Sundial

 ( Ancient Inventions ) 

) because of slow variations in the Earth's orbital and rotational motions. Therefore, tables and graphs of the equation of time that were made centuries ago are now significantly incorrect. The reading of an old sundial should be corrected by applying the present-day equation of time, not one from the period when the dial was made.

In some sundials, the equation of time correction is provided as an informational plaque affixed to the sundial, for the observer to calculate. In more sophisticated sundials the equation can be incorporated automatically. For example, some equatorial bow sundials are supplied with a small wheel that sets the time of year; this wheel in turn rotates the equatorial bow, offsetting its time measurement. In other cases, the hour lines may be curved, or the equatorial bow may be shaped like a vase, which exploits the changing altitude of the sun over the year to effect the proper offset in time.

A heliochronometer is a precision sundial first devised in about 1763 by Philipp Hahn and improved by Abbé Guyoux in about 1827.

On any given day, the Sun appears to rotate uniformly about this axis, at about 15° per hour, making a full circuit (360°) in 24 hours. A linear gnomon aligned with this axis will cast a sheet of shadow (a half-plane) that, falling opposite to the Sun, likewise rotates about the celestial axis at 15° per hour. The shadow is seen by falling on a receiving surface that is usually flat, but which may be spherical, cylindrical, conical or of other shapes. If the shadow falls on a surface that is symmetrical about the celestial axis (as in an armillary sphere, or an equatorial dial), the surface-shadow likewise moves uniformly; the hour-lines on the sundial are equally spaced. However, if the receiving surface is not symmetrical (as in most horizontal sundials), the surface shadow generally moves non-uniformly and the hour-lines are not equally spaced; one exception is the Lambert dial described below.

Some types of sundials are designed with a fixed gnomon that is not aligned with the celestial poles like a vertical obelisk. Such sundials are covered below under the section, "Nodus-based sundials".

$H\_E\; =\; 15^\{\backslash circ\}\backslash times\; t\backslash text\{\; (hours)\}\; ~.$

The uniformity of their spacing makes this type of sundial easy to construct. If the dial plate material is opaque, both sides of the equatorial dial must be marked, since the shadow will be cast from below in winter and from above in summer. With translucent dial plates (e.g. glass) the hour angles need only be marked on the sun-facing side, although the hour numberings (if used) need be made on both sides of the dial, owing to the differing hour schema on the sun-facing and sun-backing sides.

Another major advantage of this dial is that equation of time (EoT) and daylight saving time (DST) corrections can be made by simply rotating the dial plate by the appropriate angle each day. This is because the hour angles are equally spaced around the dial. For this reason, an equatorial dial is often a useful choice when the dial is for public display and it is desirable to have it show the true local time to reasonable accuracy. The EoT correction is made via the relation

$\backslash text\{Correction\}^\{\backslash circ\}\; =\; \backslash frac\{\backslash text\{EoT\; (minutes)\}\; +\; 60\; \backslash times\; \backslash Delta\; \backslash text\{DST\; (hours)\}\}\{4\}\; ~.$

Near the in spring and autumn, the sun moves on a circle that is nearly the same as the equatorial plane; hence, no clear shadow is produced on the equatorial dial at those times of year, a drawback of the design.

A nodus is sometimes added to equatorial sundials, which allows the sundial to tell the time of year. On any given day, the shadow of the nodus moves on a circle on the equatorial plane, and the radius of the circle measures the declination of the sun. The ends of the gnomon bar may be used as the nodus, or some feature along its length. An ancient variant of the equatorial sundial has only a nodus (no style) and the concentric circular hour-lines are arranged to resemble a spider-web.

