Solar Angles Explained: Azimuth, Tilt and Zenith

Last updated: November 2026

Where is the sun, and which way should the panels face? Four angles describe the sun and two describe the panel. In one line each:

• Altitude (elevation) is the sun’s height above the horizon: 0 degrees at sunrise, 90 degrees straight overhead.
• Zenith is the sun’s angle from straight overhead. Zenith plus altitude is always 90 degrees.
• Azimuth is the compass bearing, measured clockwise from north: 90 degrees is east, 180 degrees is due south, 270 degrees is west.
• Tilt is the angle of the panel from horizontal, and surface azimuth is the direction it faces.

SurgePV publishes this post and sells solar design software.

This guide covers each angle with numbers. Sun-position figures are worked from the formulas shown. Tilt, azimuth and tracker figures come from the European Commission’s PVGIS 5.3 (details under each table). For related reading, see European Solar Incentives and the tilt and azimuth calculator guide. For Europe-specific compliance details, see Europe solar compliance.

What this guide covers:

• The sun and panel angles defined, with the formulas and a worked example
• How sun position changes by hour, season, and latitude
• Optimal tilt for 15 European cities, from PVGIS
• Yield loss for each azimuth deviation from due south
• The combined tilt-azimuth sensitivity matrix
• How PV design software uses these angles
• Bifacial modules, trackers, and east-west layouts

The Six Solar Angles

Six angles govern how sunlight meets a solar panel. Four describe the sun’s position in the sky (altitude, zenith, azimuth and hour angle). Two describe the panel’s orientation (tilt and surface azimuth).

Sun Position Angles

Solar Altitude (Elevation) Angle is the angle between the sun and the horizontal plane. At sunrise or sunset, altitude is 0 degrees. When the sun is directly overhead, altitude is 90 degrees.

Solar Zenith Angle is the complement of altitude, the angle between the sun and the point directly overhead. Many simulation engines use zenith rather than altitude because it simplifies tilted-surface irradiance trigonometry.

Solar Azimuth Angle is the sun’s compass direction, measured clockwise from true north (0 degrees = north, 90 = east, 180 = south, 270 = west). The azimuth changes all day. At 55 degrees north on the summer solstice the sun rises at an azimuth of about 46 degrees (north-east) and sets at about 314 degrees (north-west), a sweep of about 268 degrees.

Hour Angle tracks the sun’s position relative to solar noon. At solar noon the hour angle is 0 degrees. The Earth turns 15 degrees an hour (360 degrees in 24 hours), so each hour before noon adds -15 degrees and each hour after adds +15 degrees. At 9:00 solar time the hour angle is -45 degrees.

Panel Orientation Angles

Tilt Angle (Slope) is the angle between the panel surface and horizontal ground. A flat panel has 0-degree tilt and a wall-mounted panel has 90-degree tilt.

Surface Azimuth Angle is the compass direction the panel faces, measured clockwise from true north. A south-facing panel has a surface azimuth of 180 degrees. The difference between the sun’s azimuth and the panel’s surface azimuth, together with tilt, decides how directly sunlight hits the panel at any moment.

How the Angles Work Together

The angle of incidence, the angle between incoming sunlight and the perpendicular to the panel surface, determines how much direct irradiance a panel captures. At 0 degrees sunlight hits head-on, and as the angle grows less energy is captured. All the angles above combine to set this value.

Zenith Angle

The zenith angle answers “how far from straight up is the sun?” At solar noon, north of the Tropic of Cancer, it equals the latitude minus the declination. At 50 degrees north on the winter solstice, noon zenith is 50 - (-23.44) = 73.44 degrees, which is a noon altitude of 16.56 degrees. At the equinoxes the noon zenith equals the latitude. Simulation engines take the zenith angle as an input to the irradiance equations, as in the GHI, DNI and DHI guide (GHI = DNI x cos(zenith) + DHI). For the glossary definition, see solar zenith and azimuth.

