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The sun's altitude and azimuth for a date, clock time, latitude, longitude and time zone, and the direction shadows are cast from.
The arithmetic is 64-bit, but the accuracy is that of the formulas: the short Fourier series for the equation of time and the declination that the file header cites from the NOAA Global Monitoring Laboratory's General Solar Position Calculations. The header states the result is good to a fraction of a degree and that refraction is ignored.
5 calculations in 1 source file. The code is read from the released app when this page loads. It is the calculation people run, not a copy kept for this page.
Tests None found by the review
The day number of a date.
N = days before the month + day (+1 after February in a leap year)
Whole-number arithmetic with the Gregorian leap rule (divisible by 4, not by 100 unless by 400).
export function dayOfYear(month, day, year = 2026) {
const leap = (year % 4 === 0 && year % 100 !== 0) || year % 400 === 0;
const cum = [0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334];
return cum[month - 1] + day + (leap && month > 2 ? 1 : 0);
}How far sun time runs ahead of clock time, and the sun's angle above the equator, for the date.
γ = 2π ÷ (365 or 366) × (N − 1 + (hour − 12) ÷ 24); eqtime = 229.18 × (0.000075 + 0.001868 cos γ − 0.032077 sin γ − 0.014615 cos 2γ − 0.040849 sin 2γ)
Two short trigonometric series with coefficients given to 6 decimals; 229.18 turns radians into minutes. The series, not the arithmetic, set the accuracy.
const g = (2 * Math.PI / (leap ? 366 : 365)) * (N - 1 + (hour - 12) / 24);
const eqtime = 229.18 * (0.000075 + 0.001868 * Math.cos(g) - 0.032077 * Math.sin(g) - 0.014615 * Math.cos(2 * g) - 0.040849 * Math.sin(2 * g));
const decl = 0.006918 - 0.399912 * Math.cos(g) + 0.070257 * Math.sin(g) - 0.006758 * Math.cos(2 * g) + 0.000907 * Math.sin(2 * g)
- 0.002697 * Math.cos(3 * g) + 0.00148 * Math.sin(3 * g);The sun's height above the horizon.
tst = hour × 60 + eqtime + 4 × lon − 60 × tz; H = tst ÷ 4 − 180°; cos Z = sin φ sin δ + cos φ cos δ cos H; altitude = 90° − Z
cos Z is clamped to [−1, 1] before acos. When the sun is almost overhead cos Z is close to 1, where acos turns a small error in its input into a larger one in the angle.
const offset = eqtime + 4 * lon - 60 * tz; // minutes
const tst = hour * 60 + offset; // true solar time, minutes
const ha = (tst / 4 - 180) * RAD; // hour angle
const phi = lat * RAD;
const cosZ = Math.sin(phi) * Math.sin(decl) + Math.cos(phi) * Math.cos(decl) * Math.cos(ha);
const zen = Math.acos(Math.max(-1, Math.min(1, cosZ)));
const altitude = 90 - zen / RAD;The sun's compass direction, in degrees clockwise from north.
azimuth = atan2(sin H, cos H sin φ − tan δ cos φ) + 180°, wrapped to 0…360
atan2 needs no clamp and keeps its digits in every quadrant. The result is wrapped with two remainders so it is never negative.
// azimuth measured from north, clockwise
const az = Math.atan2(Math.sin(ha), Math.cos(ha) * Math.sin(phi) - Math.tan(decl) * Math.cos(phi)) / RAD + 180;
const azimuth = ((az % 360) + 360) % 360;The unit vector shadows are cast from, in model axes (north is +Y, east is +X).
dir = (sin a cos alt, cos a cos alt, sin alt)
Built from the altitude and azimuth after they were converted to degrees and back to radians, which adds two roundings to each angle.
const alt = altitude * RAD, a = azimuth * RAD;
return {
altitude, azimuth, declination: decl / RAD, eqtime,
dir: [Math.sin(a) * Math.cos(alt), Math.cos(a) * Math.cos(alt), Math.sin(alt)],The arithmetic is 64-bit, but the method or the data sets the accuracy: a solver tolerance, a mesh, a step size, a datum shift, a table. The limit is stated where the result is shown.