Sunrise and Sunset: Why the Official Time Is Not When the Sun's Center Reaches the Horizon
Almanacs define sunrise and sunset by the upper edge of the Sun, not its center. That choice, plus the bending of light in air, explains the 50 arcminutes the U.S. Naval Observatory uses.
Try it in the instrument
Set the sky to sunset, as the U.S. Naval Observatory defines it.
Also called
No other names found in our sources.
A simplified model
The drawings are computed from the numbers in the sources. They simplify the real sky. For exact times and dates, use official tables.
Ask someone when the Sun sets and they will point to the moment it touches the horizon. Ask an almanac and you get a time to the minute. For both answers to mean the same thing, someone had to make a choice. The Sun is a disk, not a point of light, and it sinks slowly, so its top edge, its middle and its bottom edge all cross the horizon at different moments.
This guide explains the choice made by the U.S. Naval Observatory (USNO), where its figure of 50 arcminutes comes from, and why a printed sunset time can differ from the sunset you watch. It also covers eye safety around the Sun, and it ends with a task in the Rise & Set Dial.
What the official definition says
USNO says sunrise and sunset conventionally refer to the times when the upper edge of the Sun's disk is on the horizon. It adds two assumptions: the atmosphere is average, and the place is level ground. The Observatory also explains why a rule like this is needed. The Sun is a disk, so not all of it rises or sets at once, and a definition has to say which part counts.
For calculations, USNO turns the rule into a number. Sunrise or sunset happens when the center of the Sun is 90.8333 degrees from straight up, a direction called the zenith. Put another way, the center is geometrically 50 arcminutes below a horizontal plane. The two numbers describe the same depth: 90.8333 minus 90 is 0.8333 degrees, and 0.8333 degrees is 50 arcminutes. An arcminute is a sixtieth of a degree.
For scale, NASA's skywatching FAQ says a degree is about the width of your little finger held at arm's length. Fifty arcminutes is a little less than that.
The horizontal plane in this rule is the geometric horizon. In USNO's rise and set calculations, the observer's eye sits on the surface of the Earth, so the horizon is exactly 90 degrees from the zenith. Picture a flat sheet of glass at eye level that reaches out in every direction. That sheet is the geometric horizon.
So the official sunset is a curious moment. The center of the Sun is already below the sheet of glass, yet the upper rim of the Sun looks as if it just grazes the horizon. USNO says that is what an observer at sea level with a level, unobstructed horizon sees under average conditions.
Where the 50 arcminutes come from
USNO builds the number from two parts. The first is the Sun's own size: its average apparent radius is 16 arcminutes. The second is the bending of light by air, called atmospheric refraction, which averages 34 arcminutes at the horizon. Sixteen plus 34 is 50.
The first part is easy to picture. If the top edge of the Sun is on the horizon, the center is one radius lower, so 16 arcminutes down.
The second part is what the air does. NOAA's solar calculator glossary explains that light bends as it enters Earth's atmosphere. That makes stars and planets near the horizon look higher than they really are, and it explains how the Sun can still be visible after it has physically passed beyond the horizon at sunset. USNO adds the size of the effect: on average the atmosphere bends sunlight by about 34 arcminutes at the horizon at sea level, so the Sun appears above the horizon while it is geometrically below it.
Put the two parts together. When the top edge of the Sun appears to touch the horizon, its true top edge is 34 arcminutes below the horizon, and its center sits 16 arcminutes lower still.
The sources word this in slightly different ways. NOAA's calculator notes say they assume 0.833 degrees of atmospheric refraction for sunrise and sunset. That equals USNO's 50 arcminutes, but NOAA files the whole amount under refraction, while USNO splits it into 34 for the air and 16 for the Sun's radius. The two agree on the total. Only the labels differ.
Why a table time can differ from what you see
Tables are built for a standard situation. USNO says the actual times of rise and set depend on unpredictable atmospheric conditions that change the amount of refraction. Even under ideal conditions, such as a clear sky at sea, a computed time may be off by a minute or more. Local topography and the height of the observer can shift the times even more.
| What the table assumes | What can change it |
|---|---|
| Average air | Temperature, pressure and weather change how much light bends. The 34 arcminutes is an average. |
| An observer at sea level | The height of the observer can affect the times. |
| A level, unobstructed horizon | Local topography, such as mountains on the horizon, can affect the times. |
| A place away from the poles | Accuracy decreases at high latitudes, where the Sun meets the horizon at a very shallow angle. |
NOAA gives its own accuracy statement. Its calculator results are theoretically accurate to within a minute for places between 72 degrees north and 72 degrees south, and within 10 minutes outside those latitudes. NOAA also notes that changes in the air's composition, temperature and pressure mean observed values may vary from the calculation.
A printed sunset time is therefore a very good guide, not a stopwatch. It answers a precise question asked under standard conditions. Your own horizon is the real thing.
Equinox days and the twilight scale
An equinox shows the same rule at work. USNO says the center of the Sun is above the horizon for 12 hours everywhere on Earth on the day of an equinox. Yet day and night are not exactly equal, because sunrise counts the first edge of the disk to appear and sunset counts the last edge to disappear, and refraction lifts the disk. On the dates of the equinoxes, USNO says, the day is about 7 minutes longer than the night at latitudes up to about 25 degrees, and 10 minutes or more at latitude 50 degrees. Equal day and night falls a few days before or after an equinox. At latitude 40 degrees, USNO gives about March 17 and September 26. The guide on the spring equinox goes further.
