Determining the Sacred Direction of Islam

If the distance from the Kaʿba is small, its direction may be determined by a diligent seeker, but when the distance is great, only the astronomers can determine that direction.
 
Abūʾl-Rayhān Muhammad ibn Ahmad al-Bīrūnī, Kitāb Tahdīd Nihāyāt al-Amākin Li-Tashīh Masāfāt al-Masākin [“The Book on the Determination of the Coordinates of Positions for the Correction of Distances between Cities”] (416 AH/1025 CE)		   Note: the qibla method described on this webpage is based on the great-circle path to the Kaʿba. An alternative qibla method, followed by some Muslims, based on the rhumb line (a line with a constant compass direction connecting the observer with the Kaʿba) is not discussed on this webpage.
Aerial view of the Great Mosque of Mecca in Saudi Arabia with pilgrims arranged concentrically around the Kaʿba, the sacred centre of Islam.

Contents

This webpage is organized as follows:

Introduction

Five times each day more than a billion Muslims around the globe face Mecca as they perform their daily prayers. The compass direction of the qibla, the sacred direction of Islam, is thus of the greatest importance for every Muslim (Qurʾān, sūra 2:142-152).

The determination of the qibla has in the past exercised the minds of the greatest astronomers, geographers and mathematicians of the Islamic world. Already in the late 8th century, sophisticated mathematical solutions were developed based on spherical trigonometry and the geographical knowledge of that period. The most commonly adopted algorithm was based on the great-circle path (or shortest-distance path) connecting the observer with the Kaʿba in Mecca and determining its angle with the direction to North.

Extensive tables were prepared for each latitude and longitude of the known world and special curves were laid out on astrolabes and prayer quadrants to assist the devout in determining the hour of the day when the sun was in the direction of the qibla.

Usually, there is a moment in each day of the year when the sun (or the sun’s shadow) is in the direction to Mecca. However, this moment of the day is not easy to calculate and it varies according to the seasons and is also different for each place on earth.

However, there are two days in the year when the hour of the day – when measured in absolute time (such as UTC) – is the same for all observers situated in the hemisphere centred on Mecca. On these days one can easily determine one’s qibla within a small fraction of a degree without needing any knowledge of geometry or mathematics. The only thing that one has to do is to look at the sun at the right moment of the day and determine its compass direction.

Qibla Days

As Mecca is located within the tropics there are two days in each year when the sun passes nearly exactly over the Kaʿba. This occurs on 27 or 28 May at 9:18 UTC [12:18 Saudi local time] and on 15 or 16 July at 9:27 UTC [12:27 Saudi local time].

Every Muslim who is located in the hemisphere centred on Mecca (i.e. is less as circa 10.000 km from Mecca) can determine the direction of the qibla by observing the sun on these days at the right moment. The compass direction to the sun then gives the qibla.

Muslims who are located in the other hemisphere (i.e. are more than circa 10.000 km from Mecca) cannot use this method as the sun will then be below the horizon. However, Muslims who live in most of North America, South America, Australia and Antarctica can use the days when the sun passes exactly under the Kaʿba (i.e. exactly above the antipodes of the Kaʿba). This too occurs twice in each year on 12 or 13 January at 21:29 UTC [0:29 Saudi local time] and on 28 November at 21:09 UTC [0:09 Saudi local time]. In the latter case the qibla can be determined by simply observing the compass direction of one’s shadow at the right hour.

Hemisphere centred on the antipodes of Mecca   Hemisphere centred on Mecca
 
click for a larger image suitable for printing   click for a larger image suitable for printing
 
Qibla Days:   12/13 January (21:29 UTC)
28 November (21:09 UTC)		   Qibla Days:   27/28 May (9:18 UTC)
15/16 July (9:27 UTC)

An early description of this method can already be found in the works of the Persian astronomer Nasīr al-Dīn Abū Jaʿfar Muhammad ibn Muhammad al-Tūsī (1201–1274 CE), who wrote in his al-Tadhkira al-Nasīriyya fī ʿilm al-Hayʾa (“Memoir on the Science of Astronomy”), book III, 12.3-4:

[3] As for the qibla bearing, let it be noted that the longitude of Mecca – may God Most High protect it – is 77;10° from the Eternal Islands and 67;10° from the coast of the Western Sea. Its latitude is 21;40°. [...]

[4] There are many ways to determine the qibla bearing, but it would not be appropriate to present them here. Let us instead limit ourselves to one simple method, which is [as follows]. The sun transits the zenith of Mecca when it is in degree 8 of Gemini and in [degree] 23 of Cancer at noontime there. The difference between its noon and the noon of other localities is measured by the difference between the two longitudes. Let this [latter] difference be taken and let an hour be assumed for each 15 degrees and 4 minutes for each degree. The resulting total is the interval in hours from noon [for that locality]. Let an observation be made on that day at that time – before noon if Mecca is to the east or after if it [Mecca] is to the west; the direction of the shadow [of the sun] at that time is [opposite to that of] the qibla bearing.

al-Tūsī’s method was also mentioned in the slightly earlier al-Mulakhkhas fīʾl-Hayʾa (“Compendium of Astronomy”) of Mahmūd ibn Muhammad ibn ‛Umar al-Jaghmīnī (died in 1221), who gives the solar longitudes more precisely as 7;21° Gemini and 22;39° Cancer. Note that both al-Tūsī as al-Jaghmīnī do not specify the dates in relation to the Islamic calendar, which slips about 10 days every year with respect to the astronomical seasons, but by the solar longitude.