$\backslash \; \backslash tan\; H\_H\; =\; \backslash sin\; L\backslash \; \backslash tan\; \backslash left(\backslash \; 15^\{\backslash circ\}\; \backslash times\; t\backslash \; \backslash right)\backslash$

Or in other terms:

$\backslash \; H\_H\; =\; \backslash tan^\{-1\}\backslash left\backslash$

where L is the sundial's geographical latitude (and the angle the gnomon makes with the dial plate), $\backslash \; H\_H\backslash$ is the angle between a given hour-line and the noon hour-line (which always points towards true north) on the plane, and is the number of hours before or after noon. For example, the angle $\backslash \; H\_H\backslash$ of the 3  hour-line would equal the arctangent of since tan 45° = 1. When $\backslash \; L\; =\; 90^\backslash circ\backslash$ (at the North Pole), the horizontal sundial becomes an equatorial sundial; the style points straight up (vertically), and the horizontal plane is aligned with the equatorial plane; the hour-line formula becomes $\backslash \; H\_H\; =\; 15^\backslash circ\; \backslash times\; t\backslash \; ,$ as for an equatorial dial. A horizontal sundial at the Earth's equator, where $\backslash \; L\; =\; 0^\backslash circ\backslash \; ,$ would require a (raised) horizontal style and would be an example of a polar sundial (see below).

The chief advantages of the horizontal sundial are that it is easy to read, and the sunlight lights the face throughout the year. All the hour-lines intersect at the point where the gnomon's style crosses the horizontal plane. Since the style is aligned with the Earth's rotational axis, the style points true north and its angle with the horizontal equals the sundial's geographical latitude  . A sundial designed for one latitude can be adjusted for use at another latitude by tilting its base upwards or downwards by an angle equal to the difference in latitude. For example, a sundial designed for a latitude of 40° can be used at a latitude of 45°, if the sundial plane is tilted upwards by 5°, thus aligning the style with the Earth's rotational axis.

Many ornamental sundials are designed to be used at 45 degrees north. Some mass-produced garden sundials fail to correctly calculate the hourlines and so can never be corrected. A local standard time zone is nominally 15 degrees wide, but may be modified to follow geographic or political boundaries. A sundial can be rotated around its style (which must remain pointed at the celestial pole) to adjust to the local time zone. In most cases, a rotation in the range of 7.5° east to 23° west suffices. This will introduce error in sundials that do not have equal hour angles. To correct for daylight saving time, a face needs two sets of numerals or a correction table. An informal standard is to have numerals in hot colors for summer, and in cool colors for winter. Since the hour angles are not evenly spaced, the equation of time corrections cannot be made via rotating the dial plate about the gnomon axis. These types of dials usually have an equation of time correction tabulation engraved on their pedestals or close by. Horizontal dials are commonly seen in gardens, churchyards and in public areas.

$\backslash tan\; H\_V\; =\; \backslash cos\; L\backslash \; \backslash tan(\backslash \; 15^\{\backslash circ\}\; \backslash times\; t\backslash \; )\backslash$

where is the sundial's geographical latitude, $\backslash \; H\_V\backslash$ is the angle between a given hour-line and the noon hour-line (which always points due north) on the plane, and is the number of hours before or after noon. For example, the angle $\backslash \; H\_V\backslash$ of the 3  hour-line would equal the arctangent of since The shadow moves counter-clockwise on a south-facing vertical dial, whereas it runs clockwise on horizontal and equatorial north-facing dials.

Dials with faces perpendicular to the ground and which face directly south, north, east, or west are called vertical direct dials.; It is widely believed, and stated in respectable publications, that a vertical dial cannot receive more than twelve hours of sunlight a day, no matter how many hours of daylight there are. However, there is an exception. Vertical sundials in the tropics which face the nearer pole (e.g. north facing in the zone between the Equator and the Tropic of Cancer) can actually receive sunlight for more than 12 hours from sunrise to sunset for a short period around the time of the summer solstice. For example, at latitude 20° North, on June 21, the sun shines on a north-facing vertical wall for 13 hours, 21 minutes. Vertical sundials which do not face directly south (in the northern hemisphere) may receive significantly less than twelve hours of sunlight per day, depending on the direction they do face, and on the time of year. For example, a vertical dial that faces due East can tell time only in the morning hours; in the afternoon, the sun does not shine on its face. Vertical dials that face due East or West are polar dials, which will be described below. Vertical dials that face north are uncommon, because they tell time only during the spring and summer, and do not show the midday hours except in tropical latitudes (and even there, only around midsummer). For non-direct vertical dials – those that face in non-cardinal directions – the mathematics of arranging the style and the hour-lines becomes more complicated; it may be easier to mark the hour lines by observation, but the placement of the style, at least, must be calculated first; such dials are said to be declining dials.; ;

