Calculated sextant height and dead reckoning

Using the exact time of observation, the nautical almanac, spherical trigonometry formulas and dead reckoning, we can determine the calculated sextant height of the sun.

Calculated sextant height and dead reckoning.Tools on the chart table on board

That is to say, the calculated height of the sun of our dead reckoning position

image of a known starting point to a dead reckoning position on a nautical chart

In summary, the goal is to calculate the observer’s height using the Dead Reckoning (D.R.) position and the observed height of the sun using the sextant.

These two heights need to be compared and serve as the basis of the Marcq St. Hilaire method.


Keep in mind that the entire context of this website begins with the La Rochelle exercise, guiding you to an interactive worksheet. The singular objective is to learn how to determine your line of position at sea through eight identical exercises.


Sea Gull at Naaf River. No machine-readable author provided. Auyon assumed

Calculated sextant height and dead reckoning:

theory Hc (the calculated height)

In fact, the formulas of spherical trigonometry enable us to calculate measurements from the center of the Earth to the center of celestial bodies, including the Sun, stars, planets, and the Moon.

Calculated sextant height (Hc) and dead reckoning, image  Calculated Height from earth center
 The bassin d’Arcachon (France). Author image: Grand-Parc-Bordeaux Fr.

Calculated sextant height and dead reckoning:

The formula:

Calculated sextant height (Hc) and dead reckoning, image formula Hc

L = Latitude of our dead reckoning position.

D = Declination of the sun.

P = Polar angle

After reading through this page, you can proceed to another section where you’ll find two examples illustrating how to calculate the “calculated height (Hc)”.


Calculated sextant height and dead reckoning:

Next, we calculate the azimuth of the sun :

Next, we calculate the azimuth of the sun using the almost the same inputs and the calculated height we obtained previously.

To clarify, we always calculate the Hc first, and afterwards the azimut, since it needs the calculated height in its formula!

Calculated sextant height (Hc) and dead reckoning, image formula azimuth

D = Declination of the sun.

L = Latitude of our dead reckoning position.

Hc = Calculated height of our dead reckoning position

What to do with the calculated height? See the Principles Step 4


California, USA. Author image: Michael Sandoval

Calculated sextant height (Hc) and dead reckoning:

A very interesting site is the NOAA sun calculator

Firstly, the NOAA Sun Calculator is a tool provided by the National Oceanic and Atmospheric Administration (NOAA) that allows users to obtain information about the position of the sun at any given location and time. It provides data such as sunrise, sunset, solar noon, and twilight times.

Furthermore, the calculator takes into account various factors, including the observer’s geographic location (latitude and longitude), date, and time zone.

As a result, by inputting these parameters, users can generate accurate and detailed information about the sun’s position

To summarize, the NOAA Sun Calculator is particularly useful for a wide range of applications, including outdoor activities, photography, astronomy, and solar energy planning.