As the obliquity of the ecliptic is slowly decreasing, the solar longitudes for the zenith transit at Mecca are now slightly different. The 2000 values are respectively 66.665° [6;40° Gemini] and 113.335° [23;20° Cancer]. Similarly, the solar longitudes for the nadir transit at Mecca are respectively 246.665° [6;40° Sagittarius] and 293.335° [23;20° Capricorn].

Qibla Days for the Hemisphere Centred on Mecca

The following table specifies the Gregorian calendar dates of the first and second “Qibla Day” for the hemisphere centred on Mecca, the equivalent dates in the Umm al-Qura calendar (with the local time in Saudi Arabia) and the zenith distance (z) of the sun as it passes over the Kaʿba (note that the sun’s apparent diameter is about 30').

Year Qibla Day
(9:18 UTC)		 Umm al-Qura date
(12:18 SAT)		 z   Qibla Day
(9:27 UTC)		 Umm al-Qura date
(12:27 SAT)		 z
2010 28 May 14 Jumādā ‛l-Ākhira 1431 2.9' N   16 July 4 Sha‛bān 1431 4.4' S
2011 28 May 25 Jumādā ‛l-Ākhira 1432 0.5' N   16 July 15 Sha‛bān 1432 2.1' S
2012 27 May 6 Rajab 1433 1.9' S   15 July 25 Sha‛bān 1433 0.3' N
2013 27 May 17 Rajab 1434 4.4' S   15 July 7 Ramadān 1434 2.5' N
2014 28 May 29 Rajab 1435 3.0' N   15 July 18 Ramadān 1435 4.8' N
2015 28 May 10 Sha‛bān 1436 0.6' N   16 July 29 Ramadān 1436 2.5' S
2016 27 May 20 Sha‛bān 1437 1.8' S   15 July 10 Shawwāl 1437 0.1' S
2017 27 May 1 Ramadān 1438 4.2' S   15 July 21 Shawwāl 1438 2.3' N
2018 28 May 13 Ramadān 1439 3.2' N   15 July 2 Dhū ʾl-Qaʿda 1439 4.6' N
2019 28 May 23 Ramadān 1440 1.0' N   16 July 13 Dhū ʾl-Qaʿda 1440 2.7' S
2020 27 May 4 Shawwāl 1441 1.3' S   15 July 24 Dhū ʾl-Qaʿda 1441 0.3' S

As with the dates of the equinoxes and the solstices, the dates of “Qibla Day” in the Gregorian calendar are slightly variable. However, due to the small change in the solar declination around these days (about 9 arcmin/day) observations made one or two days before or after a “Qibla Day” will also give satisfactory results.

To convert the Gregorian calendar dates into tabular Islamic calendar dates, click here.

Qibla Days for the Hemisphere Centred on the Antipodes of Mecca

The next table specifies the Gregorian calendar dates of the first and second “Qibla Day” for the hemisphere centred on the antipodes of Mecca, the equivalent dates in the Umm al-Qura calendar (with the local time in Saudi Arabia) and the zenith distance (z) of the sun as it passes over the antipodes of the Kaʿba (note that the sun’s apparent diameter is about 30').

Year Qibla Day
(21:29 UTC)		 Umm al-Qura date
(0:29 SAT)		 z   Qibla Day
(21:09 UTC)		 Umm al-Qura date
(0:09 SAT)		 z
2010 13 January 27 Muharram 1431 2.7' N   28 November 22 Dhū ʾl-Hijja 1431 1.5' N
2011 13 January 9 Safar 1432 0.2' N   28 November 3 Muharram 1433 4.0' N
2012 13 January 19 Safar 1433 2.3' S   28 November 14 Muharram 1434 3.7' S
2013 12 January 30 Safar 1434 4.7' S   28 November 25 Muharram 1435 1.2' S
2014 13 January 12 Rabīʿ al-Awwal 1435 3.2' N   28 November 6 Safar 1436 1.4' N
2015 13 January 22 Rabīʿ al-Awwal 1436 0.6' N   28 November 16 Safar 1437 3.9' N
2016 13 January 3 Rabīʿ al-Ākhir 1437 1.8' S   28 November 28 Safar 1438 3.9' S
2017 12 January 14 Rabīʿ al-Ākhir 1438 4.4' S   28 November 10 Rabīʿ al-Awwal 1439 1.5' S
2018 13 January 26 Rabīʿ al-Ākhir 1439 3.4' N   28 November 20 Rabīʿ al-Awwal 1440 1.1' N
2019 13 January 7 Jumādā ʾl-Ūlā 1440 0.9' N   28 November 1 Rabīʿ al-Ākhir 1441 3.6' N
2020 13 January 18 Jumādā ʾl-Ūlā 1441 1.7' S   28 November 13 Rabīʿ al-Ākhir 1442 4.3' S

 

Bibliography and Useful Web Sites for Determining the Qibla

Web sites

Bibliography on the Qibla (chronological)

Relevant Entries in The Encyclopaedia of Islam: The New Edition (Leiden: E.J. Brill)

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