CalcMountain

Sunrise & Sunset Calculator

Calculate approximate sunrise and sunset times based on your latitude and the day of the year. This uses a simplified solar position algorithm to estimate civil sunrise and sunset. Results are approximate and do not account for altitude, refraction corrections, or local terrain.

Sunrise and sunset times vary significantly throughout the year and across latitudes, governed by Earth's 23.44° axial tilt and orbital motion around the sun. The relationship is complex: at the equator, day length stays close to 12 hours year-round; at higher latitudes, day length varies dramatically — Stockholm experiences 18+ hour days in summer and 6-hour days in winter; Anchorage has 19+ hour summer days and 5-hour winter days; the Arctic Circle (66.5°N) and beyond experience 24-hour sunlight in summer and 24-hour darkness in winter.

Understanding sunrise/sunset times matters for many activities: photography (golden hour timing), outdoor sports planning, gardening (plant light requirements), travel itinerary, astronomical observation, religious observance (Islamic prayer times, Jewish Sabbath, etc.), business operations (lighting needs, energy use). Solar calculations also drive renewable energy planning, airport runway lighting decisions, and broadcast scheduling in some markets.

This calculator provides approximate sunrise and sunset times based on latitude, day of year, and UTC offset. Use it for: general daylight planning, understanding seasonal patterns at different latitudes, photography planning (golden hour timing), travel preparation, or astronomy/sky watching planning. Important context: this is a simplified calculation accurate within ~10-15 minutes. For precise times (within 1-2 minutes), use astronomical APIs like sunrise-sunset.org or the National Oceanic and Atmospheric Administration's (NOAA) solar calculator, which account for atmospheric refraction, elevation above sea level, and exact longitude. Most weather apps display precise local sunrise/sunset times. For solar panel installation, gardening, or scientific purposes, use the more precise tools.

Inputs

Positive = North, Negative = South

June 21 = ~172, Dec 21 = ~355

EST = -5, CST = -6, PST = -8

Results

Sunrise

4:35 AM

Sunset

7:25 PM

Day Length

14h 51m

Solar Noon

12:00 PM

Solar Details

DetailValue
Latitude40 N
Day of Year172
UTC OffsetUTC-5
Sunrise4:35 AM
Solar Noon12:00 PM
Sunset7:25 PM
Day Length14h 51m
Night Length9h 9m
Last updated:

