How this is calculated
Each location ships with twelve monthly irradiation figures for flat ground and twelve for the diffuse share, from PVGIS 5.3 averaged over 2013 to 2020: SARAH3 over Europe, ERA5 elsewhere. Nothing is fetched while you use it.
The script rebuilds an average day per month in 48 steps of sun position, projects the beam onto the tilted plane, adds sky diffuse by Hay and Davies as documented by Sandia’s PV Performance Modeling Collaborative, and adds ground reflection at an albedo of 0.2. It then tries every tilt from 0 to 90.
Turning that light into kilowatt-hours uses a flat 0.81. PVGIS’s own ratio of yearly output to light on the panel is not flat: at each site’s optimum angle with the 14 percent default loss it runs 0.82 at Bismarck down to 0.74 at Phoenix, averaging 0.79, because hot panels give up more of what lands on them.
The 0.81 is what makes this model land on PVGIS’s annual kilowatt-hours, and it does: the annual column below is within 3 percent of PVGIS at 73 of the 83 locations, within 6 percent at all of them. Panels run cold in December, so the December figures are a floor.
Worked example, Denver. December puts 77.1 kWh per square meter on flat ground, 28 percent diffuse. At 39 degrees the model lands 159 kWh on the panel, at 68 degrees 181.
Times 0.81, a 1 kW array makes 129 kWh in December on the annual angle against 147 on the December one. PVGIS’s own December slope sweep peaks at that same 68 degrees, at 149 kWh.
The annual answer runs 1 or 2 degrees flatter than PVGIS’s optimizer at 73 of the 83 locations, never more than 3, and the peak is broad: at Denver every December angle from 62 to 72 degrees is within half a percent of the best.
Why an off-grid array is aimed at December
A grid-tied system banks a July surplus against a January deficit, so only the yearly total matters. An off-grid battery carries days, so the array has to make enough in its worst month or the generator runs.
That worst month is December at 70 of the 83 locations here, November at 7, January at 5 and February at 1.
What the December angle buys
Moving from the annual-best tilt to the December-best tilt raises December output by 13 to 37 percent, averaging 16 across the 83 locations: about 14 below 35°N, 25 above 55°N. Holding it all year costs 11 to 20 percent of the annual total. Against PVGIS’s full energy model at Denver, Birmingham, Manchester and Ostersund these percentages agree within 3 points.
Summer energy an off-grid array cannot store is energy it never had, so trading some for December headroom beats more panels or more generator hours. Size the rest around the same worst month with the off-grid solar sizing calculator.
The rules of thumb, and where they break
| Rule | What it aims at | Error against the computed answer |
|---|---|---|
| Tilt = latitude | Yearly total | About 7° too steep on average, up to 22° too steep at high latitude |
| Tilt = latitude + 15 | Winter | About 10° too flat for December, from 2° to 16° too flat |
| Latitude × 0.76 + 3.1 | Yearly total, 25–50°N | Within 6° inside that band, averaging 1.7° flatter — the best of the four |
| Latitude × 0.875 + 19.2 | The winter half, 25–50°N | 5° to 14° flatter than the December optimum, 11° on average — it aims at the winter half-year |
The two multiplier formulas are Charles Landau’s, and the annual one holds up inside the 25 to 50 degree band it was written for. Past 50 the plain latitude rule fails fastest: at Reykjavik, 64.2°N, it overshoots by 22 degrees.
The reason is diffuse light. A rule from clear-sky beam geometry assumes the sun is a point you aim at; where half the December light arrives from the whole sky dome, the optimum drifts flatter for the year and steeper for the darkest month.
Roof pitch against the tilt you want
Most people do not get to choose. A panel flat on a pitched roof takes the roof’s angle, and a frame that changes it buys wind load with the degrees.
| Pitch | Degrees | Pitch | Degrees |
|---|---|---|---|
| 2/12 | 9.5 | 8/12 | 33.7 |
| 3/12 | 14.0 | 9/12 | 36.9 |
| 4/12 | 18.4 | 10/12 | 39.8 |
| 5/12 | 22.6 | 12/12 | 45.0 |
| 6/12 | 26.6 | 14/12 | 49.4 |
| 7/12 | 30.3 | 16/12 | 53.1 |
A 6/12 roof gives 26.6°: within a degree or two of the annual optimum along the Gulf coast, 6 to 8 degrees flat across the Southwest, and far short of any December angle.
| Degrees | Rise per meter of run | Degrees | Rise per meter of run |
|---|---|---|---|
| 10 | 0.18 m | 35 | 0.70 m |
| 15 | 0.27 m | 40 | 0.84 m |
| 20 | 0.36 m | 45 | 1.00 m |
| 25 | 0.47 m | 50 | 1.19 m |
| 30 | 0.58 m | 55 | 1.43 m |
Tiled roofs across northern Europe sit at 35 to 45 degrees: close to the annual optimum, 30 degrees short for December.
