Learn · sun geometry and off-grid solar

How the sun moves, and what it means for panels.

Short, exact explanations — each with the formula, a worked example and a link to a tool that does the arithmetic for you.

Angles of the sun

The compass direction of the sun, and why it swings so far between June and December.

How high the sun stands, the noon formula, refraction and shadow lengths.

The sun's latitude — the single number behind the seasons.

Why solar noon drifts by up to sixteen minutes through the year.

Exact instants for ten years, and what each one does to the sun.

Why a system sized for December should be tilted steeply.

The angle between sunlight and the panel, and what it costs.

Light reflected from the ground, and why snow helps steep panels.

How long the battery must carry the load, by climate.

Every algorithm and data source this site uses.