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Sunrise Calculator

Sunrise marks the moment the Sun's upper edge crosses the eastern horizon, but the calculation involves more than simple geometry. Your location's latitude and longitude, the date, time zone, and even atmospheric refraction all influence when dawn arrives. This tool computes precise sunrise times for nearly any place on Earth, accounting for both the geometry of Earth's rotation and how the atmosphere bends sunlight.

Last updated:

Creators Dominik Czernia, PhD
3,797 people find this calculator helpful

Understanding Sunrise and Dawn

Sunrise is not a single instant but part of a graduated transition from night to day. The moment we calculate—when the upper limb of the solar disk reaches the horizon—is the standard astronomical definition. Before this, twilight begins, a period when indirect sunlight illuminates the sky without the Sun being visible.

Professionals in navigation, agriculture, and astronomy recognize three types of dawn:

  • Civil twilight: The Sun is 6° below the horizon. The horizon is clearly defined, and bright enough for outdoor work without artificial light.
  • Nautical twilight: The Sun is 12° below the horizon. The horizon is faintly visible, used historically for celestial navigation.
  • Astronomical twilight: The Sun is 18° below the horizon. This marks when the night sky becomes truly dark for observational astronomy.

Each definition shifts the calculated sunrise time backward by 20–45 minutes, depending on latitude and season.

The Mathematics of Sunrise Calculation

Sunrise time depends on three geographic and one temporal parameter. The calculation follows this sequence:

Step 1: Normalize coordinates

φ = sign(hemisphere) × latitude (degrees)

λ = sign(hemisphere) × longitude (degrees)

Where φ is positive for the Northern Hemisphere and negative for the Southern, and λ is positive for the Eastern Hemisphere and negative for the Western.

Step 2: Calculate solar declination and hour angle

The solar declination (δ) describes the Sun's angular position relative to the celestial equator. It varies from −23.44° at the winter solstice to +23.44° at the summer solstice.

h = arccos(−tan(φ) × tan(δ))

Here h is the hour angle in degrees, computed for the refraction-corrected angle of 90.833°.

Step 3: Convert to local time

Sunrise (UTC) = 12:00 − (h + λ) / 15

Sunrise (Local) = Sunrise (UTC) + Time Zone + Daylight Saving Offset

  • φ — Latitude in degrees (positive = North, negative = South)
  • λ — Longitude in degrees (positive = East, negative = West)
  • δ — Solar declination, the Sun's angular distance from the celestial equator
  • h — Hour angle, describing the Sun's position relative to the meridian
  • Refraction angle — 90.833° accounts for the Sun's apparent radius (0.267°) and atmospheric refraction (0.567°)

How Atmospheric Refraction Shifts Sunrise Earlier

Earth's atmosphere is not transparent to light in a straight line. As photons from the Sun travel through increasingly dense air layers near the horizon, their path curves. This bending, governed by Snell's law of refraction, is most pronounced at sunrise and sunset, when light travels the longest path through the atmosphere.

The effect is measurable and significant: atmospheric refraction typically shifts sunrise earlier by about 5 minutes compared to a calculation assuming a vacuum. The refraction angle of 0.567° means the Sun appears higher in the sky than its true geometric position. Combined with the Sun's angular radius of 0.267°, we use a correction angle of 90.833° instead of the geometric 90° when calculating the hour angle.

At extreme latitudes near the Arctic or Antarctic circles, refraction can become the difference between a sunrise occurring and the Sun never rising above the horizon on a given date. In Reykjavik, Iceland (64.16° N), this effect is crucial for accurate predictions during the season of midnight sun and polar night.

Practical Example: Sunrise in Reykjavik

Reykjavik, Iceland's capital, sits at 64.164° N, 22.022° W. Let's calculate sunrise for the winter solstice (December 21):

  • Input coordinates: Ensure the calculator recognizes the Northern and Western hemispheres correctly. The latitude is 64.164° N; the longitude is 22.022° W.
  • Set time zone: Iceland uses UTC (GMT) year-round, with no daylight saving time changes.
  • Solar declination: On the winter solstice, δ ≈ −23.44°. At this latitude, the Sun remains low in the sky for much of the day.
  • Result: Sunrise occurs around 11:20 AM local time, hours later than in more southerly locations. This reflects how the Sun's daily arc is compressed at high latitudes during winter.

