Sunrise, Sunset & Golden Hour Calculator

What golden hour and blue hour actually are

Both are defined by the sun's angle above or below the horizon, not by a number of minutes. That is why they are twenty minutes long in Singapore and three hours long in Iceland in June, and why "the hour after sunrise" is a rule of thumb that fails everywhere outside the middle latitudes.

• Golden hour is the sun between roughly −4° and +6°. The light travels through enough atmosphere to lose its blue end, so it goes warm; it comes in nearly horizontally, so shadows are long and faces are lit from the side rather than from above. It brackets sunrise and sunset — part of it is before the sun appears.
• Blue hour is the sun between −6° and −4°. The sun is under the horizon, the sky is lit indirectly, and the light is even, shadowless and strongly blue. It is the twenty minutes when artificial lights and the sky are the same brightness, which is the whole reason city photographs are taken then.
• The cutoffs are conventions, not physics. Different tools use −4°, −6° or 0° for the golden hour boundary, so times differ by a few minutes between sites. This page uses −4° to +6° and says so, rather than presenting one convention as the answer.

The three twilights, and why there are three

Civil twilight runs from the horizon to −6°: enough light to read by outdoors, and the legal basis for lighting-up times in a lot of countries. Nautical twilight runs to −12°, the point at which the horizon is still distinguishable at sea, which is what you need to take a sextant sight. Astronomical twilight runs to −18°, below which the sky contributes no measurable light and faint objects are visible. Above about 48° of latitude the sun never reaches −18° at midsummer, which is exactly what "white nights" means.

How this is calculated

These are the NOAA solar position equations — the same ones behind NOAA's own solar calculator. The sun's mean longitude and anomaly give its apparent position; from that come the declination and the equation of time, and from those the hour angle at which the sun sits at any chosen altitude. Sunrise uses −0.833°, which accounts for the sun's radius and for average atmospheric refraction bending the image up over the horizon. The calculation is run twice per event, the second time using the declination at the event rather than at noon, which keeps it within a few seconds of NOAA's published figures.

The remaining error is refraction. The −0.833° standard assumes average atmospheric conditions at sea level; a cold morning, a temperature inversion or a hill on the horizon will all move real sunrise by a minute or more, and no calculator can know about any of them.

Polar cases

Above the Arctic Circle and below the Antarctic there are dates with no sunrise and dates with no sunset, and the hour angle has no solution. Most calculators print an empty cell or the word NaN. This one works out which side the answer fell off — sun permanently above the horizon or permanently below — and says which. Try Tromsø in June and again in December.