How do you calculate sunset time for a specific location and date?

The calculation requires three inputs: date, latitude, and longitude. Simplified algorithm (accurate to ~2 minutes): Step 1 — calculate the day of year (N). January 15 = day 15, March 1 = day 60 (non-leap year). Step 2 — calculate solar declination: δ = 23.44° × sin(360/365 × (N + 284)°). This approximation assumes a circular orbit. Step 3 — calculate the hour angle at sunset: cos(ω) = -tan(φ) × tan(δ), where φ = latitude. If cos(ω) > 1: no sunset (polar night). If cos(ω) < -1: no sunset because the Sun doesn't set (midnight sun). Step 4 — sunset time in UTC: T_sunset = 12 + ω/15 + equation_of_time_correction + longitude_correction. The Equation of Time correction (in minutes) accounts for Earth's elliptical orbit and axial tilt: EoT ≈ -7.655 sin(B) + 9.873 sin(2B + 3.5932), where B = 360/365 × (N - 81)°. Longitude correction: (standard_meridian - longitude) / 15 hours. More precise algorithms (NOAA, Jean Meeus) account for: nutation (slight wobble of Earth's axis), aberration (light travel time), Earth's slightly varying orbital speed, and precise atmospheric refraction modeling. These achieve accuracy within 15–30 seconds. For practical purposes, use the NOAA Solar Calculator (online) or astronomy apps — they implement the full precision algorithm. The simplified method above is useful for understanding the physics but can be off by several minutes.

What factors cause the latest and earliest sunsets at different times of year?

The latest sunset does NOT occur on the summer solstice (longest day). Due to the Equation of Time, the latest sunset at mid-northern latitudes (~40°N) occurs around June 27–28, about a week after the solstice. Similarly, the earliest sunset occurs around December 7–10, about two weeks before the winter solstice. The mechanics: around the June solstice, solar noon is shifting later each day (the Equation of Time is becoming more positive). This pushes both sunrise and sunset later. The day is also getting shorter (losing about 1 minute per day of total daylight). The 'later push' on sunset from the shifting solar noon temporarily exceeds the 'earlier pull' from the shortening day, creating a latest sunset after the longest day. Latitude affects the offset: near the equator, the latest sunset and longest day nearly coincide (within 1–2 days) because day-length changes are tiny. At 40° latitude: the offset is about 7 days. At 60° latitude: the offset can be 10+ days. The asymmetry near the December solstice is different: the earliest sunset occurs about 2 weeks before the solstice, while the latest sunrise occurs about 2 weeks after. This creates the curious effect where days start getting lighter in the evening (later sunsets) while mornings are still getting darker (later sunrises) — a phenomenon many people notice in late December and early January. This asymmetry is more pronounced than the June version because Earth is near perihelion in January, making the Equation of Time effect stronger in winter.

What is the significance of solar noon in determining sunset time?

Solar noon is the moment when the sun is highest in the sky, typically occurring at 12:00 PM local standard time. It serves as a reference point for calculating sunset time, as the sunset time is determined by adding the sunset angle time to solar noon. For example, if solar noon is at 12:00 PM and the sunset angle time is 2 hours and 30 minutes, the sunset time would be 2:30 PM. This calculation ensures an accurate determination of sunset time for a given location and date.

How does the latitude of a location affect the sunset time throughout the year?

The latitude of a location significantly affects the sunset time throughout the year due to the Earth's axial tilt. At higher latitudes, the sunset time can vary by up to 6 hours between summer and winter, while at lower latitudes, the variation is typically less than 2 hours. For instance, a location at 40°N latitude may experience a sunset time of 8:30 PM in June and 4:30 PM in December, whereas a location at 10°N latitude may experience a sunset time of 6:30 PM in June and 5:30 PM in December.

What is the typical range of sunset angle times for locations near the equator and at higher latitudes?

The sunset angle time, which is the time difference between solar noon and sunset, typically ranges from 1 hour and 30 minutes to 2 hours and 30 minutes for locations near the equator. In contrast, locations at higher latitudes, such as 50°N or 50°S, can have sunset angle times ranging from 2 hours to 4 hours due to the Earth's curvature and atmospheric refraction. For example, a location at 0° latitude may have a sunset angle time of 1 hour and 45 minutes, while a location at 60°N latitude may have a sunset angle time of 3 hours and 15 minutes.

DigiCalcs

実用

Sunset Time 計算機

質問する

この計算機について質問がありますか？詳細な回答を取得できます。

Mathematically verified

Reviewed August 2026

Our methodology

Get Weekly Math Tips

Join 12,000+ subscribers who get calculator tips every week.

🔒

100% 無料

登録不要

✓

正確

検証済み数式

⚡

即座

即座に結果を表示

📱

モバイル対応

全デバイス対応

Sunset Time 計算機

設定