Formula

Solar position calculation (simplified): Step 1: Solar declination angle (Earth's tilt relative to current sun position): δ = 23.44° × sin(360° × (n + 10) / 365) Where n = day of year (1-365) Maximum at summer solstice (~June 21, day 172): δ ≈ +23.44° Minimum at winter solstice (~December 21, day 355): δ ≈ -23.44° Zero at equinoxes (~March 21, September 21): δ ≈ 0° Step 2: Hour angle for sunrise/sunset (when sun reaches horizon): cos(H) = -tan(latitude) × tan(δ) H = hour angle in degrees from solar noon If |cos(H)| > 1: polar day (24h sun) or polar night (24h darkness) Convert H to hours: H (hours) = H (degrees) / 15 Step 3: Solar noon time (local): Solar noon (UTC) = 12:00 - (longitude / 15) Or use ~12:00 local time as approximation Equation of time corrections apply for precision Step 4: Sunrise and sunset: Sunrise = Solar Noon - H (hours) Sunset = Solar Noon + H (hours) Day length: Day Length = 2 × H (hours) Example: 40°N latitude, day 172 (June 21). Declination: δ = 23.44° × sin(360° × (172 + 10) / 365) = 23.44° × sin(179.5°) ≈ 23.44° cos(H) = -tan(40°) × tan(23.44°) = -0.839 × 0.434 = -0.364 H = arccos(-0.364) = 111.4° H in hours: 111.4 / 15 = 7.43 hours Solar noon ~12:00 local Sunrise: 12:00 - 7:26 = 4:34 AM (solar) Sunset: 12:00 + 7:26 = 7:26 PM (solar) Day length: 14h 52m Same location, day 355 (December 21): δ ≈ -23.44° cos(H) = -tan(40°) × tan(-23.44°) = -0.839 × -0.434 = 0.364 H = arccos(0.364) = 68.6° H in hours: 68.6 / 15 = 4.57 hours Sunrise: 12:00 - 4:34 = 7:26 AM Sunset: 12:00 + 4:34 = 4:34 PM Day length: 9h 09m Same location, day 80 (March 21, near equinox): δ ≈ 0° cos(H) = 0 H = 90° H in hours: 90 / 15 = 6 hours Sunrise: 6:00 AM Sunset: 6:00 PM Day length: 12h 00m (equinox property: equal day/night everywhere) Day length by latitude (summer solstice / winter solstice): Equator (0°): 12h 07m / 12h 07m (nearly constant year-round) Tropic of Cancer (23.5°N): 13h 35m / 10h 41m 30°N (Houston, Cairo): 14h 04m / 10h 14m 40°N (NYC, Madrid): 14h 52m / 9h 09m 50°N (Vancouver, Berlin): 16h 21m / 7h 48m 60°N (Anchorage, Helsinki): 18h 53m / 5h 53m 66.5°N (Arctic Circle): 24h (polar day) / 0h (polar night) 70°N: 24h sun for ~2 months in summer; 24h dark for ~2 months in winter 80°N: 24h sun for ~5 months; 24h dark for ~4 months 90°N (North Pole): 6 months of continuous sun (March-Sept); 6 months continuous dark Southern Hemisphere mirrored: longest days December, shortest June. Twilight phases: Civil twilight: sun 0-6° below horizon Bright enough for outdoor activities Most "sunrise/sunset" reports refer to civil sunrise/sunset Lasts 20-35 minutes typically (longer at higher latitudes) Nautical twilight: sun 6-12° below horizon Horizon visible; bright stars appear Used historically by sailors for celestial navigation Astronomical twilight: sun 12-18° below horizon Faintest stars become visible Truly dark sky for astronomical observation requires sun >18° below Total daily twilight: 1.5-3 hours typically (longer at higher latitudes) Golden hour: When sun is 0-10° above horizon. Soft, warm-toned lighting prized by photographers. Morning golden hour: ~1 hour after sunrise Evening golden hour: ~1 hour before sunset Blue hour: When sun is 4-8° below horizon. Cool blue tones, popular for photography. Morning blue hour: ~30-60 min before sunrise Evening blue hour: ~30-60 min after sunset Practical applications: Photography: Plan shoots around golden hour (best light) Avoid harsh midday sun (10 AM - 2 PM) Blue hour for cityscapes Stars become visible at end of astronomical twilight Gardening: Plants need 6+ hours direct sun for most flowering/fruiting Track sun exposure across your garden through year Plan plant placement based on sun patterns Solar energy: Solar panels productive during daylight hours Peak generation at solar noon Annual production depends on latitude (lower better) and weather Outdoor activities: Hiking: plan return before dark (especially in mountains where sun sets earlier) Fishing: dawn and dusk often most productive Wildlife: many species crepuscular (active at dawn/dusk) Religious observance: Islamic prayer times: 5 daily times tied to solar position Jewish Sabbath: begins at sunset Friday, ends Saturday after stars visible Christian Easter date: based on first Sunday after first full moon after vernal equinox Health/circadian: Sunlight exposure regulates sleep-wake cycle Insufficient daylight (high-latitude winters) linked to seasonal affective disorder (SAD) Bright light therapy helps SAD by simulating sunrise Travel/business: Hotel guests planning early activities Tourism (sunrise/sunset destinations like Santorini, Bryce Canyon) Flight scheduling considerations (especially polar routes) Lighting needs for evening events

How to use this calculator

  1. Enter your latitude (positive for Northern Hemisphere, negative for Southern). Examples: New York 40.7°N; Los Angeles 34.0°N; London 51.5°N; Sydney -33.9°S.
  2. Enter day of year (1-365). Approximate: Jan 1 = 1; Jul 4 = 185; Dec 25 = 359.
  3. Enter UTC offset (your time zone): EST -5; CST -6; PST -8; UTC 0; CET +1; Japan +9.
  4. Review approximate sunrise and sunset times plus day length.
  5. For precise times (1-2 minute accuracy): use NOAA solar calculator or weather app.
  6. For golden hour photography: golden hour is roughly 1 hour after sunrise and before sunset.
  7. For travel planning: solstice extremes (June and December) show maximum day length variation.
  8. For gardening: track sun position to plan plant placement; most flowering plants need 6+ direct sun hours.
  9. For high-latitude planning: 60°N+ has dramatic summer/winter day length differences. Plan accordingly.
  10. For southern hemisphere: pattern reversed — longest days December, shortest June.
  11. For Daylight Saving Time: add 1 hour to results during DST period in observing regions.
  12. For exact longitude correction: adjust based on your specific position within time zone.

Worked examples

New York City summer solstice

Latitude 40.7°N. Day 172 (June 21). UTC offset -5 (EST). Approximate sunrise: 5:25 AM EST (with DST: 6:25 AM EDT) Approximate sunset: 8:31 PM EST (with DST: 9:31 PM EDT) Day length: 15h 06m Long summer day. Late evening light extending past 9 PM (with DST) makes summer activities expansive. Photography golden hours: Morning: ~6:25-7:25 AM EDT Evening: ~8:30-9:30 PM EDT For tourism: famous "sunset cruises" along Hudson River around 9:30 PM EDT in late June.

