From a sextant angle to a line on the chart.
Celestial navigation looks like a dark art until you see the four moves that never change. Read them below, then work a whole sight in the interactive workbench — it shows every correction and draws the position line, so the method stops being a formula to memorise and becomes something you can see.
What a sight actually is
You measure the angle between a body and the horizon with a sextant. That single angle puts you somewhere on a circle drawn on the Earth. One sight is one line; two crossing lines are a fix.
Correct the altitude
The raw sextant angle (Hs) isn't the true one. Take off index error and dip, then refraction, then the sun's semi-diameter and parallax. What's left is the observed altitude, Ho.
Reduce from an assumed position
Pick a position close to your DR. From the almanac's GHA and Declination, work the calculated altitude (Hc) and the bearing to the body (Zn) as if you were standing there.
Plot the intercept
The difference between Ho and Hc, in minutes, is your distance in miles from the assumed position — towards the body if Ho is greater, away if less. Draw the position line square across the bearing.
Sight reduction workbench
Start in Practice scenario— set a time and a rough position and it fills the almanac figures for you, so you can work the whole sight end to end. When you're ready for the real skill, switch to Almanac values and enter GHA and Declination from the Nautical Almanac yourself.
The sextant reading
Assumed position (your DR)
Time of sight (UTC)
GHA and Declination are filled from a low-precision practice ephemeris so you can work a whole sight without a paper almanac. Good to a fraction of a mile — never use it for real navigation.
Step 1 — correct the altitude
| Sextant altitude Hs | 60° 24.6' |
| Index error (on the arc) | −2.0' |
| Dip (height of eye 4 m) | −3.5' |
| Refraction (always subtracts) | −0.6' |
| Semi-diameter (lower limb, add) | +15.7' |
| Parallax (sun, small +) | +0.1' |
| Observed altitude Ho | 60° 34.3' |
Step 2 — reduce from the assumed position
Body position practice ephemeris (not for real navigation).
| GHA / Dec | 335° 57.1' / N21° 9.0' |
| LHA | 330° 57.1' |
| Calculated altitude Hc | 60° 39.3' |
| Azimuth Zn | 112.5° |
| Intercept | 5.0 nm Away |
Step 3 — the position line
From your assumed position 36° 0.0' N 5° 0.0' W, step 5.0 nm awaythe sun's bearing (112°), then draw the white position line square across it. You are somewhere on that line — cross it with a second sight for a fix.
The exam is four calculations
The MCA celestial paper asks the same four things every time: a full sight reduction and plot (the workbench above), an azimuth compass check, a latitude by meridian passage or Polaris, and an amplitude compass check. Here are the other three, each with its working shown.
Azimuth compass check
What it's for:every steering compass lies a little, and you have to prove how much before you can trust a course. The sun is the one reference that can't be wrong — so you take a compass bearing of it, calculate where it truly was at that moment, and the difference is your compass error. Done every watch at sea; asked every time in the exam.
- 1. Take a compass bearing of the sun (azimuth mirror) and note the time.
- 2. DR latitude from the chart; Dec and GHA from the almanac daily page for that time; LHA = GHA ± longitude.
- 3. Calculate the true azimuth Zn (Pub 249 or the formula — this tool does that part).
- 4. Error = true − compass, named East when true is greater. Variation (chart) taken off the error leaves deviation for the deviation card.
True azimuth Zn 130.0°
Compass error 2.0° E
Deviation 4.0° E
Error = True − Compass, named East when true is greater. Deviation = error − variation.
Latitude by meridian passage
What it's for:once a day the sun crosses your meridian — local noon — and for that one moment the geometry collapses into simple addition: no hour angles, no tables, just a straight latitude. This is the oldest fix at sea and the exam's gift question, if the naming of the zenith distance doesn't trip you.
- 1. Predict mer-pass time from the almanac daily page; be on deck early.
- 2. Follow the sun up with the sextant. When it stops rising and hangs, that maximum altitude (corrected) is your Ho.
- 3. Declination from the daily page for that time.
- 4. ZD = 90° − Ho, named OPPOSITE to where the body bears. Latitude = ZD combined with Dec (same names add, opposite subtract).
Zenith distance ZD = 90° − Ho = 29° 30.0'
Body bears south → ZD is named N
Latitude = ZD N combined with Dec N21° 12.0' = 50° 42.0' N
Latitude 50° 42.0' N
Amplitude compass check
What it's for:the same compass check as Q2, but caught at the one moment it needs almost no work — sunrise or sunset. With the sun's centre on the horizon, its true bearing comes from a single line of maths (sin A = sin Dec ÷ cos Lat), measured as an offset from due east or west. Compare that with your compass bearing and the error falls out.
- 1. At sunrise or sunset, take the compass bearing as the sun's centre sits on the horizon.
- 2. Declination from the almanac for that time; DR latitude from the chart.
- 3. Amplitude A from sin A = sin Dec ÷ cos Lat — named from E (rising) or W (setting), toward the declination's name.
- 4. Turn the amplitude into a true bearing, compare with the compass: that difference is your error.
Amplitude E 24.4° N
True bearing 65.6°
Compass error 0.4° W
Sanity check the name: amplitude is always named from E (rising) or W (setting), toward the declination's name.
For learning, not for real navigation. The practice scenario uses a low-precision built-in ephemeris — close enough to learn the method, never accurate enough to navigate by. At sea you always work from the current Nautical Almanac and check your working. This tool teaches the method; the sea demands the real book.
Ready to learn it properly? The four-day guided course teaches the exam-room method lesson by lesson — almanac card, daily pages, Pub 249 — with these tools built in. Part of the OOW prep suite.