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Sunset Calculator

Predicting when the Sun touches the horizon requires understanding Earth's orbital mechanics, atmospheric physics, and your position on the globe. Photographers, astronomers, sailors, and outdoor planners rely on precise sunset predictions to time their activities. This calculator accounts for geographic coordinates, atmospheric refraction, and different definitions of sunset to deliver results accurate to the minute.

Last updated:

Creators Davide Borchia, PhD
8,590 people find this calculator helpful

Understanding Sunset and Its Varieties

Sunset marks the instant when the Sun's upper limb crosses the horizon at your location. However, astronomers distinguish between several related phenomena, each occurring at different solar angles below the horizon:

  • Civil twilight ends when the Sun reaches 6° below the horizon—enough light remains to read outdoors without artificial lighting.
  • Nautical twilight ends at 12° below—the horizon becomes indistinct, making navigation by stars difficult.
  • Astronomical twilight extends to 18° below, marking the point where the Sun no longer influences the night sky.
  • Geometric sunset is the precise moment the Sun's centre crosses 0° (the horizon itself).

Each definition has practical applications. Sailors use nautical twilight for navigation; photographers favour civil twilight for landscape work; and astronomers employ astronomical twilight to identify the true start of night.

The Mathematics of Sunset Calculation

Computing sunset requires determining where the Sun appears in the sky at your location, then finding when it reaches the defined angle below the horizon. The process involves converting geographic coordinates into solar angles:

φ = sign(latitude) × |latitude|

λ = sign(longitude) × |longitude|

Day of year = day number from 1 to 365 (or 366)

Sunset time = f(Day, φ, λ, timezone, daylight saving, twilight type)

  • φ — Latitude in degrees (positive north, negative south)
  • λ — Longitude in degrees (positive east, negative west)
  • Day — Calendar date converted to ordinal day of the year
  • timezone — Hour offset from UTC for your location
  • twilight type — The solar angle definition: civil, nautical, astronomical, or geometric

Atmospheric Refraction and the 0.833° Correction

The Sun you see at sunset is not where it actually is. Earth's atmosphere bends light rays, an effect called refraction, which becomes pronounced near the horizon where light traverses the densest atmospheric layers at a grazing angle.

This bending shifts the apparent position of the Sun upward by approximately 0.833 degrees—equivalent to the Sun's angular diameter. Consequently, when we observe the Sun touching the horizon, it has already dipped geometrically below the true horizon by that amount.

Atmospheric refraction varies with:

  • Temperature and pressure at your location
  • Humidity in the lower atmosphere
  • Elevation above sea level
  • Clarity and dust content in the air

The 0.833° correction represents a standard average; real refraction can range from 0.75° to 0.9° depending on conditions. For most applications, this constant offers sufficient accuracy. The calculator provides both refraction-corrected and uncorrected results for comparison.

Finding Sunset at Your Location

To calculate sunset accurately, the tool needs four essential pieces of information:

  • Date—converted internally to the day of year (1–365), which determines the Sun's position along the ecliptic
  • Latitude and longitude—your geographic coordinates, which establish your position on the rotating Earth
  • Timezone and daylight saving offset—to convert the result from UTC to local civil time

The calculation then proceeds through these stages:

  1. Determine the Sun's declination (its angular distance from the celestial equator) based on the day of year
  2. Compute the hour angle—the angle the Sun has travelled from solar noon
  3. Solve for the hour angle when the Sun reaches your chosen twilight angle
  4. Convert this hour angle to UTC time using the Sun's 15° per hour angular speed
  5. Adjust to local time by adding your longitude correction (4 minutes per degree of longitude from your time zone meridian) and timezone offset

Locations at extreme northern or southern latitudes may experience midnight sun (no sunset) or polar night (no sunrise), cases the calculator detects and reports.

Common Pitfalls and Practical Considerations

Account for these factors to interpret sunset calculations correctly.