Vertical dials are commonly mounted on the walls of buildings, such as town-halls, and church-towers, where they are easy to see from far away. In some cases, vertical dials are placed on all four sides of a rectangular tower, providing the time throughout the day. The face may be painted on the wall, or displayed in inlaid stone; the gnomon is often a single metal bar, or a tripod of metal bars for rigidity. If the wall of the building faces toward the south, but does not face due south, the gnomon will not lie along the noon line, and the hour lines must be corrected. Since the gnomon's style must be parallel to the Earth's axis, it always "points" true north and its angle with the horizontal will equal the sundial's geographical latitude; on a direct south dial, its angle with the vertical face of the dial will equal the colatitude, or 90° minus the latitude.

$X\; =\; H\backslash \; \backslash tan(\backslash \; 15^\{\backslash circ\}\; \backslash times\; t\backslash \; )\backslash$

where is the height of the style above the plane, and is the time (in hours) before or after the center-time for the polar dial. The center time is the time when the style's shadow falls directly down on the plane; for an East-facing dial, the center time will be 6 , for a West-facing dial, this will be 6 , and for the inclined dial described above, it will be noon. When approaches ±6 hours away from the center time, the spacing diverges to +∞; this occurs when the Sun's rays become parallel to the plane.

$\backslash tan\; H\_\backslash text\{VD\}\; =\; \backslash frac\{\backslash cos\; L\}\{\backslash \; \backslash cos\; D\backslash \; \backslash cot(\backslash \; 15^\{\backslash circ\}\; \backslash times\; t\backslash \; )\; -\; s\_o\backslash \; \backslash sin\; L\backslash \; \backslash sin\; D\backslash \; \}$

where $\backslash \; L\backslash$ is the sundial's geographical latitude; is the time before or after noon; $\backslash \; D\backslash$ is the angle of declination from true south, defined as positive when east of south; and $\backslash \; s\_o\backslash$ is a switch integer for the dial orientation. A partly south-facing dial has an $\backslash \; s\_o\backslash$ value of those partly north-facing, a value of When such a dial faces south ($\backslash \; D\; =\; 0^\{\backslash circ\}\backslash$), this formula reduces to the formula given above for vertical south-facing dials, i.e.

$\backslash \; \backslash tan\; H\_\backslash text\{V\}\; =\; \backslash cos\; L\backslash \; \backslash tan(\backslash \; 15^\{\backslash circ\}\; \backslash times\; t\backslash \; )\backslash$

When a sundial is not aligned with a cardinal direction, the substyle of its gnomon is not aligned with the noon hour-line. The angle $\backslash \; B\backslash$ between the substyle and the noon hour-line is given by the formula

$\backslash tan\; B\; =\; \backslash sin\; D\backslash \; \backslash cot\; L$

If a vertical sundial faces trUe south Or north ($\backslash \; D\; =\; 0^\{\backslash circ\}\backslash$ or $\backslash \; D\; =\; 180^\{\backslash circ\}\backslash \; ,$ respectively), the angle $\backslash \; B\; =\; 0^\{\backslash circ\}\backslash$ and the substyle is aligned with the noon hour-line.

