Solar Angles

As the world continues to move toward an increase in renewable energy sources, one of the most important components of a successful solar energy system is understanding the solar angles of your property. The first step to understanding solar angles is to understand the difference between orientation and tilt. The orientation of solar panels is the direction they face relative to the sun, while the tilt is the angle of the panel in relation to the ground. Both orientation and tilt are important considerations when designing a solar energy system.

Understanding Tilt and Orientation

Orientation is important because the best way to maximize solar energy is to have the panels face the sun directly. This ensures that the panels are receiving the most direct sunlight and therefore producing the most energy.

Generally, a higher tilt angle will capture more sunlight, however, the optimal tilt angle can vary depending on the location and the time of year. If the solar panel is too flat, it will not capture enough sunlight and the system will be inefficient, while if the solar panel is too steep, it will not capture enough sunlight either.

More deep on solar angles?

The axis about which the earth rotates is tilted at an angle of 23.45 degrees to the plane of the earth’s orbital plane and the sun’s equator. The earth’s axis results in a day-by-day variation of the angle between the earth–sun line and the earth’s equatorial plane called the solar declination δ. This angle may be estimated by the following equation:

where N = year day, with January 1 + 1


The position of the sun can be defined in terms of its altitude β above the horizon and its azimuth ϕ measured in horizontal plane.

To determine the angle of incidence θ between a direct solar beam and the normal to the surface, the surface azimuth ψ and the surface-solar azimuth γ must be known. The surface-solar azimuth is designated by γ and is the angular difference between the solar azimuth ϕ and the surface azimuth ψ. For a surface facing the east of south, γ = ϕ − ψ in the morning, and γ = ϕ + ψ in the afternoon. For surfaces facing the west of south, γ = ϕ + ψ in the morning and γ = ϕ − ψ in the afternoon. For south-facing surfaces, ψ = 0 degree, so γ = ϕ for all conditions. The angles δ, β, and ϕ are always positive.



Solar angles with respect to a tilted surface.

For a surface with tilt angle Σ (measured from the horizontal), the angle of incidence θ is given by


For vertical surfaces, Σ = 90 degrees, cosΣ = 0, and sinΣ = 1.0, so Eq. above becomes


For horizontal surfaces, Σ = 0 degree, sinΣ = 0, and cosΣ = 1.0, so Eq. leads to


Latitude φ is the angular location north or south of the equator, north positive; −90 degrees ≤ φ ≤ 90 degrees.

Zenith angle θz, the angle between the vertical and the line to the sun, is the angle of incidence of direct (beam) radiation on a horizontal surface (θz = θ).

Hour angle ω is the angular displacement of the sun east or west of the local meridian due to rotation of the earth on its axis at 15 degrees per hour; morning negative (−ωs) and afternoon positive (+ωs) (Fig.). The sun position at any hour τ can be expressed as follows: