ABC Tools

The Day and Night World Map, Explained

After reading this you can predict where the sun is directly overhead on any date, why the shadow line (the terminator) bends the way it does, and how to read the twilight bands on the map.

What the map shows

The Earth is a sphere lit by one very distant light. At any instant, exactly half of it faces the sun and half faces away. The boundary between the two halves is a great circle called the terminator. The Day and Night World Map draws that boundary on a flat projection, shades the night side, and marks the subsolar point, the single spot where the sun sits straight overhead.

Here is one hook. Pick any equinox, around March 20 or September 22. Drag the time slider through a full day and watch the terminator. It stays a nearly straight vertical line that passes through both the North and South poles. Now jump to the June solstice. The same line bows into a deep arc, and the whole Arctic stays lit even at local midnight. Nothing about the map changed except the date. The shape of the shadow encodes the season.

When to use it, and when not

Use this map when you want a fast, visual answer to a lighting question: is it dark in Tokyo right now, when does twilight reach a given coast, why does the Antarctic have 24-hour daylight in December, or where the sun is overhead at noon on your birthday.

Do not use it as a precision timing tool for a single point. The subsolar position here comes from a low-precision ephemeris, good to a fraction of a degree. That is far finer than a pixel on a world map, but it is not the tool for computing an exact sunrise to the second for one town. For the offset between clock time and true solar time at one location, use Solar Time vs Clock Time.

The two angles that place the sun

You only need two numbers to know where the sun is overhead. The first is the sun's declination \delta, its latitude on the celestial sphere. Over a year it swings between the tropics:

-23.4^\circ \le \delta \le +23.4^\circ

At the June solstice \delta \approx +23.4^\circ, so the sun stands over the Tropic of Cancer. At the December solstice \delta \approx -23.4^\circ, over the Tropic of Capricorn. At both equinoxes \delta \approx 0^\circ, so the sun is over the equator.

The second number is the subsolar longitude, which just tracks the clock. The Earth turns 360^\circ in 24 hours, so it moves 15 degrees of longitude per hour. The subsolar longitude in degrees, using Greenwich time in hours, is approximately:

\lambda_{sun} \approx -15 \cdot (t_{UTC} - 12) + \text{EoT}

Here t_{UTC} is the hour of day in UTC, and \text{EoT} is a small correction called the equation of time, usually within \pm 16 minutes. Ignore \text{EoT} for a first pass. At 12:00 UTC the sun is roughly over longitude 0. At 18:00 UTC it is over about -90^\circ (near the eastern Pacific).

Why the terminator bends

The terminator is the set of points where the sun sits exactly on the horizon, its altitude equal to zero. The altitude a of the sun at any latitude \phi and hour angle H comes from the standard relation:

\sin a = \sin\phi \sin\delta + \cos\phi \cos\delta \cos H

\phi is your latitude, \delta is the sun's declination, and H is the hour angle, the angular distance in longitude between you and the subsolar meridian. Set a = 0 and you get the horizon circle. Set a = -6^\circ, -12^\circ or -18^\circ and you get the three twilight boundaries.

When \delta = 0 (equinox), the equation collapses so the horizon passes exactly through both poles, and on a plate carree projection that draws as a vertical straight line. When \delta grows, one pole tips fully into daylight and the other into darkness, so the curve bows away from the lit pole. That bow is the visible signature of the season.

The terminator is always a perfect great circle in three dimensions. It only looks curved because you are flattening a sphere onto a rectangle. The equinox case looks straight only because the circle happens to align with two meridians.

A worked example with the demo defaults

The demo button loads the field defaults: the current date and time. To get a number you can check by hand, take the March equinox at exactly 12:00 UTC, with \delta \approx 0^\circ and \text{EoT} \approx 0.

Placing the subsolar point at equinox noon

  1. Declination at the equinox: \delta = 0^\circ. The sun is over the equator, so subsolar latitude is 0.
  2. Subsolar longitude: \lambda_{sun} = -15 \cdot (12 - 12) = 0^\circ. The sun is over the Prime Meridian.
  3. So the subsolar point is (0, 0), in the Gulf of Guinea. The map should place its overhead marker there.
  4. Check the terminator. With \delta = 0, the equation gives \cos H = 0, so H = \pm 90^\circ. The night boundary sits 90^\circ of longitude east and west of the subsolar meridian: at +90^\circ and -90^\circ, independent of latitude. That is your straight vertical line through both poles.
  5. Advance the time to 18:00 UTC. Longitude becomes -15 \cdot (18 - 12) = -90^\circ. The subsolar point and the whole pattern shift 90^\circ west, a quarter turn of the Earth.

