# How to Calculate Solar Insolation

Written by ryan fergerson
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Solar insolation is the amount of electromagnetic energy, or solar radiation, received at a point on the earth's surface. Cloud coverage, solar declination angle, zenith angle and hour angle are necessary variables to consider when determining solar insolation. Units for solar insolation are generally expressed in kWh/m2/day -- this represents the amount of daily solar energy in a kilowatt hour striking a square meter of the earth's surface.

Skill level:
Challenging

## Instructions

1. 1

Calculate the hour angle (H) using this formula: H = 15 degrees x (time - 12). Time equals the hour of day from midnight -- for example, noon equals 12 and 4 p.m. equals 16.

2. 2

Calculate the zenith angle (Z) using this formula: Z = cos-1 (sinXsinY + cosXcosYcosH). Zenith angle is the angle from the point directly overhead to the point of the sun's position in the sky. In this equation, X is latitude, Y is the solar declination angle and H is the hour angle -- solar declination angle is the angle between a plane perpendicular to incoming solar radiation and the earth's rotational axis. The solar declination angle varies from +23.5 degrees on summer solstice to -23.5 degrees on winter solstice. The solar declination angle is 0 degrees on the vernal equinox and autumnal equinox.

3. 3

Calculate solar insolation (I) using this formula: I = ScosZ. S is the solar constant -- roughly 1000W/m2 depending on the angle and weather conditions. Z is the zenith angle from the equation in step 2.

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