The height of the gnomon, that is the angle the style makes to the plate, $\backslash \; G\backslash \; ,$ is given by :

$\backslash \; \backslash sin\; G\; =\; \backslash cos\; D\backslash \; \backslash cos\; L\; ~$

$\backslash \; \backslash tan\; H\_\{RV\}\; =\; \backslash cos(\backslash \; L\; +\; R\backslash \; )\backslash \; \backslash tan(\backslash \; 15^\{\backslash circ\}\; \backslash times\; t\backslash \; )\backslash$

where $\backslash \; R\backslash$ is the desired angle of reclining relative to the local vertical, is the sundial's geographical latitude, $\backslash \; H\_\{RV\}\backslash$ is the angle between a given hour-line and the noon hour-line (which always points due north) on the plane, and is the number of hours before or after noon. For example, the angle $\backslash \; H\_\{RV\}\backslash$ of the 3pm hour-line would equal the arctangent of since When (in other words, a south-facing vertical dial), we obtain the vertical dial formula above.

Some authors use a more specific nomenclature to describe the orientation of the shadow-receiving plane. If the plane's face points downwards towards the ground, it is said to be proclining or inclining, whereas a dial is said to be reclining when the dial face is pointing away from the ground. Many authors also often refer to reclined, proclined and inclined sundials in general as inclined sundials. It is also common in the latter case to measure the angle of inclination relative to the horizontal plane on the sun side of the dial. In such texts, since $\backslash \; I\; =\; 90^\backslash circ\; +\; R\backslash \; ,$ the hour angle formula will often be seen written as :

$\backslash tan\; H\_\{RV\}\; =\; \backslash sin(L\; +\; I)\backslash \; \backslash tan(\backslash \; 15^\{\backslash circ\}\; \backslash times\; t\backslash \; )\backslash$

The angle between the gnomon style and the dial plate, B, in this type of sundial is :

$B\; =\; 90^\{\backslash circ\}\; -\; (L\; +\; R)$

or :

$B\; =\; 180^\{\backslash circ\}\; -\; (L\; +\; I)$

The formulae describing the spacing of the hour-lines on such dials are rather more complicated than those for simpler dials.

There are various solution approaches, including some using the methods of rotation matrices, and some making a 3D model of the reclined-declined plane and its vertical declined counterpart plane, extracting the geometrical relationships between the hour angle components on both these planes and then reducing the trigonometric algebra.

One system of formulas for Reclining-Declining sundials: (as stated by Fennewick)

The angle $\backslash \; H\_\backslash text\{RD\}\backslash$ between the noon hour-line and another hour-line is given by the formula below. Note that $\backslash \; H\_\backslash text\{RD\}\backslash$ advances counterclockwise with respect to the zero hour angle for those dials that are partly south-facing and clockwise for those that are north-facing.

$\backslash \; \backslash tan\; H\_\backslash text\{RD\}\; =\; \backslash frac\{\backslash \; \backslash cos\; R\backslash \; \backslash cos\; L\; -\; \backslash sin\; R\backslash \; \backslash sin\; L\backslash \; \backslash cos\; D\; -\; s\_o\; \backslash sin\; R\; \backslash sin\; D\; \backslash cot(15^\{\backslash circ\}\; \backslash times\; t)\backslash \; \}\{\backslash \; \backslash cos\; D\backslash \; \backslash cot(15^\{\backslash circ\}\; \backslash times\; t)\; -\; s\_o\; \backslash sin\; D\backslash \; \backslash sin\; L\; \}\backslash$

within the parameter ranges : and

Or, if preferring to use inclination angle, $\backslash \; I\backslash \; ,$ rather than the reclination, $\backslash \; R\backslash \; ,$ where $\backslash \; I\; =\; (90^\{\backslash circ\}\; +\; R)\backslash$ :