The chart below traces subsolar latitude across the year. It is a smooth sine-like curve topping out at +23.4^\circ in June and bottoming at -23.4^\circ in December, crossing zero at the two equinoxes.

Declination over 365 days. The vertical marker at day 79 is the March equinox, where the curve crosses zero.

Reading the twilight bands

The map shades three bands between full day and full dark, set by how far the sun is below the horizon.

Civil twilight
Sun 0 to 6 degrees below the horizon. Bright enough to see outdoors and read large print. The brightest planets appear.
Nautical twilight
Sun 6 to 12 degrees below. The horizon at sea is still faintly visible, which once let sailors take star sights.
Astronomical twilight
Sun 12 to 18 degrees below. Faint enough for most stargazing, but the sky is not yet fully black.

Below 18 degrees the sky is fully dark. On the map, the width of these bands tells you something real. Near the equator the sun drops almost straight down, so it passes through all 18 degrees quickly and the bands are narrow. Near the poles the sun grazes the horizon at a shallow angle, so it takes hours to sink 18 degrees, and the bands are wide. At high summer latitude the sun may never reach 18 degrees below at all, which is why northern cities get "white nights" with no true darkness.

Without JavaScript: as the sun's declination moves from 0 degrees (equinox) to +23.4 degrees (June solstice), the terminator on a flat map changes from a straight vertical line into a curve that bows south, leaving the North Pole fully lit and the South Pole fully dark.

Common mistakes

The errors below trip up almost everyone the first time.

Do not read the curved terminator as the sun's path or as a time zone boundary. It is a single frozen snapshot of the day-night edge. Time zones are political and run mostly along meridians; the terminator ignores them entirely.

  • Confusing UTC with local time. The subsolar longitude formula uses UTC. If you feed it your local clock, the sun lands in the wrong ocean. Convert first.
  • Expecting sunrise exactly at the terminator. The drawn edge is geometric horizon. Real sunrise happens a bit earlier because atmospheric refraction lifts the sun's image by roughly 0.57 degrees, and because the sun is a disk about 0.5 degrees wide, not a point.
  • Reading twilight-band width as a mistake. Wide bands at high latitude are correct physics, not a projection glitch.
  • Forgetting the equation of time. Ignoring \text{EoT} shifts the subsolar point by up to about 4^\circ of longitude (16 minutes) in early November. Harmless on a world map, but real.

Related tools

If you want the point directly opposite the subsolar spot, where it is deepest night, use the Antipode Finder. To turn any latitude and longitude you read off this map into DMS, UTM or a Plus Code, use the Coordinate Converter. To understand why the great-circle terminator looks curved on a flat map, compare paths in Great Circle vs Rhumb Line. And to plot your own points onto a map from a file, use the GeoJSON and CSV Map Viewer or dress a coastline up in the Old Map Renderer.

Frequently asked questions

Why is the terminator a straight line at the equinox?

Because the sun's declination is zero, so the day-night great circle passes through both geographic poles. On a plate carree map, a circle through both poles projects to a vertical straight line. Set \delta = 0 in the altitude equation and you get \cos H = 0, meaning the edge sits at a fixed longitude for every latitude.

What is the subsolar point exactly?

It is the one location where the sun is at the zenith, directly overhead, at that instant. Its latitude equals the sun's declination and its longitude tracks UTC at 15 degrees per hour. At equinox noon UTC it is at (0, 0).

Why do the poles get midnight sun?

When declination is +23.4^\circ in June, every point north of latitude 66.6^\circ keeps the sun above the horizon for the full 24 hours, because the Earth's tilt keeps that cap turned toward the sun as it spins. The map shows this as the North Pole staying inside the lit region all day.

How accurate is the sun position here?

It uses a standard low-precision ephemeris, accurate to a fraction of a degree. On a world map one degree of latitude is only a couple of pixels, so the error is invisible. For second-level timing at a single site, use a dedicated calculation instead.

Does the map account for daylight saving time?

The lighting is computed from UTC and does not care about local clocks or daylight saving. If a town's wall clock reads 20:00 but the map shows it in twilight, that gap is exactly the point the Solar Time vs Clock Time tool measures.

Try it yourself in the tool

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