NauticTools2Celestial navigation
Sextant altitude corrections – from the reading Hs to the observed altitude Ho
The altitude read off the sextant is not yet the altitude you work with. Only after index error, dip, refraction and – depending on the body – semi-diameter and parallax do you get the observed altitude Ho. NauticTools2 works the whole chain and shows every step.
- Index error
- Dip
- Refraction
- Semi-diameter
- Horizontal parallax
- Sun · moon · planets · stars
Which corrections are applied?
| Correction | Size | Applies to |
|---|---|---|
| Index error | ± a few ′ | all bodies |
| Dip | − 1.779 · √HE | all bodies |
| Refraction | − 0′ to 34′ | all bodies |
| Semi-diameter | ± about 16′ | sun, moon |
| Parallax | + HP · cos H | moon, Venus, Mars |
The index correction compensates the error of the sextant itself. Dip arises because the eye is above the water: the visible sea horizon lies below the rational horizon. Refraction lifts every body apparently – by over half a degree near the horizon, not at all at the zenith. For the sun and moon you measure a limb; the semi-diameter refers the altitude to the centre. Parallax converts from the observer to the centre of the Earth for the nearby moon and the planets Venus and Mars.
When do you need it?
- Every celestial position line: The observed altitude Ho is compared with the computed altitude – without corrections the position line would be several miles out.
- Noon sight: Latitude from the meridian altitude also needs the corrected altitude.
- Checking exercises: The working shows every correction with its sign.
Formulas and working
Index correction
Hs + IC – the reading corrected for the index error.
Dip
1.779 · √HE in minutes of arc, with the height of eye HE in metres; subtracted.
Semi-diameter
For the sun about 15.7′ to 16.3′ depending on the season, for the moon 0.2725 · HP. Lower limb: add, upper limb: subtract.
Refraction
Depends on the apparent altitude – about 34′ at the horizon, about 2.6′ at 20°, just under 1′ at 45°. Subtracted.
Parallax
HP · cos H for the moon, Venus and Mars; NauticTools2 calculates the horizontal parallax HP from date and time. Added.
Result
Observed altitude Ho and the total correction.
Worked examples
Star Vega: Hs = 58°33.0′, index correction −1.0′, height of eye 3 m. What is Ho?
Hs + IC = 58°33.0′ − 1.0′ = 58°32.0′
Dip = −3.1′ · refraction = −0.6′
Total correction = −3.7′
Ho = 58°28.3′
Sun, lower limb, on 22 October 2026: Hs = 30°00.0′, index correction −1.0′, height of eye 3 m.
Hs + IC = 29°59.0′
Dip −3.1′ · semi-diameter +16.1′ · refraction −1.7′
Total correction = +11.3′
Ho = 30°10.3′
Star Shaula: Hs = 26°59.0′, index correction −1.0′, height of eye 3 m.
Hs + IC = 26°58.0′ · total correction = −5.0′
Ho = 26°53.0′
Things to watch out for
- Sign of the index correction: The correction is the opposite of the error – if the sextant reads too high, the correction is negative. NauticTools2 can determine it with the index error tool.
- Estimate height of eye honestly: It means the height of the eye above the waterline, not above the deck. Between 2 m and 3 m height of eye there is already 0.6′ of dip.
- Avoid low altitudes: Below about 15° refraction becomes uncertain because it depends strongly on temperature and pressure.
- Choose the right limb: For the sun and moon specify lower or upper limb; the wrong limb means an error of over 30′.
How it works in NauticTools2
Enter the reading
Sextant altitude Hs in degrees and minutes, index correction and height of eye.
Choose the body
Sun, moon, Venus, Mars or star (also for Jupiter and Saturn). For the sun and moon the app asks for lower or upper limb; a line under or over the name shows the choice.
Date and time
For the sun only the date, for the semi-diameter. For the moon, Venus and Mars also the time: NauticTools2 calculates the horizontal parallax from it, which can still be overwritten.
Calculate
Altitude above the horizon, total correction and Ho appear in the result, every correction with its sign in the working. Inputs can be saved and the result printed.
Frequently asked questions
What is the difference between Hs and Ho?
Hs is the sextant reading. Corrected for index error it becomes the altitude above the sea horizon. After dip, refraction and – depending on the body – semi-diameter and parallax you get the observed altitude Ho.
How large is the dip?
1.779 · √(height of eye) in minutes of arc: about 3.1′ at 3 m, about 5.6′ at 10 m.
Why is the sun usually measured on its lower limb?
The lower limb can be set on the horizon most precisely. To refer the altitude to the centre, the semi-diameter of about 16′ is added; for the upper limb it is subtracted.
Related tools
- Fix from 2 or 3 altitudes – from corrected altitudes to position lines and the fix
- Ephemeris calculation – GHA, declination and horizontal parallax
- Vertical sextant angle – the sextant in coastal navigation
NauticTools2 is free and runs on Windows 10 and 11. An Android version is in preparation.
Get it from the Microsoft Store