Six months later, at the summer solstice, sunrise in Reykjavik occurs before 3 AM, and the Sun barely dips below the horizon.

Common Pitfalls When Calculating Sunrise

Several factors often trip up users or lead to inaccurate predictions.

  1. Confusing civil and astronomical sunrise — The standard 'sunrise' (when the upper edge touches the horizon with refraction) differs from civil twilight by roughly 20 minutes. Choose the correct definition based on your need: navigation typically uses civil, while astronomy uses astronomical.
  2. Neglecting daylight saving time — Many regions shift time zones seasonally. Always verify whether daylight saving time applies on your target date. Forgetting this step introduces a 1-hour error instantly.
  3. Forgetting hemisphere signs in coordinates — Latitude and longitude must include sign information. North/South and East/West buttons exist precisely to avoid mistakes. Entering 22° W as +22° instead of −22° will shift your result by nearly an hour.
  4. Assuming the same sunrise time year-round — Sunrise time shifts by 30–90 minutes across the year, depending on latitude. The variation is extreme near the poles and smallest at the equator. Always specify the date.

Frequently Asked Questions

What causes the pink and orange colors during sunrise?

The phenomenon is Rayleigh scattering, which affects shorter wavelengths (blue and violet) more strongly than longer ones (red and orange). During sunrise and sunset, sunlight travels a longer path through the atmosphere. Blue wavelengths scatter so much that they are dispersed away before reaching the observer, leaving the warmer red and orange hues to dominate the sky. This same effect makes the daytime sky blue—the blue light has been scattered toward you from all directions.

Does the Sun always rise due east?

The Sun rises exactly due east only on the equinoxes (around March 21 and September 23), when day and night are equal length. On other days, it rises north of east in the Northern Hemisphere summer and south of east in winter. The further you are from the equator, the more pronounced this shift. At the Arctic and Antarctic circles, this deviation reaches its extreme, and at the poles themselves, the concept of 'east' becomes meaningless.

Why does sunrise time vary so much more at higher latitudes?

The Sun's daily arc becomes increasingly tilted as you move toward the poles. At the equator, the Sun's path across the sky is steep, so it crosses the horizon quickly. At higher latitudes, the Sun's path is shallower, and it spends more time near the horizon. A tiny change in the Sun's declination can therefore shift the sunrise time by many minutes at 60° latitude but only a few minutes near the equator. This effect becomes extreme near the Arctic Circle, where the Sun may never set in summer or never rise in winter.

How accurate is this sunrise calculator?

The calculator is accurate to within a few minutes for most populated locations on Earth. Accuracy depends on correctly entering your latitude, longitude, time zone, and local daylight saving rules. The main source of remaining error is local topography: a mountain to the east will delay sunrise compared to a flat horizon, and the calculator assumes a horizon at sea level. Additionally, extreme atmospheric conditions (very high or low pressure, unusual temperature inversions) can occasionally shift sunrise by a minute or two.

What is the day with the earliest sunrise?

This commonly surprises people: the earliest sunrise does not occur on the summer solstice. In the Northern Hemisphere, the earliest sunrise occurs a few days before the summer solstice (around June 19), while the latest sunrise occurs after the winter solstice (around January 4). This lag is caused by the equation of time, which describes the mismatch between the Sun's actual position and mean solar time. The effect is especially pronounced at higher latitudes.

Can the Sun fail to rise at all?

Yes. Beyond the Arctic and Antarctic circles (approximately 66.5° latitude), there is a period in winter when the Sun never rises above the horizon—the polar night. Conversely, there is a period in summer when the Sun never sets, called the midnight sun. The duration of these periods increases as you approach the poles. At the North Pole itself, the Sun rises once per year (near the vernal equinox) and sets once per year (near the autumnal equinox), leaving six months of continuous daylight and six months of continuous darkness.

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