TheCalculatorsHub

Sunrise Sunset Calculator

The sunrise and sunset calculator computes the precise times of sunrise, sunset, solar noon, civil twilight, nautical twilight, astronomical twilight, golden hour, and blue hour for any latitude, longitude, and date. It uses the NOAA solar position algorithm with the standard 0.833-degree atmospheric refraction correction that shifts sunrise earlier and sunset later by 2 to 5 minutes compared to the geometric horizon. All six twilight periods (morning and evening for each type) are computed by solving for the hour angle at which the sun crosses each depression angle. Day length, azimuth at sunrise and sunset with compass direction, the equation of time correction, and a day-length trend compared to the previous day are included. A practical use-cases panel translates solar times into Islamic prayer windows, hunting and fishing legal light, Jewish Shabbat candle-lighting, and photographer golden-hour windows. An annual calendar table shows weekly sunrise, sunset, and azimuth data for the full year.

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Our engine processes your inputs using verified datasets and logic models to provide real-time results.

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Sun Angle Calculator

The sun angle calculator computes solar elevation (altitude above the horizon), azimuth (compass bearing), declination, hour angle, solar noon, air mass, and shadow length for any latitude, longitude, date, and time. It uses the standard NOAA solar position algorithm: declination from the day of year, equation of time for clock-to-solar-time conversion, and the spherical trigonometry equations relating elevation to declination, latitude, and hour angle. Additional outputs include sunrise and sunset times, day length, optimal solar panel tilt by season, and golden hour windows for photography. The hour-by-hour table shows all positions across the full day.

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Smartphone Projector Calculator

A DIY smartphone projector uses a single convex lens to form a real, inverted image of the phone screen on a wall or screen. The thin lens equation (1/f = 1/do + 1/di) links the focal length of the lens, the phone-to-lens distance, and the throw distance. Magnification equals the ratio of those two distances, and the projected image diagonal equals the phone screen diagonal multiplied by the magnification. This calculator solves for any unknown, outputs exact box dimensions for the build, and rates projected brightness based on magnification.

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Immersed Weight Calculator

An object submerged in fluid experiences a buoyant force equal to the weight of fluid it displaces, reducing its apparent weight by exactly that amount. The two-weight method -- weighing an object in air and again fully submerged -- lets you calculate its density without measuring its volume directly, a technique Archimedes used to test the king's crown. For body composition, hydrostatic weighing uses this principle with temperature-corrected water density and residual lung volume to derive body density and body fat percentage via the Siri or Brozek equations.

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Sunrise Sunset Calculator Logic

cos(H)=[sin(dep°)sin(dec)sin(lat)]/[cos(dec)cos(lat)]sunrise=noonH/15sunset=noon+H/15dep:0.833°(standard),6°(civil),12°(nautical),18°(astronomical)cos(H) = [sin(-dep°) - sin(dec)sin(lat)] / [cos(dec)cos(lat)] | sunrise = noon - H/15 | sunset = noon + H/15 | dep: 0.833° (standard), 6° (civil), 12° (nautical), 18° (astronomical)
Disclaimer: Results are estimates only. Always verify important calculations with a qualified professional before making decisions. Learn about our methodology.

How Sunrise and Sunset Times Are Calculated

Sunrise and sunset are defined as the moments when the upper edge of the sun's disc crosses the horizon. Because light is bent by Earth's atmosphere, the sun appears on the horizon when it is geometrically about 0.833 degrees below it -- a combined effect of approximately 0.567 degrees of atmospheric refraction and 0.267 degrees from the sun's angular radius. This standard correction means the real sun is already partially below the geometric horizon at the moment you see it rise, and the light you are seeing has been bent around the curve of Earth. The NOAA algorithm used here accounts for this refraction so that computed times match what you observe with your eyes, not a theoretical airless planet. The calculation requires only three inputs: your latitude, your longitude, and the date, which together determine the solar declination (the sun's angular height above or below the celestial equator) and the equation of time (a seasonal correction of up to 16 minutes that accounts for Earth's elliptical orbit and axial tilt). Our Sun Angle Calculator uses the same algorithm and adds real-time elevation, azimuth, air mass, and shadow length for any given time of day.