Formulas for Zenith, Altitude and Azimuth

With latitude φ, declination δ and hour angle h:

• Zenith: cos(θz) = sin φ x sin δ + cos φ x cos δ x cos h
• Altitude: α = 90° - θz
• Azimuth: cos(A) = (sin δ - cos θz x sin φ) / (sin θz x cos φ). This gives the bearing from north before solar noon (h negative). After noon use 360° - A.

Declination δ is the sun’s latitude on the celestial sphere. It is +23.44° at the June solstice, 0° at the equinoxes and -23.44° at the December solstice, because 23.44° is the tilt of the Earth’s axis (NASA Earth fact sheet). For other dates use the sun angle calculator or the NOAA solar calculator.

Worked example. Munich (48.14°N), 21 December, 10:00 solar time. The hour angle is h = -2 x 15° = -30° and δ = -23.44°.

• cos(θz) = sin 48.14° x sin(-23.44°) + cos 48.14° x cos(-23.44°) x cos(-30°) = 0.7448 x (-0.3978) + 0.6673 x 0.9175 x 0.8660 = -0.2963 + 0.5302 = 0.2340
• θz = 76.47°, so altitude α = 90° - 76.47° = 13.53°
• cos(A) = (-0.3978 - 0.2340 x 0.7448) / (0.9722 x 0.6673) = -0.5720 / 0.6488 = -0.8817, so A = 151.85°, about south-south-east

For comparison, the open-source library pvlib, which implements full solar-position algorithms, returns an altitude of 13.56° and an azimuth of 151.9° for the same site and time. The small difference comes from using δ = -23.44° exactly.

How Solar Angles Change Throughout Day and Year

The sun’s position changes every minute and shifts with the seasons.

Daily Sun Path

On any day the sun rises in the east, peaks at solar noon, and sets in the west. The arc depends on date and latitude. At solar noon the sun reaches its maximum altitude and crosses due south (Northern Hemisphere), when direct beam irradiance on a south-facing panel is strongest. At 55 degrees north the day from sunrise to sunset is about 6.9 hours at the December solstice and 17.1 hours at the June solstice (geometric day length, without atmospheric refraction).

Seasonal Variation

The Earth’s 23.44-degree axial tilt drives the seasons. On the June solstice the sun’s declination is +23.44 degrees and noon altitude peaks. On the December solstice it is -23.44 degrees, and at northern latitudes the sun barely climbs above the horizon.

What Direction Is the Sun at Solar Noon on the Winter Solstice?

South, for anyone north of the Tropic of Cancer. At solar noon the sun is on your meridian, so its azimuth is 180 degrees. In the Southern Hemisphere, south of the Tropic of Capricorn, it is north. Its altitude that day is the lowest of the year: 90 - latitude - 23.44 degrees.

Solar Altitude at Noon by Latitude and Season

Noon altitude = 90° - latitude + declination. Values are geometric, without atmospheric refraction.

The winter solstice noon altitude at 55 degrees north is 11.6 degrees, so the sun barely clears a neighbouring roofline. That is why shading analysis software matters most for winter months.

Winter Solstice for Row Spacing

Inter-row spacing on flat roofs is commonly sized for the low winter sun. One criterion is to keep the back row clear of the front row’s shadow at solar noon on the winter solstice. The gap needed between the back of one row and the front of the next is:

Gap = Module length x sin(tilt) / tan(solar altitude at winter solstice noon)

With a 1.7 m module at a 30-degree tilt, the front row’s top edge is 1.7 x sin 30° = 0.85 m above the roof.

• At 52°N the noon altitude is 14.56°, so the gap is 0.85 / tan 14.56° = 0.85 / 0.2597 = 3.27 m. Row pitch, from front edge to the next front edge, is 1.7 x cos 30° + 3.27 = 1.47 + 3.27 = 4.74 m.
• At 40°N the noon altitude is 26.56°, so the gap is 0.85 / tan 26.56° = 0.85 / 0.5 = 1.70 m, and the pitch is 1.47 + 1.70 = 3.17 m.