What facing away from south actually costs
Azimuth is where people over-worry. Hold Munich at 39 degrees of tilt and swing only the bearing, and the loss stays gentle a long way round.
| Degrees off south | Annual kWh per kW | Loss |
|---|---|---|
| 0 (due south) | 1,141 | — |
| 15 | 1,132 | 0.8% |
| 30 | 1,106 | 3.0% |
| 45 | 1,065 | 6.7% |
| 60 | 1,011 | 11.3% |
| 90 (due east or west) | 877 | 23.1% |
Thirty degrees off south costs three percent, which one extra panel in ten covers. If a roof forces a compromise, give up bearing before tilt.
Bearing still decides when the power arrives: swung west it lands in the evening, swung east it fills the battery earlier.
Snow, wind and the case for steep
The steep winter angle brings a benefit no irradiation model shows. Cooper, Burnham and Braid read inverter data from three utility-scale sites of differing tilt (Photovoltaic inverter-based quantification of snow conditions and power loss, EPJ Photovoltaics 15, 2024): the higher-tilt systems shed snow faster and more completely every time.
Normalized for snowfall, their seasonal snow losses tracked tilt inversely and non-linearly, so the first few degrees of extra tilt buy more than the last few.
- Steep also sheds leaf litter and drains rain, all of it free as far as the model is concerned.
- It loads mounts harder and needs more row spacing: a steep roof frame is a sail bolted to your rafters.
- A seasonal flip gets most of both, for two trips outside a year.
Row spacing on a flat roof or the ground
On a flat roof or in a field the next row sits in the shadow of the last. The usual design point is the winter solstice, 9 a.m. to 3 p.m. solar time, where sun elevation follows from latitude and a declination of −23.45 degrees.
A row of slant length L at tilt β casts L × sin β ÷ tan(elevation); only its northward part pushes the next row back. Add the footprint, L × cos β, for the pitch the calculator prints.
At Denver, 39.7°N, the 9 a.m. sun sits 14.1° up. A row of 5.7 ft panels needs 15 ft between row fronts at the 39° annual angle, 18 ft at the 68° December angle. Steep costs land.
At Munich, 48.1°N, the 9 a.m. solstice sun sits 7.8° up. A row of 1.75 m panels needs 7.3 m between row fronts at the 38° annual angle, 9.7 m at the 72° December angle. Steep costs land.
North of 60 degrees the solstice sun barely clears the horizon at 9 a.m. and the spacing turns absurd. Accept shading early and late, or go near-vertical on a south wall.
Past the Arctic Circle at 66.6°N the sun does not rise at all in December. There is no December angle to find, so the calculator aims at the October-to-March window instead and the darkest weeks fall to the generator.
Optimum tilt by location
Computed from the same PVGIS data the calculator uses. Click a heading to sort; two positions means summer, then winter.
| Location | Latitude | Annual tilt | December tilt | Two positions | Annual kWh/kW | December gain |
|---|---|---|---|---|---|---|
| Albany, New York | 42.6 | 37 | 67 | 20 / 58 | 1321 | +14% |
| Albuquerque, New Mexico | 35.1 | 34 | 64 | 14 / 55 | 1934 | +15% |
| Anchorage, Alaska | 61.2 | 48 | 81 | 36 / 71 | 1010 | +17% |
| Atlanta, Georgia | 33.8 | 31 | 61 | 12 / 52 | 1437 | +14% |
| Austin, Texas | 30.3 | 27 | 58 | 9 / 48 | 1464 | +15% |
| Baltimore, Maryland | 39.3 | 36 | 66 | 17 / 56 | 1373 | +14% |
