<p>One may define three forms of <a href="https://en.wikipedia.org/wiki/Twilight" rel="noreferrer">twilight</a> on Earth.  Although the actual amount of light depends on weather, topography, and land cover, they are defined as:</p>

<ul>
<li>Civil twilight: Solar angle > -6°</li>
<li>Nautical twilight: Solar angle > -12°</li>
<li>Astronomical twilight: Solar angle > -18°</li>
</ul>

<p>Human eyes see logarithmically so % of sunlight left is not a very useful measure, unless you are interested in incoming shortwave radiation for solar panel or other energy calculations.</p>

<p>To answer your question, you need to calculate at what time the Sun will be at those elevations below the horizon; this is calculated in a similar fashion to sunrise and sunset times.  However, on top of that you also need to consider atmospheric refraction.  See <a href="https://en.wikipedia.org/wiki/Position_of_the_Sun" rel="noreferrer">position of the Sun</a> and <a href="https://en.wikipedia.org/wiki/Sunrise_equation" rel="noreferrer">sunrise equation</a>.  The formulae are quite complicated, but you may be able to simplify them if you're only interested in the duration, not the absolute times.</p>







<p>The time after sunset at which those occur are a function of latitude and time of year.  On this <em>carpet plot</em> from Wikipedia you can read the length of different forms of twilight at 70°N (north of the Arctic circle):</p>

<p><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Carpet_Plot_of_Sun-Elevation_over_a_whole_Year_-_North_of_the_Polar_Circle.png/1024px-Carpet_Plot_of_Sun-Elevation_over_a_whole_Year_-_North_of_the_Polar_Circle.png" alt="carpet plot, 70°N"></p>

CC BY-SA 3.0
2017-06-21T22:36:19.230Z
Stop with all the upvotes please, this answer is not complete! :-)
gerrit
CC BY-SA 3.0
2017-06-21T23:13:54.113Z
A Google search: [astronomical twilight time app](https://www.google.com/search?q=astronomical+twilight+time+app&ie=utf-8&oe=utf-8)
Mazura
CC BY-SA 3.0
2017-06-29T07:17:13.710Z
Is the solar angle equivalent to the sun declination?
JobHunter69
CC BY-SA 3.0
2017-06-29T07:27:16.310Z
Also, this is the solar elevation angle, not the solar zenith angle right?
JobHunter69
CC BY-SA 3.0
2017-06-29T20:37:49.487Z
Yes.  Subtract it from 90 to get the solar zenith angle.
gerrit
CC BY-SA 3.0
2017-06-21T13:35:33.857Z
2017-06-21T13:49:38.783Z
2017-06-21T13:49:38.783Z
gerrit
<p>I would like to know the time it takes to go from sunset to dark based on GPS location.</p>

<p>In addition, ideally I would also like to have a formula that determines the percentage of sunlight at each minute past sunset. For example, after 15 minutes, there is only 50% sunlight left. </p>

CC BY-SA 3.0
2017-06-21T13:34:02.630Z
You will have to define "actual darkness", which may depend on the weather.
gerrit
CC BY-SA 3.0
2017-06-21T19:26:46.383Z
There is an Excel VBA written by Greg Pelletier that can calculate Astronomical and Civil Dusk. It is pretty darned accurate.
BillDOe
CC BY-SA 4.0
2022-03-18T23:38:22.427Z
While not an answer, if you just want to find out when it's really "dark dark" i.e. no sunlight at all to the human eye, that's called "astronomical dusk" or "end of astronomical twilight" or simply "night". Two websites that give this info are https://www.timeanddate.com/sun/usa/new-york and http://suncalc.net/#/39.2313,-77.4688,2/2022.03.18/19:17
CoolHandLouis
<the-sun><earth><light><sun-rays>
How can I calculate the time between sunset and actual darkness?
JobHunter69
# How can I calculate the time between sunset and actual darkness?

(Asked by: username_0 on 2017-06-21)

I would like to know the time it takes to go from sunset to dark based on GPS location.

In addition, ideally I would also like to have a formula that determines the percentage of sunlight at each minute past sunset. For example, after 15 minutes, there is only 50% sunlight left.

**Tags:** the-sun, earth, light, sun-rays
> **Comments:**
> **username_1**: You will have to define "actual darkness", which may depend on the weather.  
> **username_2**: There is an Excel VBA written by Greg Pelletier that can calculate Astronomical and Civil Dusk. It is pretty darned accurate.  
> **username_3**: While not an answer, if you just want to find out when it's really "dark dark" i.e. no sunlight at all to the human eye, that's called "astronomical dusk" or "end of astronomical twilight" or simply "night". Two websites that give this info are https://www.timeanddate.com/sun/usa/new-york and http://suncalc.net/#/39.2313,-77.4688,2/2022.03.18/19:17  

---

## 1 answers

### Answer by username_1 on 2017-06-21. Score: 15 | Accepted answer

One may define three forms of [twilight](https://en.wikipedia.org/wiki/Twilight) on Earth. Although the actual amount of light depends on weather, topography, and land cover, they are defined as:

* Civil twilight: Solar angle > -6°
* Nautical twilight: Solar angle > -12°
* Astronomical twilight: Solar angle > -18°

Human eyes see logarithmically so % of sunlight left is not a very useful measure, unless you are interested in incoming shortwave radiation for solar panel or other energy calculations.

To answer your question, you need to calculate at what time the Sun will be at those elevations below the horizon; this is calculated in a similar fashion to sunrise and sunset times. However, on top of that you also need to consider atmospheric refraction. See [position of the Sun](https://en.wikipedia.org/wiki/Position_of_the_Sun) and [sunrise equation](https://en.wikipedia.org/wiki/Sunrise_equation). The formulae are quite complicated, but you may be able to simplify them if you're only interested in the duration, not the absolute times.

The time after sunset at which those occur are a function of latitude and time of year. On this *carpet plot* from Wikipedia you can read the length of different forms of twilight at 70°N (north of the Arctic circle):

![carpet plot, 70°N](https://upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Carpet_Plot_of_Sun-Elevation_over_a_whole_Year_-_North_of_the_Polar_Circle.png/1024px-Carpet_Plot_of_Sun-Elevation_over_a_whole_Year_-_North_of_the_Polar_Circle.png)

> **Comments:**
> **username_1**: Stop with all the upvotes please, this answer is not complete! :-)  
> **username_4**: A Google search: [astronomical twilight time app](https://www.google.com/search?q=astronomical+twilight+time+app&ie=utf-8&oe=utf-8)  
> **username_0**: Is the solar angle equivalent to the sun declination?  
> **username_0**: Also, this is the solar elevation angle, not the solar zenith angle right?  
> **username_1**: Yes.  Subtract it from 90 to get the solar zenith angle.  

---