$\backslash \; \backslash tan\; H\_\backslash text\{RD\}\; =\; \backslash frac\{\backslash \; \backslash sin\; I\backslash \; \backslash cos\; L\; +\; \backslash cos\; I\backslash \; \backslash sin\; L\backslash \; \backslash cos\; D\; +\; s\_o\; \backslash cos\; I\backslash \; \backslash sin\; D\backslash \; \backslash cot(15^\{\backslash circ\}\; \backslash times\; t)\backslash \; \}\{\backslash \; \backslash cos\; D\backslash \; \backslash cot(15^\{\backslash circ\}\; \backslash times\; t\backslash \; )\; -\; s\_o\; \backslash sin\; D\backslash \; \backslash sin\; L\backslash \; \}\backslash$

within the parameter ranges : and

Here $\backslash \; L\backslash$ is the sundial's geographical latitude; $\backslash \; s\_o\backslash$ is the orientation switch integer; is the time in hours before or after noon; and $\backslash \; R\backslash$ and $\backslash \; D\backslash$ are the angles of reclination and declination, respectively. Note that $\backslash \; R\backslash$ is measured with reference to the vertical. It is positive when the dial leans back towards the horizon behind the dial and negative when the dial leans forward to the horizon on the Sun's side. Declination angle $\backslash \; D\backslash$ is defined as positive when moving east of true south. Dials facing fully or partly south have $\backslash \; s\_o\; =\; +1\backslash \; ,$ while those partly or fully north-facing have an $\backslash \; s\_o\; =\; -1\; ~.$ Since the above expression gives the hour angle as an arctangent function, due consideration must be given to which quadrant of the sundial each hour belongs to before assigning the correct hour angle.

Unlike the simpler vertical declining sundial, this type of dial does not always show hour angles on its sunside face for all declinations between east and west. When a Northern Hemisphere partly south-facing dial reclines back (i.e. away from the Sun) from the vertical, the gnomon will become co-planar with the dial plate at declinations less than due east or due west. Likewise for Southern Hemisphere dials that are partly north-facing. Were these dials reclining forward, the range of declination would actually exceed due east and due west. In a similar way, Northern Hemisphere dials that are partly north-facing and Southern Hemisphere dials that are south-facing, and which lean forward toward their upward pointing gnomons, will have a similar restriction on the range of declination that is possible for a given reclination value. The critical declination $\backslash \; D\_c\backslash$ is a geometrical constraint which depends on the value of both the dial's reclination and its latitude :

$\backslash \; \backslash cos\; D\_c\; =\; \backslash tan\; R\backslash \; \backslash tan\; L\; =\; -\; \backslash tan\; L\backslash \; \backslash cot\; I\backslash$

As with the vertical declined dial, the gnomon's substyle is not aligned with the noon hour-line. The general formula for the angle $\backslash \; B\backslash \; ,$ between the substyle and the noon-line is given by :

$\backslash \; \backslash tan\; B\; =\; \backslash frac\; \{\backslash sin\; D\}\{\backslash sin\; R\backslash \; \backslash cos\; D\; +\; \backslash cos\; R\backslash \; \backslash tan\; L\}\; =\; \backslash frac\; \{\backslash sin\; D\}\{\backslash \; \backslash cos\; I\backslash \; \backslash cos\; D\; -\; \backslash sin\; I\backslash \; \backslash tan\; L\backslash \; \}\backslash$

The angle $\backslash \; G\backslash \; ,$ between the style and the plate is given by :

$\backslash \; \backslash sin\; G\; =\; \backslash cos\; L\backslash \; \backslash cos\; D\backslash \; \backslash cos\; R\; -\; \backslash sin\; L\backslash \; \backslash sin\; R\; =\; -\; \backslash cos\; L\backslash \; \backslash cos\; D\backslash \; \backslash sin\; I\; +\; \backslash sin\; L\backslash \; \backslash cos\; I\backslash$

Note that for $\backslash \; G\; =\; 0^\{\backslash circ\}\backslash \; ,$ i.e. when the gnomon is coplanar with the dial plate, we have :

$\backslash \; \backslash cos\; D\; =\; \backslash tan\; L\backslash \; \backslash tan\; R\; =\; -\; \backslash tan\; L\backslash \; \backslash cot\; I\backslash$

i.e. when $\backslash \; D\; =\; D\_c\backslash \; ,$ the critical declination value.

where R is the radius of the Foster-Lambert dial and δ again indicates the Sun's declination for that time of year.