| Bangor, Maine | 44.8 | 41 | 70 | 23 / 61 | 1345 | +14% |
| Baton Rouge, Louisiana | 30.4 | 28 | 58 | 9 / 48 | 1437 | +14% |
| Bend, Oregon | 44.1 | 38 | 69 | 23 / 60 | 1620 | +16% |
| Billings, Montana | 45.8 | 42 | 72 | 24 / 63 | 1635 | +15% |
| Birmingham, Alabama | 33.5 | 30 | 60 | 12 / 51 | 1441 | +14% |
| Bismarck, North Dakota | 46.8 | 42 | 72 | 25 / 63 | 1515 | +15% |
| Boise, Idaho | 43.6 | 39 | 70 | 22 / 60 | 1710 | +15% |
| Boston, Massachusetts | 42.4 | 38 | 68 | 20 / 59 | 1370 | +15% |
| Burlington, Vermont | 44.5 | 37 | 67 | 22 / 59 | 1277 | +14% |
| Casper, Wyoming | 42.9 | 41 | 70 | 22 / 61 | 1838 | +14% |
| Charleston, West Virginia | 38.4 | 34 | 64 | 17 / 54 | 1339 | +14% |
| Charlotte, North Carolina | 35.2 | 33 | 62 | 13 / 53 | 1445 | +14% |
| Columbia, South Carolina | 34.0 | 32 | 62 | 12 / 52 | 1467 | +14% |
| Columbus, Ohio | 40.0 | 35 | 65 | 18 / 55 | 1354 | +13% |
| Concord, New Hampshire | 43.2 | 39 | 69 | 21 / 60 | 1365 | +15% |
| Denver, Colorado | 39.7 | 39 | 68 | 19 / 59 | 1827 | +14% |
| Des Moines, Iowa | 41.6 | 38 | 68 | 20 / 58 | 1467 | +14% |
| Dover, Delaware | 39.2 | 36 | 66 | 17 / 56 | 1447 | +14% |
| Harrisburg, Pennsylvania | 40.3 | 36 | 66 | 18 / 56 | 1349 | +14% |
| Hartford, Connecticut | 41.8 | 38 | 68 | 20 / 59 | 1375 | +14% |
| Honolulu, Hawaii | 21.3 | 21 | 52 | 0 / 42 | 1785 | +15% |
| Indianapolis, Indiana | 39.8 | 35 | 65 | 18 / 56 | 1373 | +14% |
| Jackson, Mississippi | 32.3 | 30 | 60 | 11 / 50 | 1457 | +14% |
| Lansing, Michigan | 42.7 | 36 | 65 | 20 / 57 | 1320 | +13% |
| Las Vegas, Nevada | 36.2 | 35 | 65 | 15 / 56 | 1973 | +15% |
| Lincoln, Nebraska | 40.8 | 38 | 68 | 19 / 59 | 1550 | +14% |
| Little Rock, Arkansas | 34.8 | 32 | 62 | 13 / 53 | 1451 | +15% |
| Louisville, Kentucky | 38.3 | 34 | 64 | 17 / 55 | 1395 | +14% |
| Madison, Wisconsin | 43.1 | 38 | 68 | 21 / 58 | 1377 | +14% |
| Minneapolis, Minnesota | 45.0 | 40 | 69 | 23 / 60 | 1383 | +13% |
| Nashville, Tennessee | 36.2 | 33 | 63 | 15 / 53 | 1401 | +14% |
| Oklahoma City, Oklahoma | 35.5 | 33 | 63 | 14 / 54 | 1593 | +15% |
| Orlando, Florida | 28.5 | 27 | 57 | 7 / 47 | 1466 | +14% |
| Phoenix, Arizona | 33.5 | 33 | 62 | 12 / 53 | 1932 | +14% |
| Providence, Rhode Island | 41.8 | 38 | 68 | 20 / 59 | 1365 | +15% |
| Rapid City, South Dakota | 44.1 | 42 | 71 | 23 / 62 | 1651 | +14% |
| Richmond, Virginia | 37.5 | 34 | 65 | 15 / 55 | 1397 | +15% |
| Sacramento, California | 38.6 | 35 | 66 | 17 / 57 | 1762 | +16% |
| Salt Lake City, Utah | 40.8 | 37 | 68 | 19 / 58 | 1807 | +16% |
| San Juan, Puerto Rico | 18.5 | 19 | 49 | 0 / 39 | 1709 | +15% |
| Spokane, Washington | 47.7 | 39 | 70 | 26 / 61 | 1473 | +15% |
| Springfield, Illinois | 39.8 | 35 | 66 | 18 / 56 | 1424 | +15% |
| Springfield, Missouri | 37.2 | 34 | 64 | 16 / 55 | 1466 | +14% |
| Trenton, New Jersey | 40.2 | 37 | 67 | 18 / 57 | 1383 | +14% |
| Washington, D.C. | 38.9 | 36 | 66 | 17 / 56 | 1394 | +14% |
| Wichita, Kansas | 37.7 | 36 | 65 | 16 / 56 | 1608 | +14% |
| Aarhus, Denmark | 56.2 | 40 | 77 | 30 / 64 | 978 | +22% |
| Athens, Greece | 38.0 | 32 | 64 | 16 / 54 | 1619 | +16% |
| Bratislava, Slovakia | 48.1 | 36 | 69 | 25 / 58 | 1194 | +17% |
| Brussels, Belgium | 50.9 | 38 | 72 | 26 / 61 | 1053 | +18% |
| Budapest, Hungary | 47.5 | 37 | 69 | 24 / 59 | 1219 | +15% |
| Cluj-Napoca, Romania | 46.8 | 36 | 67 | 24 / 58 | 1216 | +14% |
