator says so rather than giving an angle.

Does the direction the blades run matter?

Yes, because it decides which part of the sun's movement the blades see. The table is the profile angle β in New York City (40.7°N, 74.0°W) from the same maths, for blades running east-west and north-south. Times are local clock time.

Date and time	Sun height	Sun direction	Profile angle, blades east-west	Profile angle, blades north-south
21 Dec, 9 am	14°	SE (139°)	18°	21°
21 Dec, noon	26°	S (181°)	26°	87°
21 Dec, 3 pm	13°	SW (223°)	17°	18°
21 Jun, 8 am	26.5°	E (81°)	72°	27°
21 Jun, noon	69°	SE (140°)	73°	76°
21 Jun, 4 pm	48°	W (260°)	81°	49°

With east-west blades the profile angle follows the sun's height whenever the sun is in the south, which in winter is nearly all day, so the tilt hardly changes from morning to afternoon. In summer the sun swings through the east and west, along the blades, and the profile angle stays high, between 71° and 81° in the table. With north-south blades the angle sweeps: 27° early on a June morning, 76° at noon and back to 26° by 6 pm, so the blades must rock from one side to the other during the day. Which is better depends on what you want from the roof. If you want a setting you can leave alone, east-west blades are steadier; if the sun on the east or west side is the problem, north-south blades see it at its true height. The direction is usually fixed by the pergola's frame, so enter yours. The louvered pergola guide covers choosing a position, and how the sun moves across your garden explains the swing in the table.

Why the blades need to be wider than their pitch

A roof of flat blades is closed only if each blade at least reaches the next. With the blades flat, w ≥ s means a ray at any height meets a blade, so the roof is closed to direct sun and to sky light alike, as the calculator shows. Makers build for that: StruXure says its interlocking louvers form a watertight seal when closed, and Renson says its Algarve roof is fully waterproof when closed, with the water drained away through integrated channels. Your maker's spec sheet gives the width and pitch to enter; measure a blade and the gap between pivots if you do not have one.

How far can your blades turn?

The calculator measures tilt from flat, 0° being closed, and counts “toward the sun” when the blade's edge on the sun's side is the higher one. A maker's own controller may number the angles differently, so check which end is closed on yours. The turning range also matters, because one of the two settings that stop the sun is often a lean away from it, past upright. Renson says its Algarve louvers can turn by up to 150° so that you can adjust solar shading and ventilation through the day. Blades that turn from flat to 150° in one direction reach every lean on one side, but on the other side only leans of 30° or more from flat (180° − 150°; this is geometry, not a maker's figure). So for the sun on one side of the roof a setting like 11° toward the sun may be out of reach, and the other setting, 68° away, is the one to use. The calculator does not know your blades' range; compare its settings with it.

Rain, wind and sensors

A louvered roof closes for rain and opens for wind, and the makers sell the automation. StruXure says optional rain sensors can close its louvers at the first sign of rain, and that its smart sensors can be programmed to open the louvers in high wind to prevent uplift. Renson's Camargue page describes a Somfy remote that closes or tilts the louvers. The sensors the makers describe are for weather. This page gives the angle to set for the sun, and whether your own controller can hold it at a given hour is a question for your maker. Retractable and fixed awnings has the same wind trade-off for fabric, and shade sail, awning or pergola compares the three.

What it leaves out

The blades are treated as flat strips with no thickness, turning on their centre lines, in a row long enough to ignore its ends. Real blades have a thickness, a gasket and a frame, so a closed roof is never quite as dark as the model's 0%, and the sky-light figure assumes an evenly bright sky. Only light through the roof is counted: low sun that comes in from the side, under the beams, is not stopped by louvers at all, and a pergola's low sun in the morning or evening needs a side screen or a blind. Blades that block the sun are warmed by it, and the calculator says nothing about heat; shade for hot climates looks at that, and the best shade for a south-facing garden at what suits a garden where the sun is high through the middle of the day.

Sources: NOAA Global Monitoring Laboratory, solar calculation details (the sun's position); Renson Algarve (rotation up to 150°, waterproof when closed); Renson Camargue (remote control); StruXure (rain and wind sensors, watertight seal). Maker pages read 19 October 2026. The blocking formula and the sky-light share are geometry, written out above and tested in the calculator's own test file against rays traced through the blades.