Inputs
Formula used
The calculator uses a standard solar-position approximation. First, compute the day of year N, then the fractional year:
γ = 2π/365 · (N − 1)
The equation of time E (minutes) and solar declination δ are estimated from trigonometric series:
E ≈ 229.18 · (0.000075 + 0.001868 cosγ − 0.032077 sinγ − 0.014615 cos2γ − 0.040849 sin2γ)
δ ≈ 0.006918 − 0.399912 cosγ + 0.070257 sinγ − 0.006758 cos2γ + 0.000907 sin2γ − 0.002697 cos3γ + 0.00148 sin3γ
For a chosen zenith angle Z, the hour angle H satisfies:
cosH = (cosZ − sinφ · sinδ) / (cosφ · cosδ)
Local solar noon (minutes) is:
Noon = 720 − 4·λ − E + 60·TZ
Sunrise and sunset are Noon − 4H° and Noon + 4H°. If elevation adjustment is enabled, the zenith is reduced by an approximate horizon dip 0.0293·√h degrees.
How to use this calculator
- Choose the date you want to evaluate.
- Enter latitude and longitude in degrees (east positive).
- Set your timezone offset in hours, including half-hours if needed.
- Select the twilight definition, or use a custom zenith.
- Optionally add elevation and enable adjustment.
- Press Calculate to show results and export options.
Example data table
| Date | Latitude | Longitude | Timezone | Mode | Elevation (m) | Expected (approx.) |
|---|---|---|---|---|---|---|
| 2026-01-19 | 24.8607 | 67.0011 | +5 | Official | 0 | Sunrise ~07:10, Sunset ~17:55 |
| 2026-06-21 | 51.5074 | -0.1278 | +1 | Civil | 35 | Long daylight, late twilight |
| 2026-12-21 | 40.7128 | -74.0060 | -5 | Official | 10 | Short daylight, early sunset |
Example times are approximate; results depend on inputs and selected definition.
Professional article
1) Why sunrise and sunset times shift daily
Sunrise and sunset are not fixed clock events. Earth’s axial tilt changes the Sun’s apparent declination through the year, while Earth’s orbit geometry and rotation cause small timing offsets. The calculator combines these effects to estimate daily changes that can exceed several minutes, especially near solstices and at higher latitudes.
2) Inputs that matter most
Latitude dominates seasonal daylight range, while longitude and timezone determine how solar events map onto local clocks. A one-degree longitude error shifts results by about four minutes. Accurate timezone offsets (including half-hour zones) prevent systematic timing drift when comparing locations within the same region.
3) Twilight definitions and the zenith angle
This tool supports official sunrise/sunset and civil, nautical, and astronomical twilight. Each mode uses a different zenith angle threshold: larger zenith values place the Sun farther below the horizon, yielding earlier “sunset-like” endpoints and later “sunrise-like” starts. Custom zenith lets you match local standards.
4) Equation of time and solar declination
Two modeled quantities drive most timing corrections: solar declination and the equation of time. Declination describes the Sun’s angular position north or south of the equator, shaping day length. The equation of time captures the difference between mean clock time and apparent solar time, often varying by up to about ±15 minutes across a year.
5) Solar noon as a stable reference
Solar noon is when the Sun reaches its highest daily altitude for a given location. Because sunrise and sunset are symmetric around solar noon in this approximation, the calculator first determines solar noon and then offsets by the hour angle. This improves numerical stability when day length is very short or very long.
6) Elevation adjustment and horizon dip
Observers at higher elevations can see slightly “over” the geometric horizon. The calculator can reduce the effective zenith using a common horizon-dip approximation proportional to √h (h in meters). This tends to advance sunrise and delay sunset by seconds to a few minutes, depending on height and latitude.
7) Polar regions and edge cases
Near the Arctic and Antarctic circles, the Sun may not rise or set on certain dates. When the hour-angle expression becomes invalid, the calculator reports polar night or midnight sun conditions. For these cases, twilight definitions may still yield partial “light” periods even when official sunrise/sunset does not occur.
8) Practical uses and exporting results
Sunrise and sunset planning supports photography, fieldwork, safety briefings, agriculture scheduling, and navigation practice. Exporting to CSV helps integrate results into logs and spreadsheets, while PDF is useful for printouts and reports. For best accuracy, confirm coordinates from a reliable map source and keep consistent conventions for longitude sign.
FAQs
1) What does “official” sunrise/sunset mean here?
It uses a standard threshold where the Sun’s center is about 0.833° below the horizon, approximating refraction and the solar disk radius for typical conditions.
2) Why do my results differ from a phone weather app?
Apps may use different atmospheric models, elevation datasets, or time standards. Small coordinate differences and rounding can also shift times by one to several minutes.
3) Should longitude be positive or negative?
Use east longitudes as positive and west longitudes as negative. This matches common geospatial conventions and keeps the solar-noon formula consistent.
4) What is the equation of time in simple terms?
It is the difference between clock time and apparent solar time caused by Earth’s tilted axis and slightly non-circular orbit, producing seasonal timing offsets.
5) When should I use civil, nautical, or astronomical twilight?
Civil is useful for everyday outdoor visibility, nautical for horizon-based navigation conditions, and astronomical for darker-sky planning when the Sun is well below the horizon.
6) How much does elevation usually change sunrise and sunset?
At modest heights the change is often seconds to under a minute. Higher elevations can shift events by a few minutes, especially where the Sun’s path is shallow.
7) Can this calculator handle polar night or midnight sun?
Yes. If the solar geometry indicates no sunrise or no sunset for the selected date and latitude, the tool displays a clear message instead of producing misleading times.