Optimal Tilt Angle by Latitude

The common rule of thumb is to set tilt equal to latitude. The PVGIS results below show the optimum sits below latitude in every city tested.

The Tilt-Equals-Latitude Rule and When It Breaks

Three factors move the optimal tilt away from latitude:

1. Summer weighting. Most of the year’s sunlight arrives in summer. In PVGIS 5.3 (2005 to 2023), April to September brings 69% of annual horizontal irradiation in Madrid, 74% in Munich and 84% in Stockholm. A flatter tilt favours those months, so the optimal tilt is below latitude.

2. Diffuse radiation. Diffuse light comes from the whole sky, so flatter tilts capture more of it. In cloudy climates, where diffuse light is half of annual GHI, the optimum drops further below latitude.

3. Snow and soiling. In snowy or dusty places a steeper tilt can be worth a small yield cost. Check local guidance before you trade yield for it.

Fixed vs. Seasonal Tilt

Adjusting tilt by season gains some energy over the best fixed tilt. A common rule of thumb is a summer tilt of latitude minus 15 degrees and a winter tilt of latitude plus 15 degrees. In Munich (latitude 48.1°), PVGIS gives 1,433.7 kWh/m² a year on a 39-degree fixed plane. Using 33 degrees from April to September and 63 degrees from October to March gives 1,472.8 kWh/m², 2.7% more. Whether that justifies the labour and hardware is a project decision. It is rarely worth it on a residential roof.

Optimal Fixed Tilt for 15 European Cities

The table shows the fixed south-facing tilt that maximises annual yield in PVGIS 5.3 (SARAH-3 data, 2005 to 2023, queried on 28 October 2026 for city-centre coordinates). Irradiation is on the plane at that tilt. Yield is for 1 kWp with PVGIS’s 14% default system loss. The table is sorted by latitude.

Also see: solar panel ROI in Italy, Germany solar subsidies, France solar feed-in tariffs and Spain net metering.

The optimum is between 2 degrees below latitude (Seville) and 14 degrees below (Copenhagen). The gap is smallest in the sunny south and widest in the cloudier north, the opposite of what a “flatter in the south” rule would suggest. For the choice by roof pitch and region, read optimal tilt angle by latitude and roof pitch and performance.

Azimuth Orientation Impact

In the Northern Hemisphere, due south (180 degrees azimuth) captures the most annual energy. Most roofs are not due south, so how much does deviation cost?

Yield Loss by Azimuth Deviation

The table shows annual yield as a percentage of the due-south yield at the tilt that is optimal for each site (39 degrees in Munich, 37 degrees in Madrid). Values are from PVGIS 5.3 for 1 kWp with 14% system loss (2005 to 2023 averages).

The table uses deviations to the west of south. Facing east instead gives almost the same result: at a 10-degree tilt Munich’s east- and west-facing yields differ by under 0.1% and Madrid’s by about 1%.

A 30-degree deviation costs about 3% to 3.6%. A 45-degree deviation costs about 7% to 7.5%. The steep drop comes past 60 degrees, where east- or west-facing panels lose about a quarter of the due-south yield.

When East-West Orientations Make Sense

East-west (E-W) mounting is common on flat commercial roofs for several reasons, even with the yield cost. In the same PVGIS runs, a 10-degree tilt facing east or west yields about 942 kWh/kWp a year in Munich against 1,141 for the best south-facing fixed tilt (about 17% less), and about 1,349 against 1,620 in Madrid (also about 17% less). Both figures are the average of the east- and west-facing runs.

Flat roof density. E-W layouts use low-tilt panels facing opposite directions, which cast short shadows and let rows sit close together, so more modules fit on the same roof. Whether the extra capacity outweighs the lower yield per kWp is a layout question that a simulation answers.

Flatter production curve. E-W arrays produce earlier in the morning and later in the evening than a south-facing array, which can match some commercial load profiles better.

