Sun & louvres· 3 min read
How to Calculate the Shadow of a Pergola or Patio Roof in Summer and Winter
How much shade an overhang or pergola gives a south-facing patio: shadow on the wall and floor at the summer and winter solstice, plus louvred roof angles.
An overhang or a solid pergola roof on the south side should shade in summer and let the sun into the house in winter. A simple section tells you whether it does. Example: a south wall at 48.15° N (Bratislava), roof underside 2,500 mm above the floor, a canopy projecting 1,000 mm and a pergola 3,000 mm deep.
The sun in summer and winter
On 21 June 2026 at 13:00 summer time the sun is 65.3° above the horizon (azimuth 183.6°); on 21 December at 12:00 winter time only 18.4° (azimuth 182.5°). The calculator uses the NOAA algorithm. At both times the sun is almost due south, so the profile angle on a south wall is nearly the same as the elevation: 65.3° and 18.4°.
The formulas
- Shade on the wall below the roof edge = projection × tan(profile angle).
- If that is more than the height, the whole wall is shaded and the shadow continues on the floor: floor in shade from the wall = projection − height ÷ tan(profile angle).
- So the shadow edge on the floor sits height ÷ tan(profile angle) closer to the wall than the roof edge.
Canopy projecting 1,000 mm
| Date and time | Profile angle | Wall in shade | Floor in shade |
|---|---|---|---|
| 21 June, 13:00 | 65.3° | 2,175 mm | — |
| 21 Dec, 12:00 | 18.4° | 333 mm | — |
In summer the canopy shades the top 2,175 mm of the wall; the sun only reaches the bottom 325 mm. A window below it is fully shaded at noon. In winter the shadow reaches only 333 mm below the edge and the sun falls on almost the whole window.
Sun & louvresCanopy in summer in the calculatorSolid pergola roof 3,000 mm deep
| Date and time | Profile angle | Wall in shade | Floor in shade |
|---|---|---|---|
| 21 June, 13:00 | 65.3° | whole wall | 1,850 mm from the wall |
| 21 Dec, 12:00 | 18.4° | 1,000 mm | — |
Summer: 3,000 × tan 65.3° = 6,524 mm, more than 2,500 mm, so the whole wall is shaded. Floor: 3,000 − 2,500 ÷ tan 65.3° = 3,000 − 1,150 = 1,850 mm. Although the roof is 3 m deep, only 1.85 m of floor next to the wall is shaded at noon; the outer 1.15 m under the roof is in the sun. Put the table and seating closer to the wall.
Winter: 3,000 × tan 18.4° = 1,000 mm. The sun reaches under the roof all the way to the wall — the bottom 1,500 mm of the wall and the whole floor under the pergola are sunlit.
In the morning the sun comes in at an angle: on 21 June at 10:00 its azimuth is 110.2° and the profile angle 72.7°, so in the section 2,219 mm of floor is shaded. But the sun is then in the south-east, and under a pergola that is not much longer than it is deep it shines in from the side. The section assumes a long roof.
Sun & louvresPergola in summer in the calculatorLouvred pergola roof
A louvred (bioclimatic) pergola has rotating slats in the roof. Example: 100 mm slats at 95 mm spacing, slat axes running east–west. The calculator measures the sun's angle from the vertical in the section across the slats. Open slats (on edge) stop sun that comes in at more than 43.5° from the vertical.
- 21 June, 13:00: sun 24.7° from the vertical; the slats need at least 35.0°.
- 21 June, 9:00 and 17:00: the sun shines from the east and west almost along the slats; they need 61.4° and 65.2°.
- 21 December, 12:00: sun 71.6° from the vertical — open slats block it. To let winter sun in, turn the slats to about 70° towards the sun; at that tilt direct sun passes.
- Slats running north–south would need 70.1° on 21 June at 13:00, but open slats would do at 9:00 and 17:00.
The calculator does shadow geometry only, not structural design. Snow and wind loads and the anchoring of the pergola are for the manufacturer or a structural engineer; whether it needs a permit, check with your local building authority.