Solar Panel Angle Calculator

How the angle is worked out

A fixed solar array collects the most energy over a year when it tilts at about the latitude of the site. A site at 40° north tilts its panels about 40° up from flat, and a site closer to the equator tilts them less. NREL’s PVWatts uses exactly this as its default tilt, and Sandia’s modeling guide says the error is least near the latitude tilt. The calculator rounds your latitude to a whole degree and uses that for the year-round angle.

Pick your state to fill in the latitude of its largest city, or type your own. Your own latitude is better, because a state covers a lot of ground. A map app or the weather page for your town shows it. Use a minus sign for the southern hemisphere.

The two-season angles

The rule most installers quote is to add 15° to the latitude for the dark half of the year and subtract 15° for the bright half. The calculator shows both, with the months each one is for. We checked the rule against NREL PVWatts and the EU JRC PVGIS. Both models agree it works, and both agree on how little it is worth: roughly 4-5% more energy over a year than leaving the array at the latitude angle. If climbing onto a roof twice a year sounds like a poor trade for that, the models agree with you. The two-season angles are useful for adjustable ground mounts and for understanding why a steep array does well in December.

Summer never goes below flat. Close to the equator the subtraction would give a negative angle, so the tool shows 0° and calls it flat.

Which way to face

In the northern hemisphere, point the array at true south, which is an azimuth of 180°. In the southern hemisphere, point it at true north, an azimuth of 0°. The south-facing and north-facing numbers differ because the sun sits in the other half of the sky.

Moving away from south costs energy slowly at first and faster later. The Sandia guide notes that the loss is greatest as the array points away from due south. An east or west facing array makes about 18-27% less in the model runs, which is the figure the calculator prints. A roof that faces somewhat east of south or west of south is often a fine place for panels, and the right choice there is a design decision for your installer.

True south versus your compass

Compasses point to magnetic north, which is not the same place as true north. The difference is the magnetic declination. It is positive where magnetic north lies east of true north and negative where it lies west. To find true south with a compass, subtract the declination from 180°. With a declination of 7.5° east, as in Denver, true south reads 172.5°. In Boston magnetic north lies west of true north, so the declination is negative and true south reads 193.9°.

Enter your declination and the tool does the subtraction for you, including the case where the answer wraps around the compass circle. Declination changes slowly from year to year, so look it up on NOAA’s calculator instead of trusting an old table.

Roof pitch

Roofers state pitch as rise over 12 inches of run. The angle in degrees is the arctangent of the rise divided by 12, so a 12/12 roof is 45°. The calculator turns the year-round tilt into the nearest half step of pitch. If you enter your own pitch, it tells you how many degrees flatter or steeper the roof is than the year-round angle. Flush-mounted panels take the roof’s angle. The Department of Energy describes south-facing roofs between 15° and 40° as working well, which covers most pitched roofs.

What this does not cover

The tool gives angles, not energy. It does not account for shade, snow, the heat of the roof, or the horizon. For how many panels a home needs, use the panel count calculator. For the real design of your system, the installer’s site survey beats any online tool.

Common mistakes

• Using magnetic south as true south. In parts of the country the two differ by more than 10°.
• Entering the latitude with the wrong sign. North is positive, south is negative. The tool reads the sign to pick which way to face.
• Re-tilting for a few percent. The two-season gain is about the size of a normal year-to-year change in weather.
• Tearing up a roof for the angle. A roof within 10° of the year-round angle loses about 2% or less in the zone where most US homes sit.

Worked example

1. Inputs: latitude 39.74° N (Colorado), magnetic declination 7.5° E.
2. Year-round tilt = latitude = 39.74°, rounded to 40°
3. October-March tilt = latitude + 15° = 39.74° + 15° = 54.74°, rounded to 55°
4. April-September tilt = latitude − 15° = 39.74° − 15° = 24.74°, rounded to 25°
5. Compass reading = azimuth − declination = 180° − 7.5° = 172.5°
6. Roof pitch = 12 × tan(40°) = 10.07 per 12, about 10/12

Questions people ask