Sun Position

The horizontal coordinate system

Every observer's view of the sky has its own coordinate system, anchored to the local horizon. Two angles pin any celestial object:

"True north" matters here. The sun rises in the east and sets in the west on average, but its exact compass bearing on any given day depends on the season and your latitude. If you're comparing the tool's azimuth to a magnetic-compass reading in the field, apply magnetic declination first — see /tools/magnetic-declination for the local correction.

The astronomical quantities behind it

Azimuth and altitude are derived from three more fundamental astronomical numbers:

How sunrise and sunset are computed

Sunrise and sunset are when the upper limb of the sun is at the horizon — not the geometric centre. Atmospheric refraction bends light so the apparent horizon-grazing position is at a geometric altitude of about -0.833°(the standard refraction at the horizon, 0.567°, plus half the sun's angular diameter, 0.266°). The tool solves the altitude equation for that threshold to get the rise and set times.

Ten worked examples — sun at solar noon on the June solstice 2026

The pattern: at the June solstice the sun is directly overhead at 23.44°N (the Tropic of Cancer), drops in altitude proportionally with the latitude difference, and is below the horizon at the South Pole. Six months later (December solstice) the pattern flips: overhead at 23.44°S, polar night at the North Pole.

Misconceptions worth getting straight

"The sun rises exactly in the east"

Only on the equinoxes (around March 20 and September 22). The rest of the year, sunrise is north of east in summer (Northern Hemisphere) and south of east in winter. The azimuth at sunrise can swing by 50–60° between solstices at mid-latitudes. Photographers planning a sunrise shoot need the date-specific azimuth, not the abstract "east".

"Solar noon is when the sun is highest"

Yes — that's the definition. But "the sun's highest point of the day" is also onlyat solar noon. The sun's altitude is highest along the meridian crossing; before and after the crossing it's lower. Photography apps that compute "golden hour" use the altitude curve to find when the sun is roughly 0–6° above the horizon.

"Day length is the same as time-between-sunrise-and-sunset"

Almost — that's exactly how the tool computes it. But two subtleties affect real-world day length: (a) terrain occlusion (a mountain east of you delays sunrise); (b) altitude above sea level (a higher observer sees sunrise earlier and sunset later than the lib's sea-level horizon calculation). For aviation or summit photography, bake in the elevation correction.

"The sun is exactly south at solar noon"

In the Northern Hemisphere at mid-latitudes, yes — approximately. But at the equator the sun crosses northof zenith from March 20 to September 22 and south of zenith the other half of the year. At the tropics the sun passes directly overhead twice a year. In the Southern Hemisphere it's north at solar noon for most of the year.

"Solar position is affected by atmospheric refraction"

Only near the horizon. The geometric sun position (the Meeus formula) computes where the sun would be in vacuum. Refraction adds ~0.567° at the horizon (i.e. the sun appears higher than it geometrically is), dropping to ~0.0° at the zenith. The tool builds refraction into sunrise/sunset times (using the -0.833° threshold) but reports geometric altitude for the "current sun" reading. For survey-grade alignment, apply the refraction correction yourself: refraction ≈ 0.0167° × tan(90° − altitude).

When to use this tool, when to upgrade

How to verify the result

1. Sun-noon altitude check. Use the pocket formula: altitude = 90° − |latitude − declination|with declination from the report (or from a tabulated almanac). The tool's solar-noon altitude should match within ~0.01°.
2. Day-length symmetry on equinoxes. On March 20 and September 22, day length at any latitude should be 12 hours ± a few minutes (refraction makes it a bit longer than 12 h). If the tool reports wildly different values, your input date is off.
3. Compare against NOAA Solar Calculator. The NOAA online calculator (gml.noaa.gov/grad/solcalc/) is well-tested. Azimuth and altitude should match within ~0.02°; sunrise/sunset within ~1 min.

How this tool is built

Sun-position math lives in src/lib/coords/sun-position.ts — a from-scratch JavaScript implementation of the NOAA / Meeus simplified formulas. The whole computation runs in the browser; the observer coordinate and UTC time never leave the page. Twilight times re-use the same hour-angle math against the -6°, -12°, and -18° thresholds. The sun-path arc samples the algorithm every 15 min across the day to draw the track on the horizon plot in SunPathArc.tsx. Nearest-place and elevation in the deep report come from Mapbox v6 and USGS 3DEP via server-side proxies with Cache-Control: no-store.