The UV Index, From First Principles

The UV index is the erythemal (sunburn) irradiance expressed in units of 25 mW/m². Under a clear sky it is controlled almost entirely by solar elevation: UVI ≈ 12.5 × sin(h)^1.7. This calculator derives the elevation from latitude, date, and time using standard solar geometry — solar declination plus the hour angle.

Why the Geometry Matters

Earth's 23.44° axial tilt drives the seasons: the sun climbs highest at the summer solstice, so sin(elevation) peaks in June — and the 1.7 power amplifies that peak into the dramatic summer UV spike. Near the equator the sun passes nearly overhead year-round, keeping UV in the 10+ range all year.

From Index to Skin

The Fitzpatrick scale quantifies how much UV each skin type tolerates before reddening — the minimal erythema dose, 200–1,000 J/m². Dividing the MED by the UV irradiance gives the time to burn, the number every beachgoer actually cares about. Clouds, ozone, and altitude adjust the clear-sky estimate: high mountains can raise UVI by 10–20%.