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Sunrise, sunset and grey line calculator

Why it works

By day the D layer absorbs low-band signals while the F2 layer reflects them. At sunset D disappears faster than F2, and a short window opens in which the absorption is already small and the reflection still there. That is when 160 and 80 metres come alive on paths that stay silent the rest of the day.

nightdayterminatorsunrisesunset
The grey line is a narrow band along the terminator, where the D layer has gone but F2 is still alive
Location
Locator
Date
Local time offset from UTC (h)
Half-width of the grey-line window (min)
Sunrise and sunset
Sunrise
Noon
Sunset
Day length
Grey-line windows (UTC)
Morning
Evening
Astronomy
Solar declination
Equation of time
Day of the year

📐 The formulas​

Solar declination and the equation of time (the NOAA approximation, with γ from the day of the year):

δ = 0.006918 − 0.399912·cos γ + 0.070257·sin γ − 0.006758·cos 2γ
    + 0.000907·sin 2γ − 0.002697·cos 3γ + 0.00148·sin 3γ          [rad]

EoT = 229.18 · (0.000075 + 0.001868·cos γ − 0.032077·sin γ
      − 0.014615·cos 2γ − 0.040849·sin 2γ)                        [min]

Hour angle of sunrise and sunset:

cos H = ( cos(90.833°) − sin φ · sin δ ) / ( cos φ · cos δ )

The 90.833° instead of 90° allows for refraction and the apparent radius of the disc.

Times:

noon (minutes UTC) = 720 − 4·longitude − EoT
sunrise = noon − 4·H
sunset  = noon + 4·H

A check on the algorithm:​

at δ = 0 and a geometric horizon (without the −0.833° correction) cos H = 0, so H is exactly 90° at any latitude, and sunrise and sunset fall at 06:00 and 18:00 local solar time.

Where this calculator stops:
  • The NOAA approximation is good to about a minute — more than enough for radio, not enough for astronomy
  • At polar latitudes arccos goes out of range: that is polar day or polar night, and the calculator says so
  • The width of the grey-line window is a convention: it depends on the band, the season and the state of the ionosphere
  • Local time is computed from the UTC offset you enter: daylight saving is for you to account for

🎯 In practice​

  • Planning work on 160 and 80 metres — when to be on the air.
  • Grey-line DX: the most interesting directions are those where the terminator passes through both stations at once.
  • Understanding why the window moves through the year along with the solar declination.
Practical advice:
  1. The grey-line window is short — 30–40 minutes. Be on the air beforehand.
  2. The morning window often works better than the evening one: the ionosphere has had the night to recover.
  3. The longest grey-line paths open twice a year, around the equinoxes.
  4. The equation of time moves sunrise by a quarter of an hour over the year — a phone accounts for that, a rule of thumb does not.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Sunrise, sunset and grey line calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/others/grayline (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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