Time-of-use pricing. In markets that pay more for morning or evening energy, a west- or east-facing array can earn more per kWh than a south-facing one.

Magnetic vs. True South

A recurring error is using a magnetic compass to find south. In the Munich run above, a 10-degree azimuth error costs 0.3% of yield and a 15-degree error 0.8%, so a small compass error is a minor loss. Still, reference true south using GPS coordinates or satellite imagery for large arrays.

Combined Tilt and Azimuth Sensitivity

Real roofs fix tilt and azimuth by architecture, so the combined effect decides the penalty.

Yield Impact Matrix

The matrix shows annual yield for Munich (48.1°N) as a percentage of the best case (39-degree tilt, due south), from PVGIS 5.3 (2005 to 2023, 14% system loss).

The “Good Enough” Zone

In this run the 30, 39 and 50 degree tilts with an azimuth within 30 degrees of south all stay at 95% or more of the best case. A roof at 39 degrees facing 15 degrees off south gives up 1%. Outside this zone losses escalate: a 60-degree tilt facing 45 degrees off south keeps 87%, and a vertical facade facing south-west keeps 65%.

For a direct comparison of design tools, see Arka 360 vs SurgePV.

Solar Angles in Design Software

A modern solar design platform replaces manual angle calculations with site-specific simulation. SurgePV covers roof modeling, array layout, shading analysis and energy-yield modeling:

1. Roof modeling gives the tilt and azimuth of each roof face.
2. Shading analysis models hourly sun paths, seasonal changes and obstruction geometry against the 3D model.
3. Energy-yield modeling combines the angles, shading and weather data into hourly production.
4. Array layout sets row spacing and module placement against the roof.

The result accounts for the sun and panel angles, weather data and 3D obstructions in a way that a tilt-equals-latitude rule cannot. Results still depend on the source data, assumptions and equipment models, and the responsible engineer reviews them.

From Angles to Proposals

SurgePV feeds yield data into the energy and financial modeling tool for ROI, payback, and bill savings, and into customer-ready solar proposals.

Advanced: Bifacial, Trackers, and East-West Layouts

Three configurations change the angle equation.

Bifacial Modules

Bifacial panels generate electricity from both sides. The rear side collects light reflected from the ground (albedo) and diffuse light from the sky, so tilt, ground surface and row spacing all affect the rear gain. A lighter ground surface raises rear irradiance, and tight row spacing reduces the ground area lit between rows. For more on this topic, see the Bifacial Solar Panel Design Guide and the Ground Mounted Solar Design Guide. The PVGIS figures on this page are for monofacial modules.

Single-Axis Trackers

Single-axis trackers rotate panels east to west through the day. In PVGIS 5.3 a single horizontal north-south axis tracker yields 21.4% more per kWp than the best fixed tilt in Madrid (1,966 against 1,620 kWh/kWp) and 15.4% more in Munich (1,317 against 1,141 kWh/kWp). These are per-kWp figures for a single tracker. A real tracker field needs row spacing, which reduces the gain, so test a layout rather than a single array.

Dual-Axis Trackers

Dual-axis trackers adjust both tilt and azimuth. In the same PVGIS runs they yield 37.9% more than the best fixed tilt in Madrid (2,234 kWh/kWp) and 32.3% more in Munich (1,509 kWh/kWp). Dual-axis systems add mechanical complexity and maintenance, and the extra yield has to be weighed against that cost.

East-West Flat Roof Layouts

As covered above, E-W configurations give up yield per panel for roof utilization.

• Typical tilt: low, such as the 10 degrees used in the PVGIS runs above
• Azimuth: 90 degrees (east) and 270 degrees (west)
• Inter-row spacing: short, because low-tilt panels cast short shadows

On a given roof the E-W layout can fit more modules, but each yields about 17% less per kWp than a south-facing one in the PVGIS runs for Munich and Madrid. Compare total annual energy and economics from a simulation for the real roof, using specific yield per module as an input.

