Sunset time calculator

Sunset time is a closed trigonometric function of three quantities: the observer's geographic latitude, the Sun's declination on that date, and the hours that the local clock sits ahead of apparent solar time. This sunset calculator evaluates the geometric identity cos ω equals minus tan φ times tan δ, converts the sunset hour angle ω into decimal hours after solar noon, then adds the time-zone offset to produce a local clock time in decimal hours. Polar night, where the Sun never rises, is rejected for the same reason: there is no sunset to report.

What the sunset hour angle is and how it becomes a local clock hour

Apparent solar noon is the instant when the local hour angle is zero: the Sun stands on the observer's meridian and shadows point true north or south. Sunset sits after that noon at plus a single angle ω, the sunset hour angle. The same cosine can be written without tangents as minus sin φ sin δ over cos φ cos δ, which stays finite at the poles where tan φ diverges.

The Earth turns fifteen degrees of hour angle every civil hour, so the solar-time sunset is twelve plus ω in degrees divided by fifteen, or equivalently twelve plus twelve ω over π when ω is in radians. Decimal hours are the contract: 18.5 means half past six in the evening, 19.25 means 19:15. This page evaluates that identity only.

It does not convert a calendar date into declination, it does not add the conventional minus zero point eight three three degrees that civil sunset tables use for refraction plus the solar semi-diameter, and it does not fold in longitude or the equation of time. Those corrections answer different search intents. Here the question is strictly geometric: given φ, δ, and a clock offset from apparent solar time, at what decimal hour does the Sun meet the true horizon, or does it never set at all.

What you enter, midnight sun and what you get

When |tan φ tan δ| exceeds one the Sun either never sets or never rises. Midnight sun — the product of the tangents greater than one with φ and δ the same sign — is rejected with a message that the Sun never sets at this latitude and declination. Polar night — opposite signs past the same threshold — is rejected because there is no sunset hour when the disk never clears the horizon.

Poles and a declination of plus or minus ninety degrees use the sign of sin φ sin δ for the same test, because the tangent form diverges. At the equator tan φ vanishes, so ω is always a right angle and solar sunset is 18.0 for every declination; a zero offset leaves the local result at 18 as well. Pair the decimal hour with your own formatter if you need HH:MM on a label.

Where a sunset time calculator earns its keep

Architecture and daylighting studios use a sunset time calculator to place the geometric dusk hour on a given latitude and design-day declination without opening an astronomy almanac. Field biologists and agronomists who already know δ from a day-of-year formula need the matching clock hour so feeding, irrigation, or observation windows sit after true dusk rather than after an arbitrary civil table.

Outdoor event planners, photographers, and film units convert a site latitude plus a chosen declination into a decimal hour they can drop into a call sheet, then add the local offset so the number matches the clocks on set. Prefer this page when the search intent is sunset time itself — the local decimal hour from φ, δ, and a timezone offset — rather than daylight duration, sunrise, civil twilight, or a calendar date converted through an ephemeris. Those related tools answer different queries and should not cannibalize this landing.

Failed validation, including midnight sun, does not consume balance. The calculator will not invent a sunset on a polar day; if your site is inside the midnight-sun belt, treat the error as the physical answer and switch to a day-length or solar-altitude tool for the rest of the story.