Horizontal Sundial

horizontal dial
Figure 29: Horizontal sundial

side view of horizontal dial
Figure 30: Side view of a horizontal sundial


The horizontal dial is pole - style. It is the one of the most commonly used sundial because it can be used to tell the time whenever the Sun is shining since the dial plate is placed horizontal to the ground. Some other types of sundials, such as the vertical dials can only be used during restricted hours of the day.

General Appearance

A horizontal sundial consists of a flat horizontal dial plate with hour lines which radiate outwards from the tip of the gnomon, which is the upright triangular plate. See Figure 31 for the general configuration. If the line OA is orientated in a true north-south direction, with O toward south and A toward north, the shadow of the style, falling among the hour lines will indicate the time of the day.

general appearance of horizontal sundial
Figure 31: Dial plate of a horizontal sundial

The Mathematics of Horizontal Sundial

We will now show the mathematics of how the hour lines are being drawn for a horizontal sundial.

formula picture 1
Figure 32

In Figure 32, OP is the style pointing to the pole, P. PNS is the meridian, NPT is the hour angle and TON is the shadow angle. By using one or more of the relations of spherical trigonometry, we can deduce that

cos NP cos PNT = sin NP cot TON - sin PNT cot NPT

in which PNT = 90, NP = Ø and TON =

Since cos PNT = 0, sin PNT = 1, therefore

0 = sin Ø cot - cot (HA)

tan = sin Ø tan (HA)

table of calculated values
Figure 33: The calculated shadow angles at latitude 51N.

How it works

We will show in the below animation how the shadow of the gnomon is cast in a year.

Click here for the animation.

Adjustment for various latitudes

Most sundials that are available in the market do not work without a little adjusting.

Many of these "popular" horizontal dials have a gnomon which is set at 45. This means that this dial is, hopefully, designed for use at latitude 45.

The gnomon needs to point to the north celestial pole, so unless the angle of the gnomon is equal to the latitude, the horizontal dial must be "tipped".

If the gnomon was set at 45 to the dial plate, but the latitude is 30, then there is a difference of -15 between the gnomon and the latitude. So we must tip the whole dial so that the gnomon is lowered 15. If the latitude was greater than the angle of the gnomon then we would tip the whole dial so that the gnomon is raised the correct magnitude.

These adjustments will correctly adjust for the new latitude.

Figure 34