Solar Tilt Angle Calculator Widget

Add a panel-angle helper to a solar installer's or off-grid site. Visitors enter their latitude and hemisphere and get the year-round optimum fixed tilt from a peer-reviewed global fit, the direction to face, the equivalent roof pitch and rule-of-thumb winter and summer angles.

Solar & Energy Calculator Runs in your browser Free · no ads

Customize your widget

Theme
Auto follows the visitor's light/dark setting.
Style
Attribution on your page
Optional and entirely your choice. The exact line is shown in the code below; it links to the tool with rel="nofollow".
More options
Starting values
Leave blank to use the widget's defaults. Visitors can still change every value.

Live preview

Exactly what your visitors will see

Embed code

<iframe src="https://a2z.tools/embed/w/solar-tilt-angle-calculator" title="Solar Tilt Angle Calculator by A2Z Tools" width="100%" height="600" style="border:0;width:100%" loading="lazy" allow="clipboard-write"></iframe>

A plain iframe. Works everywhere, including site builders that strip scripts. Adjust height if your content needs more room.

Works with

How it works

The year-round tilt comes from Jacobson and Jadhav (2018, Solar Energy), who modelled the optimal fixed tilt for PV sites in countries around the world and fitted a third-order polynomial to latitude for each hemisphere. In the north the tilt is 1.3793 + 1.2011 phi - 0.014404 phi² + 0.000080509 phi³; at 40 degrees N that gives 31.5 degrees, flatter than the old 'tilt = latitude' rule because diffuse light and summer sun favour a lower angle. The southern fit uses negative latitudes and gives 27.3 degrees at 30 degrees S. Following the paper, tilts within 10 degrees of the equator are raised to 10 degrees so rain can wash the panels. Panels face the equator: true south (azimuth 180 degrees) in the Northern Hemisphere and true north (0 degrees) in the Southern - true, not magnetic, north. The result is also shown as a roof pitch (12 x tan(tilt) in 12), and the common seasonal rule of latitude + 15 degrees in winter and - 15 degrees in summer is shown and labelled as a rule of thumb.

Calculation method

  • Northern: tilt = 1.3793 + phi(1.2011 + phi(-0.014404 + phi x 0.000080509)), phi = latitude in degrees
  • Southern: tilt = |-0.41657 + phi(1.4216 + phi(0.024051 + phi x 0.00021828))|, phi negative
  • Tilts below 10 degrees are raised to 10 degrees (the paper's practice near the equator)
  • Roof pitch = 12 x tan(tilt) in 12; seasonal rule of thumb = latitude +/- 15 degrees

Worked examples

New York area

Inputs: Latitude 40 degrees N

Result: Tilt 31.5 degrees, facing true south; roof pitch 7.4/12; winter 55 degrees, summer 25 degrees

1.3793 + 40(1.2011 + 40(-0.014404 + 40 x 0.000080509)) = 31.53.

Southern Hemisphere

Inputs: Latitude 30 degrees S

Result: Tilt 27.3 degrees, facing true north

-0.41657 + (-30)(1.4216 + (-30)(0.024051 + (-30)(0.00021828))) = -27.31; negative means facing north.

Near the equator

Inputs: Latitude 5 degrees N

Result: Tilt 10 degrees (fit gives 7 degrees)

Raised to the 10-degree minimum the paper applies within 10 degrees of the equator.

Limitations

  • A latitude-only fit: local weather, horizon shading, snow and ground reflectance can shift the true optimum; PVGIS or PVWatts can model a specific site.
  • Optimises yearly energy for a fixed panel; systems valuing winter output or with time-of-use tariffs may prefer another angle.
  • Seasonal angles are a rule of thumb and are not from the cited paper.

Where publishers use it

  • Ground-mount and RV/off-grid solar guides
  • Installers explaining why a roof's pitch is close enough
  • Solar-kit sellers' setup instructions
  • Geography and physics teaching about sun angles
  • Balcony-solar and plug-in panel blogs in Europe

Questions

Should my solar panel tilt equal my latitude?

That old rule over-tilts at mid and high latitudes. The Jacobson and Jadhav fit gives 31.5 degrees at 40 degrees N and 20.3 degrees at 20 degrees N, because diffuse light and the high summer sun favour a flatter panel over a whole year.

Which direction should solar panels face?

Towards the equator: true south in the Northern Hemisphere and true north in the Southern. Use true north, not a compass reading - magnetic declination can be more than 10 degrees in some places.

What is the best angle near the equator?

The fitted optimum is close to flat, but panels are usually set at 10 degrees or more so rain washes off dust; the paper limits tilts between -10 and +10 degrees latitude to 10 degrees, and so does the widget.

Should I adjust the tilt by season?

If your mount allows it, a common rule of thumb is latitude + 15 degrees in winter and latitude - 15 degrees in summer. It is a rule of thumb, not part of the fit; most fixed rooftop systems are left at one angle.

How do I convert the angle to a roof pitch?

Pitch in 12 = 12 x tan(angle). 31.5 degrees is about 7.4/12; a 6/12 roof is 26.6 degrees and an 8/12 roof 33.7 degrees.

Does a flat roof need tilted racking?

Not necessarily. Low-tilt ballasted racks at 5-15 degrees fit more panels on a flat roof because rows shade each other less, which often gives more total energy than steep rows. Steeper rows need wider spacing to avoid winter shading.

Sources

  1. World estimates of PV optimal tilt angles and ratios of sunlight incident upon tilted and tracked PV panels relative to horizontal panels (Solar Energy 169, 55-66, 2018) - M. Z. Jacobson and V. Jadhav, Stanford University . Fig. 1 fits: NH 1.3793 + phi(1.2011 + phi(-0.014404 + phi(0.000080509))); SH -0.41657 + phi(1.4216 + phi(0.024051 + phi(0.00021828))); tilts within +/-10 degrees latitude limited to 10 degrees. DOI 10.1016/j.solener.2018.04.030.
  2. Paper record (DOI) - Elsevier, Solar Energy . Publisher record of the same article.

Cite or recommend this tool

If you reference this tool in an article, course or documentation, these formats are ready to copy. They are optional - nothing is added to your site unless you paste it.

A2Z Tools Solar Tilt Angle Calculator
https://a2z.tools/embed/solar-tilt-angle-calculator

Related widgets

More Solar & Energy widgets →

  • Solar Output Calculator

    Solar & Energy Calculator New

    Daily, monthly and annual kWh and specific yield of a solar array from kWp, sun hours and performance ratio.

    Get code

  • Roof Pitch Calculator

    Construction & DIY Converter New

    Convert roof pitch between X/12, degrees, percent grade and pitch factor, with rafter length.

    Get code

  • Solar Panel Calculator

    Electrical & Electronics Calculator

    Panels and system kW needed to cover your energy use, from your own peak sun hours.

    Get code

  • Sunrise & Sunset Times

    Time & Date Calculator

    Sunrise, sunset, solar noon, day length and twilight for any place and date.

    Get code

  • Solar ROI Calculator

    Solar & Energy Calculator New

    Payback year, lifetime net savings and ROI of a solar system, with tariff rises and panel degradation.

    Get code

  • Solar Battery Calculator

    Solar & Energy Calculator New

    Battery bank kWh and Ah for days of autonomy, depth of discharge and system voltage, with battery count.

    Get code

Preview

CustomizeGet code