Sun Position Calculator

In short The sun position at any moment is two numbers: altitude, how high above the horizon it is, and azimuth, which compass direction it is in. Both come from your latitude, the sun declination on that date, and the local hour angle — how far past your meridian the sun has travelled, at 15 degrees per hour. Azimuth here is measured clockwise from TRUE north, which is not what a compass shows; a magnetic compass is offset by your local declination, and near metal, speakers or a car a phone magnetometer can be several degrees out on top of that. Two details make the difference between an approximate answer and a usable one. The first is refraction: the atmosphere bends light, so the sun appears higher than it geometrically is, by an amount that is negligible overhead and reaches about half a degree at the horizon. That correction is applied here, and it is the reason the sun is still visible after it has technically set. The second is that hour angle is measured from SOLAR noon, not clock noon, and the two differ by the equation of time plus your offset from the centre of your time zone. Shadow length follows directly from altitude: a vertical object casts a shadow equal to its height divided by the tangent of the sun altitude, so at 45 degrees the shadow equals the height, at 63 degrees it is half, and as the sun approaches the horizon it grows without limit.