Calculating Halachic Times

Basic Principles

The basic notions of halachic time use the following definitions:

  1. The day (24 hrs) begins at sunset.
  2. It is only ever one day at a time. It is not possible for the present moment to be, say, Shabbat and Sunday at the same time.
  3. An 'hour' is one twelfth of the interval between sunrise and sunset. The length of an 'hour' is used to work out the times for davening, end of eating chametz etc.
  4. Sunset is when on sees the sun set; sunrise is when one sees the sun rise.
  5. Dawn/nightfall are correspondingly defined as (a) when one can distinguish blue from white, or alternatively recognise a close friend at 4 cubits distance and (b) when one can see three medium magnitude stars. R Tam defined nightfall as 72 mins after sunset. It would be interesting to know how he measured this, as clockwork and the pendulum regulator were not to be invented for several centuries yet, and one cannot use a sundial after sunset.

Rule (1) is subject to some dispute in the Gemarah as to whether it should be sunset or nightfall. The final decision was (a) not to decide, (b) to leave each individual a free choice, and (c) to permit one to change one's mind. This is why one can daven mincha and maariv together between sunset and nightfall. First one says: the day begins at nightfall. This means that one can daven mincha after sunset. Having davened mincha one changes tack and says: the day begins at sunset. One can now daven maariv before nightfall.

Note that the choice mentioned above is an individual choice, it is not bound by local or communal custom (minhag hamakom).

Notwithstanding that one has a free choice, it is conventional to begin Shabbat and festivals at sunset and to end them at nightfall. There are exceptions for when a festival falls on a Friday or Sunday; in these cases the festival gives way to Shabbat and the festival is shortened by approximately one hour (rule 2).

For Shabbat and festivals we do not start bang on sunset, instead we leave a safety margin and light candles either 15 mins or 18 mins before sunset (customs vary). When one is relying on seeing sunset there is, of course, no way of knowing when this is going to be; this rule is only relevant when we are using computed times.

Problems and Solutions

Observational timekeeping raises several problems:

  1. It may be cloudy so that one cannot see the sun rise or set.
  2. Pollution (chemical, light and heat) nowadays makes it impossible to see stars at all over much of Europe.
  3. One cannot do things at a given time before sunset if one does not know when sunset is going to be.

To work around these issues we use computed times for sunrise and sunset. However one must bear in mind that these times are only approximations. It is not possible to predict the times accurately as they depend on atmospheric conditions such as temperature.

Calculating times

The earth rotates on its axis once every approximately 23 hrs 56 mins. This is called sidereal (relative to the stars) day.

At the end of a sidereal day the earth has moved in its orbit around the sun. It therefore has to rotate a little bit extra to bring the same point to face the sun as was facing it at the start of the day.

The earth's orbit is an ellipse. This means that the speed with which the earth moves in its orbit is not constant. Therefore the 'little bit extra' of rotation varies from day to day. A day with respect to the sun is approximately 24 hrs, sometimes a little bit over, sometimes a bit under; the average day length over a whole year is exactly 24 hrs. The variation of day length is called The Equation of Time. The word 'equation' does not here mean what you learnt in mathematics at school; it is an old-fashioned usage and nowadays would maybe be called the 'equalisation of time'. The Equation of Time is not something that can be computed: it has to be observed by comparing an accurate clock with a sundial and then tabulated.

One would think that sunset/rise are when the sun is 90° from the zenith. This would be (more or less) true if the earth had no atmosphere. However the earth does have an atmosphere, and that atmosphere is a refracting medium. The result is that the light from the sun curves down to us as it passes through the air. The curvature is least when the sun is high, and greatest when the sun is low (sunrise/set). The amount of curvature is not predictable: a cloud passing over the ground between us and the sun can affect it quite noticeably. For this reason navigators will not take observations on the sun or a star close to the horizon.

We approximate this problem by taking a 'halachic' sunrise/set to be when the sun is 91° from the zenith: 1° below the tangent plane. Computing this involves solving a spherical triangle using either the spherical cosine rule or the haversine rule. The three points of the triangle are the observer (you), the sun and the north (or south) pole.

This formula gives us the time interval, the hour angle (longitude) of the sun relative to the observer: 1° = 4 mins of time. To this we add the corrections for the equation of time, the standard time meridian (0 for London, which is actually on a standard meridian, but 25 mins for Dublin) and summer time, and we have the actual time of sunrise/set.

The accepted time for nightfall varies considerably. It can be when the sun is 6°, 7°, 7.5°, 8°, 11° or even 14° below the tangent plane. The United Synagogue uses 8°. For fast days we use a slightly earlier time of 6° (R Schneur Zalman).

The Problem of High Latitudes

There are regions of the earth that at certain times of the year either:

  1. Have a sunrise/set but no dawn/nightfall.
  2. Have a dawn/nightfall but no sunrise/set.
  3. Have neither sunrise/set nor dawn/nightfall.

On the assumption that dawn/nightfall are when the sun is 8° below the tangent plane, at midsummer, regions north of 58.5N have a sunrise/set but no dawn/nightfall. In Britain this is Orkney and Shetland. If one uses 11° then everywhere from Cheviot (Scottish border) northwards has no dawn/nightfall. If one uses 14° then everywhere from Birmingham northwards has no dawn/nightfall.

Again, depending on the definition one uses of dawn/nightfall, there are regions that during part of the year have a dawn/nightfall but no sunrise/set. This region covers all of the area inside the Arctic circle, but also extends southwards.

At midsummer and midwinter regions north of 66.5N have neither sunrise/set nor dawn/nightfall. This region shrinks as we move away from the solstices.

For some ideas on how to proceed in the true polar regions see For more moderate latitudes the summary above indicates that one can be as machmir as one likes, but it is liable to lead to silly results.

There is a related problem of determining the day of the week, which turns on which date line one should use.

Code for calculating halachic times may be found in the DateTime::Event::Jewish perl module.

For a spreadsheet of sedrah portions see