In altitude dials, the time is read from where the nodus falls on a set of hour-curves that vary with the time of year. Many such altitude-dials' construction is calculation-intensive, as also the case with many azimuth dials. But the capuchin dials (described below) are constructed and used graphically.

Altitude dials' disadvantages:

Since the Sun's altitude is the same at times equally spaced about noon (e.g., 9am and 3pm), the user had to know whether it was morning or afternoon. At, say, 3:00 pm, that is not a problem. But when the dial indicates a time 15 minutes from noon, the user likely will not have a way of distinguishing 11:45 from 12:15.

Additionally, altitude dials are less accurate near noon, because the sun's altitude is not changing rapidly then.

Many of these dials are portable and simple to use. As is often the case with other sundials, many altitude dials are designed for only one latitude. But the capuchin dial (described below) has a version that's adjustable for latitude.

describe the Universal Capuchin sundial.
     

Chaucer evokes this method a few times in his Canterbury Tales, as in his Parson's Tale.

An equivalent type of sundial using a vertical rod of fixed length is known as a backstaff.

The shepherd's dial is evoked in Henry VI, Part 3, among other works of literature.

The cylindrical shepherd's dial can be unrolled into a flat plate. In one simple version, the front and back of the plate each have three columns, corresponding to pairs of months with roughly the same solar declination (June:July, May:August, April:September, March:October, February:November, and January:December). The top of each column has a hole for inserting the shadow-casting gnomon, a peg. Often only two times are marked on the column below, one for noon and the other for mid-morning / mid-afternoon.

Timesticks, clock spear, or shepherds' time stick, are based on the same principles as dials. The time stick is carved with eight vertical time scales for a different period of the year, each bearing a time scale calculated according to the relative amount of daylight during the different months of the year. Any reading depends not only on the time of day but also on the latitude and time of year. A peg gnomon is inserted at the top in the appropriate hole or face for the season of the year, and turned to the Sun so that the shadow falls directly down the scale. Its end displays the time.

The Capuchin sundials are constructed and used graphically, as opposed the direct hour-angle measurements of horizontal or equatorial dials; or the calculated hour angle lines of some altitude and azimuth dials.

In addition to the ordinary Capuchin dial, there is a universal Capuchin dial, adjustable for latitude.

Nodus-based sundials may use a small hole or mirror to isolate a single ray of light; the former are sometimes called aperture dials. The oldest example is perhaps the antiborean sundial ( antiboreum), a spherical nodus-based sundial that faces true north; a ray of sunlight enters from the south through a small hole located at the sphere's pole and falls on the hour and date lines inscribed within the sphere, which resemble lines of longitude and latitude, respectively, on a globe.

Extremely ornate sundials can be composed in this way, by applying a sundial to every surface of a solid object.

In some cases, the sundials are formed as hollows in a solid object, e.g., a cylindrical hollow aligned with the Earth's rotational axis (in which the edges play the role of styles) or a spherical hollow in the ancient tradition of the hemisphaerium or the antiboreum. (See the History section above.) In some cases, these multiface dials are small enough to sit on a desk, whereas in others, they are large stone monuments.

A Polyhedral's dial faces can be designed to give the time for different time-zones simultaneously. Examples include the Scottish sundial of the 17th and 18th centuries, which was often an extremely complex shape of polyhedral, and even convex faces.

