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How to find north with the sun and a shadow

The sun gives you a compass if you know its rules. Some popular methods are far less accurate than they claim: worked out for London, Madrid and Singapore, the shadow-tip method can be 28 degrees out and the watch method 70. Here is what works and how well.

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The simplest rule

At solar noon the shadow points north

At solar noon the sun crosses the meridian, so the shadow of a vertical stick points exactly north in the northern hemisphere outside the tropics, and exactly south in the southern hemisphere.

The catch is knowing when solar noon is. It is rarely 12:00: in London it ranges from 11:44 to 13:07 on the clock over the year, in Madrid from 12:58 to 14:21. And around noon the shadow length hardly changes, so finding its shortest moment by eye is imprecise. Use this method only if you know the time of solar noon for the day, from the sunrise and sunset calculator for example.

The accurate one

Two equal shadows

  1. In the morning, a few hours before noon, push a straight stick upright into level ground and mark the tip of its shadow.
  2. With a string tied to the foot of the stick, draw a circle through that mark.
  3. In the afternoon the shadow shortens and then lengthens again. Mark the moment its tip touches the circle a second time.
  4. The line halfway between the two marks, through the foot of the stick, points due north (south in the southern hemisphere).

This works because the sun stands at the same elevation at equal times before and after noon, and those two positions are mirror images across the meridian. The only error comes from the sun’s declination changing over the hours between the marks. Worked out for London, with marks three hours either side of noon, the line is 0.1° out at the equinoxes and less than 0.01° at the solstices: better than most compasses.

The popular one

The shadow-tip method, and how wrong it can be

The shadow-tip method is quicker: mark the tip of a shadow, wait 15 minutes, mark it again, and the line from the first mark to the second runs west to east. It is exact at the equinoxes, when the shadow tip moves along a straight east–west line, but the rest of the year the tip traces a curve, and a short stretch of a curve is not east–west.

Error of the 15-minute shadow-tip line, degrees (+ is clockwise)
Place and date3 h before noon1.5 h beforeNoon1.5 h after3 h after
London, 21 June−19.6−10.10.0+10.1+19.6
London, 20 March0.20.10.10.10.1
London, 21 Decembersun too low+28.30.0−28.3sun too low
Madrid, 21 June−17.7−9.20.0+9.2+17.7
Madrid, 21 December+28.6+18.30.0−18.3−28.6
Singapore, 21 June−16.9−9.30.0+9.3+16.9
Singapore, 21 December+17.2+9.50.0−9.5−17.2

So the method is good near the equinoxes and around noon, and off by 10 to 30 degrees in the middle of the morning or afternoon near the solstices, which is when most people try it. If you must use it, use it close to noon.

The famous one

The watch method

Point the hour hand of an analogue watch at the sun; halfway between the hour hand and 12 lies south (northern hemisphere). The method assumes the sun moves at an even 15° an hour around the horizon and that your clock shows sun time. Neither is true, so the errors depend on season, latitude and where you are in your time zone.

Error of the watch method, degrees (+ is clockwise of south)
Place, date, clock9:0011:0013:0015:00
London, 20 March, GMT−9−6+1+5
London, 21 December, GMT+5+1−1−4
London, 21 June, GMT−24−14+12+23
London, 21 June, BST as read−38−37−16+5
Madrid, 21 December, CET−10−17−18−19
Madrid, 21 June, CEST as read−57−68−64−13
Singapore, 20 March−44−73−79+42

In a British winter the watch is a fair guide. In summer, especially if you forget to take an hour off for daylight saving time, it can be wrong by 40 degrees, in Spain by 70, and in the tropics it is useless because the sun climbs almost vertically and its azimuth jumps around noon.

Elsewhere

In the southern hemisphere and the tropics

South of the equator the noon shadow points south, and the equal-shadow line points south too. In the tropics the noon sun can be north or south of the zenith depending on the date, so the noon shadow can point either way: use the equal-shadow method, which only relies on the symmetry of the morning and the afternoon.

Whatever the method, never look directly at the sun. To see where the sun will be at any minute, the sun position map draws its direction and the shadow of a stick for any place and time.

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