Calculator
Solar Tilt and Orientation Yield Calculator
Roofs rarely face the ideal direction, and the first question every owner asks is how much that costs. The honest answer is usually less than they fear: the irradiance surface around the optimum is flat, and a roof 30° off south loses only a few percent.
This calculator estimates the annual transposition factor for a chosen tilt and azimuth against the optimum for your latitude, and shows how the choice shifts production between summer and winter.
Describe the roof
Absolute value; the model is hemisphere-agnostic.
0 = due south in the north; 90 = due west; −90 = due east.
Take the optimum-tilt figure from PVGIS for your site.
Optimum tilt for this latitude
32°
Annual energy optimum, fixed array
Yield factor versus optimum
99.9%
Expected specific yield
1,499 kWh/kWp
Expected annual production
8,993 kWh
Loss against the optimum
7 kWh/yr
0.1% of potential
Winter bias
-2%
Shallower than optimum favours summer
How the calculation works
Figure — Tilt and azimuth sensitivity
Annual irradiance on a tilted plane is a smooth surface with a single broad maximum. The optimum tilt for annual energy is close to three-quarters of the latitude plus a few degrees, lower than the latitude itself because summer has more daylight hours and clearer skies in most climates.
Away from that maximum the fall-off is quadratic, not linear, which is why small deviations barely matter and large ones matter a great deal. The azimuth penalty grows with tilt: a flat array hardly cares which way it faces, while a 45° array facing west loses a substantial fraction of the annual total.
This model reproduces the shape of that surface for temperate and Mediterranean latitudes. For a bankable figure, run the exact coordinates through PVGIS or an hourly simulation with local meteorological data.
The formula
β_opt ≈ 0.76 × |φ| + 3.1 f_tilt = 1 − k₁ × sin²((β − β_opt)/1.6) f_az = 1 − k₂ × sin²(γ/2) × sin(β)/sin(45°) Y = Y_opt × f_tilt × f_az E = Y × P_kWp φ latitude · β tilt · γ azimuth from equator-facing Y_opt optimum-tilt specific yield from an irradiance database
Assumptions behind the numbers
- The site is unshaded. Shading losses dominate orientation losses on most constrained roofs and are not modelled here.
- Ground albedo is typical (0.2) and the array is not bifacial.
- The empirical factors are fitted to mid-latitude European conditions between roughly 30° and 55°. Tropical and high-latitude sites need site-specific modelling.
- The reference yield you enter must already be the optimum-tilt figure for your location, not a horizontal-plane figure.
- Seasonal bias is a first-order indication, not an hourly result.
How to read the result
Anything above 95% of optimum is, in practice, an optimal roof: the difference is inside the uncertainty of the weather data. Between 85 and 95% the orientation is worth mentioning in a proposal but rarely worth changing the design for.
Below about 80%, consider splitting the array across two roof planes, using module-level electronics so the weaker plane does not drag a string, or accepting a smaller array on the better surface.
Orientation also shifts value, not just volume. A west-facing array produces less in total but more in the late-afternoon peak, which can be worth more under time-of-use tariffs or when the household load is in the evening.
Worked example
A house at 38° latitude has a 30° roof facing 45° west of south. PVGIS gives 1,500 kWh/kWp at optimum tilt for the site.
Optimum tilt is 0.76 × 38 + 3.1 ≈ 32°, so the 30° roof is essentially ideal in tilt. The azimuth penalty at 45° off south with a 30° tilt costs about 8%, giving a yield factor near 92% and a specific yield around 1,380 kWh/kWp.
For a 6 kWp array that is roughly 8,280 kWh a year instead of 9,000 kWh — 720 kWh lost, worth about €170 at €0.24/kWh. Against the cost of re-orienting the array with tilted frames, and the shading and wind-load penalties that would bring, the west-facing roof is the correct choice.
Mistakes that skew the answer
- Comparing the result against a horizontal-plane irradiance figure, which understates the loss.
- Assuming due south is always best. Under a tariff that pays more in the evening, or with a heavy evening load, a south-west array often produces more value.
- Treating a low tilt as a failure. Shallow tilts reduce wind load, row spacing and visual impact and cost very little energy near the equator.
- Ignoring that steeper arrays self-clean better and shed snow, which can recover part of the modelled loss in dusty or snowy sites.
- Applying one orientation factor to a roof with two or three planes instead of modelling each plane separately.
Questions readers ask
- How much does an east or west roof lose?
- At a typical 30° tilt in southern Europe, a due-east or due-west plane loses roughly 15 to 20% of the annual yield of a due-south plane. Split east-west arrays lose a similar amount per kilowatt but produce a flatter daily curve, which often raises self-consumption enough to compensate financially.
- What about a north-facing roof?
- In the northern hemisphere, a north-facing pitch at 30° or more loses 35 to 50% and is rarely worth using. A shallow north-facing pitch under about 10° loses far less and can be viable when nothing else is available.
- Should I use adjustable tilt?
- Seasonal tilt adjustment gains roughly 4 to 6% a year in mid-latitudes. That is real but small, and it requires someone to climb up twice a year and a mount that tolerates the movement. Most owners are better served by spending the same money on one more module.
- Does tilt matter more for bifacial modules?
- Yes. Bifacial gain rises sharply with height above ground and with albedo, and moderately with tilt because the rear face sees more reflected light. On a high-albedo surface a slightly steeper tilt than the monofacial optimum can be justified.
- Where do I get the optimum yield figure?
- PVGIS from the European Commission Joint Research Centre gives free optimum-tilt specific yield for any European coordinate, along with monthly breakdowns. Commercial datasets such as SolarAnywhere or Solargis are used for financed projects where the uncertainty band matters.