• Carnfunnock Country Park, County Antrim, Northern Ireland
• Upton Hall, British Horological Institute, Newark-on-Trent, Nottinghamshire
• Within the collections of St Edmundsbury Heritage Service, Bury St Edmunds
• Longleat, Wiltshire
• Jodrell Bank Science Centre
• Birmingham Botanical Gardens
• Science Museum, London (inventory number 1975-318)

In some U.S. colonial-era houses, a noon-mark might be carved into a floor or windowsill. Such marks indicate local noon, and provide a simple and accurate time reference for households to set their clocks. Some Asian countries had post offices set their clocks from a precision noon-mark. These in turn provided the times for the rest of the society. The typical noon-mark sundial was a lens set above an plate. The plate has an engraved figure-eight shape, which corresponds to the equation of time (described above) versus the solar declination. When the edge of the Sun's image touches the part of the shape for the current month, this indicates that it is 12:00 noon.

• Butterfield dial
• Equation clock
• Foucault pendulum
• Francesco Bianchini
• Horology
• Jantar Mantar
• Lahaina Noon
• Moondial
• Nocturnal—device for determining time by the stars at night.
• Qibla observation by shadows
• Schema for horizontal dials—pen and ruler constructions
• Schema for vertical declining dials—pen and ruler constructions
• Sciothericum telescopicum—a sundial invented in the 17th century that used a telescopic sight to determine the time of noon to within 15 seconds.
• Scottish sundial—the ancient renaissance sundials of Scotland.
• Shadows—free software for calculating and drawing sundials.
• Societat Catalana de Gnomònica
• Tide dial—divisions of the day on early sundials.
• Water clock
• Wilanów Palace Sundial, created by Johannes Hevelius in about 1684.
• Zero shadow day
• Clock

• Christopher St. J.H. Daniel (2025). 9780747805588, Shire Publications. ISBN 9780747805588
• A.M. Earle (1971). 9780804809689, Charles E. Tuttle. . ISBN 9780804809689
  Reprint of the 1902 book published by Macmillan (New York).
• J.L. Heilbron (2025). 9780674005365, Harvard University Press. ISBN 9780674005365
• Ralf Kern (2025). 9783865607720, Verlag der Buchhandlung Walther König. ISBN 9783865607720
• (1994). 9780933346710, Sky Publishing. ISBN 9780933346710
• R.R.J. Rohr (1996). 9780486291390, Dover. . ISBN 9780486291390
  Slightly amended reprint of the 1970 translation published by University of Toronto Press (Toronto). The original was
  
• Denis Savoie (2025). 9780387098012, Springer. ISBN 9780387098012
• Gerard L'E. Turner (1980). 9780713710687, Blandford Press. ISBN 9780713710687
• (1991). 9780951840405, British Sundial Society. ISBN 9780951840405
• Albert E. Waugh (1973). 9780486229478, Dover Publications. . ISBN 9780486229478

• Asociación Amigos de los Relojes de Sol (AARS) – Spanish Sundial Society
• British Sundial Society (BSS) – British Sundial Society
• Commission des Cadrans Solaires de la Société Astronomique de France French Sundial Society
• Coordinamento Gnomonico Italiano (CGI) – Italian Sundial Society
• North American Sundial Society (NASS) – North American Sundial Society
• Societat Catalana de Gnomònica – Catalan Sundial Society
• De Zonnewijzerkring – Dutch Sundial Society (in English)
• Zonnewijzerkring Vlaanderen – Flemish Sundial Society

• "The Book of Remedies from Deficiencies in Setting Up Marble Sundials" is an Arabic manuscript from 1319 about timekeeping and sundials.
• "Small Treatise on the Calculation of Tables for the Construction of Inclined Sundials" is another Arabic manuscript, from the 16th century, about the mathematical calculations used to create sundials. It was written by Sibt al-Maridini.
• Vodolazhskaya, L. Analemmatic and Horizontal Sundials of the Bronze Age (Northern Black Sea Coast). Archaeoastronomy and Ancient Technologies 1(1), 2013, 68-88
• Reconstruction of ancient Egyptian sundials

• Real Sun Time – Sundial as a mobile or desktop version
• Register of Scottish Sundials
• Sundialing Space – Sundial Generator
• The British Sundial Society including a register of British sundials
• The Equation of Time
• The Sundial Primer
• World Sundial Atlas