The Three Types of Twilight Explained

Twilight is the period of diffuse illumination before sunrise and after sunset when the sun is below the horizon but still illuminating the upper atmosphere. Three formally defined phases of twilight correspond to how far the sun sits below the horizon. Civil twilight (sun 0 to 6 degrees below horizon) is the brightest phase: the sky has vivid colour, the horizon is clearly defined, and there is enough natural light for most outdoor work without artificial lighting. Many jurisdictions define "daylight" for legal purposes as the period including civil twilight, meaning car headlights are not required during this phase. Nautical twilight (sun 6 to 12 degrees below horizon) is dimmer: the horizon is still visible at sea but stars are bright enough for celestial navigation with a sextant, which is why sailors historically relied on this phase to fix position. Astronomical twilight (sun 12 to 18 degrees below horizon) is the faintest phase: the sky is dark enough for most telescopic astronomical observation, though faint objects require the sun to be fully 18 degrees below the horizon. True astronomical night only exists between astronomical dusk and astronomical dawn, and at latitudes above about 48 degrees north in midsummer, astronomical night may not occur at all because the sun never drops to 18 degrees below the horizon.

Golden Hour and Blue Hour for Photographers

Golden hour is the period when the sun is between 0 and 6 degrees above the horizon, immediately after sunrise and immediately before sunset. At this angle, sunlight travels through roughly ten times more atmosphere than at the zenith, scattering the shorter blue wavelengths away and leaving warm orange and red light that is soft, directional, and flattering for portraits, landscapes, and architecture. Despite its name, golden hour rarely lasts exactly 60 minutes. Near the equator, the sun rises and sets almost vertically, traversing those 6 degrees in just 20 to 30 minutes. At mid-latitudes in summer, the shallow sun arc extends it to 45 to 90 minutes. At high latitudes near the solstice, it can persist for several hours. Blue hour occurs in civil twilight when the sun is between about 4 and 6 degrees below the horizon. The sky takes on a deep, rich blue because the sun still illuminates the upper atmosphere while ground-level artificial lighting is already on, creating a warm-cool contrast that photographers prize for urban and architectural images. This calculator shows both morning and evening golden and blue hours with exact durations so you can plan outdoor photo or film shoots precisely. The same low-angle light physics that makes photography golden also affects solar panel output -- at these angles the air mass factor exceeds 5, substantially reducing solar irradiance, as explained in our Sun Angle Calculator.

Sunrise and Sunset Azimuth: Which Direction to Face

Sunrise and sunset do not always occur due east and due west. The exact compass bearing depends on the date and your latitude. At the equinoxes (around March 20 and September 22) the sun rises almost exactly due east (90 degrees) and sets almost exactly due west (270 degrees) everywhere on Earth. As the northern hemisphere moves toward summer, the sunrise point shifts north of east: on the summer solstice at 51 degrees north latitude (London), the sun rises at about 49 degrees (NNE) and sets at about 311 degrees (NW). In winter, it shifts south of east: on the winter solstice at 51 degrees north, sunrise is around 129 degrees (SE) and sunset around 231 degrees (SW). This azimuth variation is important for photographers choosing a location to catch sunrise over a specific landmark, for architects considering which facades will receive morning or evening sun, and for solar panel installers confirming that the winter sunrise is visible from the panel location. This calculator displays the azimuth in degrees and compass direction (N, NNE, NE, ENE, etc.) for every date, filling a gap that many competitors leave as a raw number requiring separate lookup.

The Equation of Time and Why It Matters

A common puzzle: the winter solstice is the shortest day of the year, yet the earliest sunset in the northern hemisphere occurs around December 7-10, nearly two weeks before the solstice, and the latest sunrise does not occur until around January 3-7. The explanation is the equation of time -- a seasonal correction of up to plus or minus 16 minutes that shifts solar noon relative to clock noon. Two factors create it. First, Earth's orbit is slightly elliptical: Earth moves faster in January (when closest to the sun) and slower in July, which causes the apparent solar day to be longer or shorter than 24 hours by a few tens of seconds. Second, Earth's axial tilt means that the sun's east-west motion across the sky is not perfectly uniform throughout the year. These two effects combine to produce a wave that peaks at about -16 minutes in early November (solar noon 16 minutes early compared to clock noon) and +14 minutes in mid-February (solar noon 14 minutes late). This wave independently shifts the clock times of both sunrise and sunset. Around the winter solstice, the equation of time is shifting solar noon later each day, which causes sunrise and sunset to both move later even as the solstice brings the year's shortest day. The result is that sunset reaches its earliest point before the solstice and sunrise reaches its latest after it. This calculator displays the equation of time for the selected date so you can understand exactly why solar noon and clock noon diverge on any given day.