Anchorage Alaska winter

Latitude 61.2°N. Day 355 (December 21). UTC offset -9 (AKST). Approximate sunrise: 10:14 AM AKST Approximate sunset: 3:42 PM AKST Day length: 5h 28m Very short winter day. Almost no daylight; sun rises late, sets early, never reaches very high angle. Mental health impact: sustained low daylight contributes to seasonal affective disorder (SAD) common at high latitudes. Light therapy lamps widely used. Cultural adaptation: Northern communities embrace winter activities (skiing, festivals) during dark months. Summer solstice celebrations (longest day) major events. Same location at summer solstice (June 21): Sunrise: ~4:21 AM AKDT Sunset: ~11:42 PM AKDT Day length: 19h 21m Dramatic seasonal variation typical of subarctic latitudes.

Equator constant year-round

Quito, Ecuador. Latitude 0.2°S (essentially equator). Day 172 (summer solstice Northern Hemisphere): Sunrise: ~6:09 AM Sunset: ~6:21 PM Day length: 12h 12m Day 355 (winter solstice Northern Hemisphere): Sunrise: ~6:07 AM Sunset: ~6:13 PM Day length: 12h 06m Day 80 (March equinox): Sunrise: ~6:00 AM Sunset: ~6:00 PM Day length: 12h exactly Remarkably constant year-round. Equatorial cities have near-12-hour days every day of year. Sunrise and sunset times shift only 10-15 minutes across seasons. This consistency affects: agricultural rhythms (multi-cropping possible year-round), tourism (predictable lighting throughout year), wildlife behaviors (less seasonal migration), human circadian patterns (no extreme seasonal adjustment). Tropical cultures often less sleep-time-flexible than temperate cultures due to constant light patterns.

When to use this calculator

Use this calculator for sunrise/sunset planning, photography timing (golden hour), travel preparation, outdoor activity scheduling, gardening (sun exposure planning), or understanding seasonal daylight patterns.

Pair with other weather calculators for comprehensive outdoor planning.

Important sunrise/sunset considerations:

1. **Latitude drives variation.** Equator: ~constant 12-hour days. High latitudes: extreme summer/winter differences.

2. **Earth's axial tilt (23.44°) creates seasons.** Same tilt produces solstice extremes in both hemispheres (opposite seasons).

3. **Civil sunrise/sunset is convention.** Most reported times use civil twilight (sun 0° at horizon). Nautical and astronomical twilights extend usable light hours.

4. **Golden hour is photographer's favorite.** Soft warm light approximately 1 hour after sunrise and before sunset. Plan landscape/portrait photography accordingly.

5. **Polar regions experience polar day/night.** Above 66.5° latitude: continuous sun in summer, continuous dark in winter. Lasting weeks to months at extreme latitudes.

6. **DST shifts apparent times by 1 hour.** During DST period, clock times shift but solar position unchanged.

7. **Solstices and equinoxes are key dates.** Summer solstice: longest day. Winter solstice: shortest. Equinoxes: nearly 12-hour days everywhere.

8. **Elevation affects times.** Higher elevations see sun earlier in morning, later in evening (less Earth obstruction). Mountain sunrise/sunset earlier/later than valley.

9. **Atmospheric refraction extends apparent times.** Sun visible ~30 minutes after astronomical sunset due to atmospheric light bending. Already accounted for in standard calculators.

10. **Tropical regions have minimal variation.** Year-round 11.5-12.5 hour days. Tourism, agriculture, lifestyle adapted to consistency.

11. **Photo planning apps available.** PhotoPills, TPE (The Photographer's Ephemeris) provide precise sun/moon position, golden hour timing, and shadow planning for specific locations.

12. **Solar calculator for precision.** NOAA solar calculator (gml.noaa.gov) provides exact sunrise/sunset/solar position for any location and date.

Common mistakes to avoid

  • Forgetting Daylight Saving Time. Add 1 hour during DST period in observing regions.
  • Not adjusting for hemisphere. Northern and Southern hemispheres have opposite seasonal patterns.
  • Using equatorial expectations for high latitudes. Polar regions experience extreme summer/winter differences.
  • Ignoring elevation effect. Mountain locations see sunrise/sunset earlier/later than valley sea level.
  • Treating approximation as precise. This calculator within 10-15 minutes; use NOAA tools for precision.
  • Forgetting twilight extends usable light. Civil twilight adds 20-35 minutes of usable light before sunrise and after sunset.

Frequently Asked Questions

Sources & further reading

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