Conclusion

Solar angles are the practical foundation of every design decision, from which roof faces to use, to how many rows fit, to whether an E-W layout beats south-facing.

Three actions to take from this guide:

1. Use the tilt and azimuth tables to assess a roof quickly. If the combination falls in the “good enough” zone (30 to 50 degrees tilt and within 30 degrees of south in the Munich rows tested), proceed with confidence.

2. Run site-specific simulations for every project. The tables are a sanity check. A cloud solar design tool that models real 3D geometry, hourly sun position and weather data gives a more defensible estimate.

3. Check winter shading. Use the low winter sun for row spacing, shading analysis and obstruction clearance, then check the rest of the year in the simulation.

To see how tilt, azimuth, and row spacing decisions fit into the full system design process, see the 12-step residential solar system design guide.

Frequently Asked Questions

What is the best angle for solar panels?

For a fixed south-facing array in Europe the best tilt is below the latitude. In PVGIS 5.3 data the optimal tilt is 32 degrees in Athens, 37 in Madrid, 39 in Munich and 42 in Copenhagen, which is 2 degrees below latitude in Seville and 14 degrees below in Copenhagen. The curve is flat near the optimum: in Munich the yield at 33 degrees is within 0.4% of the yield at 37 degrees.

What is the difference between azimuth and zenith angle in solar?

Azimuth is the compass direction measured clockwise from north (0 degrees = north, 180 degrees = south). Zenith is the angle between the sun and the point directly overhead. Azimuth tells you where along the horizon the sun is, zenith tells you how high it is. Solar altitude (elevation) is the complement of zenith: altitude plus zenith always equals 90 degrees.

Does the direction solar panels face really matter?

Yes, but less than most people expect near south. In a PVGIS run for Munich at a 39 degree tilt, a panel facing 30 degrees off south produces 97.0% of the due-south yield, 60 degrees off south 88.7%, and a panel facing due east or west 76.9%. East-west layouts can still make sense where evening or morning power is worth more, or where roof area is the limit.

What is the optimal tilt angle for solar panels in Europe?

From PVGIS 5.3 (2005 to 2023): Athens 32 degrees, Lisbon 33, Madrid 37, Rome 37, Munich 39, Paris 39, Amsterdam 39, London 40 and Copenhagen 42. These maximise annual yield for a fixed south-facing array. East-west or non-south roofs need a site-specific simulation.

How do you calculate the sun angle at a specific location?

Solar altitude at noon equals 90 minus your latitude plus the sun’s declination. Declination is +23.44 degrees at the June solstice and -23.44 degrees at the December solstice. For example, at 50 degrees north on the winter solstice: 90 - 50 - 23.44 = 16.56 degrees. For hour-by-hour altitude and azimuth, use the SurgePV sun angle calculator at surgepv.com/tools/sun-angle-calculator or the NOAA solar calculator.

What is the zenith angle of the sun?

The solar zenith angle is the angle between the sun and the vertical, measured at the observer. It is 0 degrees when the sun is directly overhead and 90 degrees at the horizon. At solar noon it equals the latitude minus the declination (for a site north of the Tropic of Cancer), so at 50 degrees north on the winter solstice it is 73.44 degrees.

What is the direction of the sun at solar noon on the winter solstice?

South, for anyone north of the Tropic of Cancer (23.44 degrees north). At solar noon the sun is on your meridian, so its azimuth is 180 degrees. South of the Tropic of Capricorn the answer is north, and between the two tropics it depends on the date.

Sources

• European Commission JRC, Using PVGIS 5 (version 5.3, SARAH-3 2005 to 2023). Tilt, azimuth, matrix, seasonal and tracker figures come from the PVGIS 5.3 API (PVcalc and MRcalc tools), run on 28 October 2026 for 1 kWp with the default 14% system loss.
• NASA Earth Fact Sheet for the 23.44 degree obliquity
• pvlib documentation, used to cross-check the worked sun-position example
• NOAA magnetic field calculators