Solar Insolation at Surface Calculator

Solar insolation is the amount of solar radiation power reaching a given surface area, usually expressed in watts per square meter (W/m squared). At the surface, it depends on the solar constant, how directly the sun's rays strike the surface (the zenith angle), and how much sunlight the atmosphere absorbs or scatters along the way (transmittance).

It computes cos(zenith) = sin(latitude)sin(declination) + cos(latitude)cos(declination)cos(hour angle), then finds insolation as I = S x cos(zenith) x transmittance, where S is the solar constant (1361 W/m squared) and transmittance is a single adjustable value representing atmospheric absorption and scattering.

Solar declination is the angle between the sun's rays and Earth's equatorial plane, which varies from about +23.45 degrees at the summer solstice to about -23.45 degrees at the winter solstice as Earth orbits the sun. This calculator uses Cooper's equation, delta = 23.45 x sin(360 x (284+n) / 365), a standard approximation from the day of year n.

The hour angle measures how far the sun has moved across the sky from solar noon, in degrees, at 15 degrees per hour (since Earth rotates 360 degrees in 24 hours). It is zero at solar noon, negative in the morning, and positive in the afternoon: hour angle = 15 x (solar time - 12).

The solar zenith angle is the angle between the sun's position and directly overhead (the zenith), so 0 degrees means the sun is straight overhead and 90 degrees means it is exactly on the horizon. Zenith angle and solar elevation angle always add to 90 degrees.

A clear, dry sky at solar noon typically transmits about 70 to 75 percent of extraterrestrial insolation to the surface, so 0.70 to 0.75 is a reasonable default. Hazy, humid, or polluted air can drop it to 0.5 or lower, while very clean high-altitude air can push it above 0.8. This calculator uses a single simplified transmittance value rather than modeling each atmospheric absorption and scattering process separately.

When the computed zenith angle would exceed 90 degrees, the cosine of the zenith angle becomes negative, meaning the sun is geometrically below the local horizon. This calculator clamps insolation to zero in that case, since a negative value would be physically meaningless for downward-arriving sunlight.

Higher latitudes receive sunlight at a shallower average angle year-round, which increases the average zenith angle, spreads the same amount of solar energy over a larger surface area, and forces sunlight to pass through more atmosphere, all of which reduce insolation compared to the tropics at the same time of day and transmittance.

No. It uses a single simplified transmittance value to represent the combined effect of atmospheric absorption and scattering, which is standard for introductory solar geometry calculations. A full radiative transfer model would separately account for ozone absorption, water vapor absorption, Rayleigh scattering, and aerosol scattering at each wavelength.

This calculator finds the instantaneous insolation reaching a specific point on the ground at a specific latitude, day, and time, a surface-level, point-in-time geometric calculation. The Albedo and Planetary Energy Balance Calculator instead finds the whole-planet average equilibrium temperature from the solar constant and albedo, a global, time-averaged energy-balance calculation. They use related solar physics at very different scales.

This calculator gives a useful first-order estimate of clear-sky insolation at a given location, day, and time, but real solar panel siting studies also need cloud cover statistics, terrain shading, panel tilt and orientation, and seasonal transmittance variation, which are beyond this simplified geometric and transmittance model.