Day Length, Latitude, and Seasonal Change

Day length -- the duration of time between sunrise and sunset -- varies enormously with latitude and season. On the equator, day and night are always close to 12 hours each with very little change through the year. Moving toward the poles, the seasonal contrast grows dramatically. At 45 degrees north, the summer solstice gives about 15.5 hours of daylight and the winter solstice gives about 8.8 hours. At 60 degrees north (Oslo, Alaska), the midsummer day is about 18.5 hours and the midwinter day is about 5.5 hours. Above the Arctic or Antarctic Circle (roughly 66.5 degrees), there are dates when the sun does not set at all (midnight sun) and dates when it does not rise at all (polar night). The rate of day-length change is also latitude-dependent. Near the equinoxes at mid-latitudes, day length changes by 2 to 4 minutes per day. Near the solstices, the change slows to near zero (the word solstice derives from the Latin for "sun stands still"). This calculator shows the day-length trend compared to the previous day, giving you an immediate sense of whether you are in a rapidly-changing equinox window or a stable solstice period.

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Founder's Real-World Experience
Muhammad Shahbaz Siddiqui

Muhammad Shahbaz Siddiqui

Founder, TheCalculatorsHub

How a wildlife documentary cinematographer used the Sunrise Sunset Calculator to plan a 3-week polar bear migration shoot in Churchill, Manitoba in 2025

In October 2025, I was the director of photography for a wildlife documentary following the polar bear migration along Hudson Bay near Churchill, Manitoba (latitude 58.7 degrees north). The shoot was scheduled across three weeks in late October and early November, the critical window when bears gather on the coast waiting for the bay to freeze. At 58.7 degrees north in late autumn, the sun is low all day and civil twilight windows are long, which creates extended golden-hour conditions -- exactly the kind of directional, dramatic light that makes wildlife footage cinematic. But we had to plan every shooting day in advance because the bears are only active for certain windows, helicopter access is limited, and the production budget had zero room for wasted helicopter time on misread lighting conditions.

I used the Sunrise Sunset Calculator for Churchill (latitude 58.7, longitude -94.17, UTC -6) across all 21 shoot days. The results revealed immediately that October 20 to November 10 spans a period of rapid day-length change at this latitude -- losing about 3 minutes and 10 seconds of daylight per day, shifting from 10 hours 12 minutes on October 20 to 8 hours 44 minutes by November 10. The morning golden hour window (sun 0 to 6 degrees) lasted between 52 and 68 minutes depending on the specific date, substantially longer than the 25 to 30 minutes I was used to at lower latitudes. This directly shaped our helicopter deployment strategy: we planned two daily golden-hour slots rather than one, and timed ground vehicle departure to have cameras set up and rolling before the golden hour window opened.

The annual calendar table showed the azimuth at sunrise shifting from 113 degrees (ESE) on October 20 to 127 degrees (SE) by November 10, which meant the direction of the early morning light was rotating noticeably across the shoot. On October 20, the low morning sun came from ESE and lit the bears' faces when they faced the coast (east). By November 5, the sun was more southerly at sunrise and the optimal bear positions had shifted. The use-case panel's hunting and wildlife legal light data (30 minutes before sunrise) confirmed that our camera operators could legally be in position and rolling before official sunrise, which we used to capture the pre-dawn bear silhouettes against the dawn sky during astronomical twilight. The shoot produced the documentary's most-used sequence: a bear family backlit against a sky that remained golden for 58 unbroken minutes.

Day length data confirmed 21-day daylight loss of 88 minutes -- scheduled 2 golden-hour helicopter slots daily instead of 1Rise azimuth shift from 113° (ESE) to 127° (SE) over 3 weeks mapped to optimal bear-facing positions per dayGolden hour duration of 52--68 minutes at 58.7° N far exceeded the 25-minute window from previous shoots at 35° N