  1. Refraction uncertainty near the horizon — The 0.833° standard correction assumes sea-level conditions. High altitude locations experience less refraction; temperature inversions or dust layers can significantly alter it. Use the uncorrected time as a reference if local conditions are unusual.
  2. Longitude and timezone confusion — Your timezone does not align with longitude exactly—most time zones span 15° of longitude, but political boundaries shift them. The calculator applies both timezone offset and longitude correction. Double-check your timezone setting, as an error here propagates directly to the result.
  3. Daylight saving time transitions — Many regions switch to daylight saving time on specific dates. If the calculator doesn't auto-detect your region's rules, manually select the appropriate offset. Sunset times calculated near DST transitions may show times that match old clock settings.
  4. Latitude-dependent phenomena — Locations above the Arctic Circle or below the Antarctic Circle experience days with no sunset (midnight sun) during summer. The calculator flags these impossible cases. Plan trips to these regions knowing that solar noon may occur at unusual clock times.

Frequently Asked Questions

Why does the sunset time vary from day to day?

Sunset timing depends on two interrelated factors: the Sun's changing declination (height at solar noon) throughout the year, and the changing rate of the Sun's apparent westward motion near the horizon. In spring and autumn, as declination changes rapidly and the Sun's path crosses the horizon at a steep angle, sunset times shift by several minutes daily. In summer near the solstice, declination changes slowly, yielding smaller day-to-day variations. Additionally, the equation of time—a 16-minute difference between solar noon and clock noon—creates gradual shifts in sunset times.

What's the difference between refraction-corrected and uncorrected sunset times?

The uncorrected time assumes no atmosphere and represents where the Sun's geometric centre crosses the 0° horizon. The refraction-corrected time accounts for atmospheric bending, adding approximately 0.833° to the angle, which shifts the result earlier by roughly 2–3 minutes. The corrected time matches what you actually observe: the instant the Sun's upper edge touches the horizon. For practical purposes—photography, outdoor activities, astronomy—use the corrected time. Researchers comparing data across atmospheric conditions may want both values.

Can I use this calculator for the Arctic or Antarctic?

Yes, but with caveats. In polar regions during summer, the Sun never sets, creating 24-hour daylight (midnight sun). During winter, the opposite occurs: perpetual darkness (polar night) with no sunrise or sunset. The calculator detects these conditions and reports them as invalid sunset times. If you're near the poles during transition seasons (spring and autumn), sunset times can swing by hours day-to-day, and twilight may last many hours or persist throughout the night.

How accurate is this sunset calculator?

Accuracy typically lies within ±1–2 minutes for sea-level locations at mid-latitudes with standard atmospheric conditions. Accuracy degrades at high elevations (mountains), in regions with unusual atmospheric conditions (dust, pollution, temperature inversions), and near poles. The main source of error is atmospheric refraction variability; the calculator uses an average 0.833° correction. Real refraction depends on temperature, pressure, and humidity, which aren't inputs. For precision applications requiring errors below 1 minute, use specialized astronomical software with local meteorological data.

What is the equation of time and how does it affect sunset?

The equation of time is the difference between apparent solar time (based on the Sun's actual position) and mean solar time (uniform clock time). It arises because Earth's orbit is elliptical and its axis is tilted. Over the year, this difference oscillates between roughly −14 and +16 minutes. It affects sunset predictions because solar noon—the reference point for hour angle calculations—doesn't align with clock noon. The calculator applies this correction internally, shifting predicted sunset times by up to several minutes depending on the date.

Why do sunset times differ between high altitude and sea level?

Atmospheric refraction depends on the density profile of air, which decreases exponentially with elevation. At high altitude, thinner air bends light rays less, reducing the refraction correction from the standard 0.833° to perhaps 0.6° or less. Additionally, the geometric horizon drops below the true horizon as elevation increases, potentially revealing the Sun for longer. A mountain observer sees sunset several minutes later than someone at sea level on the same day and location, sometimes by 10–15 minutes at very high elevations.

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