Calculating Position from two observed Altitudes

This application determines the location of the navigator from two measured celestial altitudes as obtained from two sextant sights. A displacement between the two sights is taken into account through the evaluation of the estimated positions (EP) of both sights.
The calculated position is the position at the time of the second sight.

NOTICE: Ephemerides are available for 2023 and 2024.

Sight 1   Sight 2
Date (UTC)   YYYY-MM-DD   Date (UTC)   YYYY-MM-DD
Time (UTC)   hh:mm:ss   Time (UTC)   hh:mm:ss
Object   Object
Limb   Limb
Sextant (Hs)   dd-mm.m   Sextant (Hs)   dd-mm.m
Index Error   '   Index Error   '
Eye Height   m   Eye Height   m

Barometer   Barometer
Temperature   Temperature

Estimated Position (EP1)   Estimated Position (EP2)
Latitude  N/S  dd-mm.m   Latitude  N/S  dd-mm.m
Longitude  E/W ddd-mm.m   Longitude  E/W ddd-mm.m

Observed Altitude   Observed Altitude
Sextant (Ho)   Sextant (Ho)
Geographical Position of Celestial Object   Geographical Position of Celestial Object
Dec   Dec
    Displacement (between Estimated Positions)
    Distance  Nm
    Course  °

sail042g_A.png   Observer's Position

  Distance to EP2  Nm
Alternative Position

  Distance to EP2  Nm

Note: the intersection of two Circles-of-equal-Altitude normally yields two valid positions. The "Observer's Position" is the position closest to the estimated position for Sight 2. The "Alternative Position" is the other intersection point of the Circles-of-equal-Altitude and will usualy be far away from the current (estimated) position.

The underlying methode and mathematical background is decribed in the Note "Finding Position from two observed Altitudes" from the "Notes on Plane and Spherical Trigonometry" section.

Warning and Terms of Usage

Notice, that this is experimental software, which has NOT been debugged! Use this application ONLY for training and excercising and NEVER for real navigational tasks! If used for training at sea, please ALWAYS verify the obtained position with another reliable method of navigation. Although the information and data from this page is believed to be accurate, it is explicitly stated that no warranty is given for it's correctness.

Bugs, improvements and feedback can be reported to In case of bug reports, please add a screendump of all entries in the above form.

Scope of this Application

This application determines the location of the navigator from two measured celestial altitudes by calculating the intersection points of two "circles-of-equal-altitude". The altitudes used may result from two sextant measurments of two different celestial bodies performed within a short time interval or they may be obtained by measuring the same celestial body with a significant time span between the two measurments. In the latter case, the displacement that took place between the two measurements must be known in order to determine the correct position at the moment of the second measurment. In this form, the displacement is calculated from the entries of the estimated position of both measurements.
The precision of this analytical method is the highest if the bearings of the two measured bodies differ by about 90°. The results are unreliable if the bearings to the celestial bodies are too similar or if they are close to 180°. In this case, a warning will be issued.