The  full method of calculating your latitude from the altitude of the Sun can be found at this link.  However, in a survival situation, the following simplified method can be used.

Equipment Needed. 

1. A clinometer or other device for measuring angles.
2. A copy of the Sun’s Declination table.
3. A magnetic compass.

(A  full list of equipment required for survival astro navigation can be found here)

How to tell when it is midday in your exact geographical position.

Firstly, it is important to remember that midday in your exact position will very rarely co-incide with noon in standard time or zone time because these time systems cover very large geographical areas.  True midday is when the Sun lies directly over your meridian of longitude and so, depending on your geographical position, the Sun will bear either due north or due south at midday.

Use the following method to determine when it is midday at your position.

1. If you have a compass, use it to determine when the sun’s bearing is approaching due north or south.
2. Using a clinometer and a smoked glass filter, begin to measure the sun’s altitude at frequent intervals just as it approaches north or south.
3. Midday will occur when the sun reaches its highest altitude.
4. Make a note of the highest altitude reached.

Calculating your latitude from the Sun’s altitude at midday.

The following method depends on you having a rough idea of your latitude to begin with.  For example, in the Sahara, you will be between 15^o and 35^o North; in Nepal, you willl be between 26^o and 28^o North; and in the Amazon, you will be between 0^o and 15^o South.

Method of calculating latitude.

1. Consult the declination table to find the declination for the day.
2. Determine whether the declination is north or south.
3. Determine whether your latitude and the declination have the same or contrary  names (north or south).
4. Apply the rules below to calculate your latitude.

Rules.  The method depends on the following three simple rules:

(i)   Latitude and declination have same names and latitude greater than declination:

LAT  =  DEC + (90^o – ALT)

(ii)   Latitude and declination have same names and declination greater than latitude:

LAT  =  DEC – (90^o – ALT)

(iii)   Latitude and declination contrary names:

LAT  =  (90^o – ALT) – DEC

Examples:

1.   Using rule (ii)

Scenario:  True altitude at midday: 69.7^o

Sun’s declination: 20.8^o North

Approx latitude:  0^o – 5^o North (in a coastal region of Borneo).

Sun’s expected bearing at midday: North.

LAT  =  DEC – (90^o – ALT) (rule ii)

= 20.8^o – (90^o – 69.7^o)

= 20.8^o – 20.3^o

= 0.5^o North.

2.   Using rule (iii)

Scenario:  True altitude at midday: 80.9^o

Sun’s declination: 2.7^o  South

Approx latitude:  5^o – 10^o North (in Somalia)

Sun’s expected bearing at midday:  South (but more overhead).

LAT = (90^o – ALT) – DEC (rule iii)

= (90^o – 80.9^o) – 2.7^o

      = 9.1^o – 2.7^o  = 6.4^o North.

3.   Using rule (i)

Scenario:  True altitude at midday: 72.5^o

Approx latitude: 35^o – 45^o South  (at sea in mid Pacific)

Sun’s declination: 23.2^o South

Sun’s expected bearing at midday: North

LAT  =  DEC + (90^o – ALT) (rule i)

= 23.2^o  + (90^o – 72.5^o)

= 23.2^o  + 17.5^o

= 40.7^o South.

=  40^o  42’ South

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