Solar Panel Incidence Angle Calculator
Enter a location, day, clock time, and panel orientation to find the angle between the Sun and the panel normal. The result also shows the direct-beam capture penalty and the Sun’s position after the clock time is corrected to true solar time.
Solar incidence angle (°)13.46
- Direct-beam capture
- 97.25%
- Direct-beam geometric loss
- 2.75%
- Solar elevation (°)
- 73.45
- Solar azimuth (°)
- 178.93
- True solar time
- 11:59
- Sun-following tilt (°)
- 16.55
- Sun-following azimuth (°)
- 178.93
- Panel illumination status
- Direct sun on panel
This is a solar-geometry estimate for the selected instant; direct-beam capture excludes diffuse light and all site or equipment losses.
How to use this calculator
- Enter latitude and longitude, using positive latitude north of the equator and positive longitude east of Greenwich.
- Enter the day of year and local clock time for the instant you want to examine.
- Enter the UTC offset that applied on that date, including daylight saving time when it was in effect.
- Enter the panel tilt from horizontal and its compass azimuth, then read the incidence angle and capture factor.
How the incidence angle is calculated
Solar incidence angle is the angle between the incoming solar beam and a line perpendicular to the front of a panel. An angle of 0 degrees means the beam is square to the panel. As the angle grows, the same beam is spread over more panel area, so the direct-beam portion available to the panel falls with its cosine.
The calculation first converts local clock time to true solar time. Let N be day of year, t local time in hours, lambda longitude, and z UTC offset. The fractional year is g = (2pi / 365) x (N - 1 + (t - 12) / 24). NOAA's compact equation then supplies the equation of time E and solar declination delta. True solar time in minutes is T = mod(60t + E + 4lambda - 60z, 1440), and hour angle is H = T / 4 - 180.
With latitude phi, solar zenith is theta-z = acos(sin(phi) sin(delta) + cos(phi) cos(delta) cos(H)). The tool derives solar azimuth from the same position. For panel tilt beta, panel azimuth gamma-p, and solar azimuth gamma-s, the fixed-panel incidence angle is:
alpha = acos(sin(theta-z) cos(gamma-p - gamma-s) sin(beta) + cos(theta-z) cos(beta))
The direct-beam capture factor is max(0, cos(alpha)) while the Sun is above the horizon. It is zero below the horizon and when the beam reaches the back of the panel. Geometric loss is 1 - capture.
What moves the result most
Time, longitude, and UTC offset determine the Sun's hour angle, while latitude and day of year set its seasonal path. Panel azimuth matters most in the morning and afternoon; tilt matters more when the Sun is high or low relative to the panel. An east- or west-facing panel can have excellent incidence at the corresponding part of the day even though it does not point due south in the northern hemisphere.
What this calculator leaves out
This is a solar-geometry estimate, not an energy-production forecast. It does not include diffuse sky radiation, ground reflection, clouds, horizon obstructions, row shading, soiling, temperature, inverter losses, or module-specific optical behavior. The solar position uses a compact NOAA-style approximation and omits detailed atmospheric refraction and elevation corrections.
Worked example
For a panel at 40 degrees north, 105 degrees west on day 172, enter 12.00 local time and a UTC offset of -7 for daylight time. With a 30 degree tilt and a 180 degree azimuth, the calculator corrects the clock to about 11:59 true solar time. It finds a solar elevation of about 73.5 degrees, a solar azimuth near 178.9 degrees, and an incidence angle of about 13.5 degrees.
The direct-beam capture is therefore about 97.2%, with about 2.8% geometric loss from angle alone. Those percentages describe only the direct beam at that instant; they are not the panel's total electrical output.
Common questions
What is solar incidence angle?
Solar incidence angle is the angle between sunlight and the line perpendicular to a panel’s front surface. A value near 0 degrees means the direct beam is striking the panel squarely, while a larger value reduces the direct-beam component by the cosine of the angle.
Is a smaller incidence angle better for solar panels?
For the direct beam at one instant, yes: a smaller incidence angle gives a larger geometric capture factor. It does not alone determine energy production because diffuse light, shading, temperature, and the Sun’s changing path also matter.
How do I convert a calendar date to day of year?
Count January 1 as day 1 and add the days in the earlier months. June 21 is approximately day 172 and December 21 is approximately day 355 in a non-leap year; this calculator uses a 365-day approximation.
What is the difference between clock time and solar time?
Clock time is set by a time-zone meridian and may include daylight saving time, while solar time tracks the Sun’s apparent position at your longitude. The calculator adjusts clock time for longitude, UTC offset, and the equation of time before calculating the hour angle.
How should I enter daylight saving time?
Use the UTC offset that was actually in force on the selected date. For example, a location that uses UTC-8 in standard time and UTC-7 in daylight time should use -7 for a summer date.
Does the ideal instantaneous angle equal the best annual panel angle?
No. The sun-following tilt and azimuth point directly at the Sun only at the selected instant. A fixed system is usually chosen for annual or seasonal energy, roof geometry, wind loading, spacing, and local constraints rather than a single moment.