Sunset does not mean the sky is dark. USNO defines three kinds of twilight by how far the center of the Sun sits below the horizon: 6 degrees for civil twilight, 12 for nautical and 18 for astronomical. The twilight guide covers them. The scale below shows where sunset falls among them.
The Moon follows the same idea. USNO says moonrise and moonset times are computed for exactly the same circumstances as sunrise and sunset, with the Moon's upper edge on a level horizon. The moonrise guide shows how those times move from night to night.
Watching the Sun safely
Sunsets tempt people to stare at the Sun. NASA's eclipse safety page states the rule plainly: except during the brief total phase of a total solar eclipse, it is not safe to look directly at the Sun without specialized eye protection for solar viewing. The page gives no exception for a Sun that is low in the sky. It also says regular sunglasses, no matter how dark, are not safe for viewing the Sun.
NASA warns about optics as well. Viewing any part of the bright Sun through a camera lens, binoculars or a telescope, without a special-purpose solar filter secured over the front of the optics, will instantly cause severe eye injury.
For a safe look at the Sun's image, NASA describes a pinhole projector. A small opening, such as a hole punched in an index card, projects an image of the Sun onto a nearby surface while the Sun stays at your back. Never look at the Sun through the pinhole.
A sunset is easy to enjoy without looking at the disk. Watch the color of the sky, the glow on the clouds and the shadows stretching across the ground. For more detail, read the guide on eclipse eye safety.
Common mistakes
- Treating sunset as the moment the Sun's center crosses the horizon. The official moment is when the upper edge is on the horizon, and the center is then 50 arcminutes below it.
- Giving refraction all the credit. Refraction supplies 34 of the 50 arcminutes. The Sun's own radius supplies the other 16.
- Expecting a table to match every horizon. The table assumes sea level, level ground and average air.
- Assuming day and night are equal at an equinox. USNO says the day runs about 7 minutes longer than the night at latitudes up to about 25 degrees.
- Assuming a low Sun is safe to stare at. NASA's rule has no exception for the Sun near the horizon.
Try it in the instrument
Open the Rise & Set Dial and set the sky to sunset, as defined by the U.S. Naval Observatory. The dial models a place at a middle latitude near an equinox, where the center of the Sun reaches the geometric horizon around 6 PM in solar time. That is the sheet of glass from the first section.
USNO's definition puts the Sun's center 50 arcminutes below that sheet, so the target is a few minutes after 6 PM, not 6 PM itself. The size of the gap fits the equinox numbers above. If the day is about 7 to 10 minutes longer than the night, then split between the two ends of the day, sunrise comes a few minutes before 6 AM and sunset a few minutes after 6 PM.
Two reminders for the harder levels. The windows get narrower, so think about the relation instead of a round number: sunset comes later than the 6 PM line. And the dial is a simplified model. Real sunsets depend on the date, your latitude, your horizon and the air, and the Observatory itself says a table time can be off by a minute or more.
Questions people ask
How accurate is a printed sunset time?
USNO says a computed time for rise or set may be off by a minute or more, even under ideal conditions, and that hills and the height of the observer can shift it further. NOAA says its calculator is theoretically accurate to within a minute between 72 degrees north and south, and within 10 minutes beyond.
Are day and night equal on the equinox?
Not exactly. USNO says the day is about 7 minutes longer than the night at latitudes up to about 25 degrees, and 10 minutes or more at 50 degrees. The dates of equal day and night fall a few days before or after the equinoxes.
Does the Moon use the same rule?
Yes. USNO computes moonrise and moonset for the same circumstances as sunrise and sunset. Unlike the Sun, the Moon can rise or set at any time of day, so USNO notes it is often possible to see the Moon in daylight and to have moonless nights.
What is an arcminute?
It is a sixtieth of a degree. NASA's skywatching FAQ gives a handy yardstick for whole degrees: one degree is about the width of your little finger held at arm's length, so the 50 arcminutes of the sunset rule are a little less than that.
Sources
- Rise, Set, and Twilight Definitions, U.S. Naval Observatory, Astronomical Applications Department. https://aa.usno.navy.mil/faq/RST_defs. Opened November 10, 2026.
- Length of Day and Night at the Equinoxes, U.S. Naval Observatory, Astronomical Applications Department. https://aa.usno.navy.mil/faq/equinoxes. Opened November 10, 2026.
- First Sunrise of the New Year, U.S. Naval Observatory, Astronomical Applications Department. https://aa.usno.navy.mil/faq/first_sunrise. Opened November 10, 2026.
- Solar Calculator Glossary, NOAA Global Monitoring Laboratory. https://gml.noaa.gov/grad/solcalc/glossary.html. Opened November 10, 2026.
- Solar Calculation Details, NOAA Global Monitoring Laboratory. https://gml.noaa.gov/grad/solcalc/calcdetails.html. Opened November 10, 2026.
- Eclipse Viewing Safety, NASA Science. https://science.nasa.gov/eclipses/safety/. Opened November 10, 2026.
- Skywatching FAQ, NASA Science. https://science.nasa.gov/skywatching/faq/. Opened November 10, 2026.
We opened each source ourselves on the date shown. The drawings are our own and were checked against the numbers in these sources.
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