| Galway, Ireland | 53.3 | 38 | 73 | 26 / 61 | 912 | +19% |
| Groningen, Netherlands | 53.2 | 39 | 73 | 28 / 62 | 994 | +17% |
| Inverness, Scotland | 57.5 | 40 | 77 | 28 / 64 | 812 | +22% |
| Jyvaskyla, Finland | 62.2 | 43 | 84 | 35 / 68 | 848 | +30% |
| Lisbon, Portugal | 38.7 | 33 | 65 | 17 / 55 | 1585 | +16% |
| Ljubljana, Slovenia | 46.1 | 34 | 68 | 22 / 57 | 1166 | +17% |
| Lyon, France | 45.8 | 36 | 69 | 23 / 58 | 1299 | +16% |
| Madrid, Spain | 40.4 | 36 | 68 | 19 / 58 | 1659 | +17% |
| Manchester, England | 53.5 | 38 | 74 | 26 / 61 | 882 | +20% |
| Munich, Germany | 48.1 | 38 | 72 | 24 / 60 | 1134 | +18% |
| Nicosia, Cyprus | 35.2 | 31 | 62 | 13 / 52 | 1718 | +15% |
| Ostersund, Sweden | 63.2 | 45 | 85 | 35 / 70 | 857 | +29% |
| Prague, Czechia | 50.1 | 37 | 71 | 26 / 60 | 1095 | +18% |
| Reykjavik, Iceland | 64.2 | 42 | 86 | 34 / 69 | 687 | +37% |
| Riga, Latvia | 57.0 | 41 | 76 | 31 / 64 | 976 | +19% |
| Rome, Italy | 41.9 | 36 | 68 | 19 / 58 | 1527 | +17% |
| Sofia, Bulgaria | 42.7 | 34 | 65 | 20 / 56 | 1321 | +14% |
| Tartu, Estonia | 58.4 | 41 | 78 | 32 / 65 | 957 | +23% |
| Trondheim, Norway | 63.4 | 46 | 83 | 35 / 71 | 788 | +24% |
| Valletta, Malta | 35.9 | 30 | 62 | 13 / 52 | 1637 | +16% |
| Vienna, Austria | 48.2 | 36 | 70 | 25 / 59 | 1162 | +17% |
| Vilnius, Lithuania | 54.7 | 38 | 72 | 29 / 61 | 970 | +17% |
| Warsaw, Poland | 52.2 | 37 | 71 | 28 / 60 | 1043 | +18% |
| Zagreb, Croatia | 45.8 | 35 | 69 | 22 / 57 | 1244 | +18% |
| Zurich, Switzerland | 47.4 | 36 | 69 | 24 / 58 | 1161 | +16% |
Quick answers
What angle should solar panels be tilted at?
Less than your latitude, and the gap widens northward: about 0.9 of latitude in the thirties, 0.86 in the forties, 0.72 above 50°N. That is 19 to 48 degrees across these 83 places. An off-grid array sized by December wants 49 to 86.
Is the best tilt equal to your latitude?
No. It sits about 7 degrees steeper than the computed optimum, up to 22 in the far north, because cloudier skies pull the yearly optimum flatter.
How much extra December energy does a steeper tilt give?
Between 13 and 37 percent, averaging 16: about 14 below 35°N and 25 above 55°N. Held all year it costs 11 to 20 percent of the annual total.
Is it worth adjusting panel tilt twice a year?
A flip adds 2.4 to 6.3 percent to the year, and much more in the winter months that set an off-grid system’s size.
How much does facing away from due south cost?
At Munich, 39° tilt: 0.8 percent at 15° off south, 3.0 at 30°, 6.7 at 45°, 23.1 facing due east or west.
Sources
PVGIS 5.3, European Commission Joint Research Center: monthly radiation and PV performance APIs, 2013–2020 averages, SARAH3 at about 5 km over Europe and ERA5 at about 25 km elsewhere, and the user manual for the 14 percent default loss. Sandia PV Performance Modeling Collaborative, Hay and Davies sky diffuse model; hourly split after Collares-Pereira and Rabl, and Liu and Jordan. Charles R. Landau, solarpaneltilt.com, revised 2017. Cooper, Burnham and Braid, EPJ Photovoltaics 15, 2024. Checked September 2026.
Go deeper
Tilt only sets how much light lands on the glass. Turn it into panels, battery and generator hours with the off-grid solar sizing calculator, look up the resource in the peak sun hours atlas, and see why the darkest month sets the size in the winter design month guide and how to size an off-grid solar system.