Solar Panel Tilt Calculator

The trigonometry of panel tilt

A solar panel produces the most when sunlight strikes it at a right angle. The sun's height in the sky at solar noon is set by two numbers: your latitude and the sun's declination, which swings between −23.44° and +23.44° over the year because the Earth's axis is tilted by that amount.

Those seasonal angles are exact geometry. The single best angle for a panel that never moves is not: it depends on how much of your annual sunshine arrives in each season. The calculator uses a widely quoted fit, 0.76 × latitude + 3.1° between 25° and 50° latitude (0.87 × latitude below 25°), which lands a few degrees flatter than latitude because long summer days outweigh short winter ones. Treat it as a starting point and confirm the yield with a simulation tool such as NREL's PVWatts before you order racking.

Tilt angles by latitude

Row spacing: how long is the winter shadow?

A tilted panel is the hypotenuse of a right triangle. Its top edge sits panel length × sin(tilt) above its base, and that height casts a shadow of height ÷ tan(sun elevation). Before and after noon the sun is off to one side, so only part of that shadow points toward the next row; multiplying by cos(azimuth) gives the part that matters.

The hour angle is 15° per hour from solar noon, so 9 am and 3 pm are both 45°.

Worked example: 35° latitude, 78 in panel, 9 am to 3 pm

1. Year-round tilt = 0.76 × 35 + 3.1 = 29.7°.
2. Panel height = 78 × sin(29.7°) = 38.6 in.
3. Winter solstice, hour angle 45°: sin(elevation) = sin 35° × sin(−23.44°) + cos 35° × cos 23.44° × cos 45° = −0.2282 + 0.5315 = 0.3033, so elevation = 17.7°.
4. sin(azimuth) = cos 23.44° × sin 45° ÷ cos 17.7° = 0.681, so the sun is 42.9° off due south.
5. Gap = 38.6 ÷ tan(17.7°) × cos(42.9°) = 121.4 × 0.732 = 88.9 in (about 7' 5").
6. Row pitch = 78 × cos(29.7°) + 88.9 = 67.8 + 88.9 = 156.7 in, a ground coverage ratio of 78 ÷ 156.7 = 50%.

Designing for noon only would need just 38.6 ÷ tan(31.56°) = 62.9 in of gap, but the rows would shade each other for most of a December morning and afternoon.

Practical notes

• Steeper tilts shed snow and dust better but need more row spacing and catch more wind. Racking and foundations must be engineered for local wind and snow loads.
• On a pitched roof, mounting flush to the roof is almost always the right call; the few percent gained from re-tilting rarely pays for the racking and wind load.
• Square the array before you set posts: see how to square a ground-mounted solar array and the diagonal calculator.
• Converting a roof pitch such as 6/12 to degrees? Use the roof pitch calculator.