Live Nautical Almanac & Sight Reduction
The Nautical Almanac is the navigator’s table of where the Sun, Moon, planets and stars sit in the sky at every moment, written as a Greenwich Hour Angle and a declination. Paired with a sextant, those two numbers let you find your position at sea. This page computes them live for any date and time, so they never go out of date, and it will work a sextant sight into a line of position for you.
Almanac data for any moment (UT)
Pick a moment in Universal Time and read off each body’s position, exactly as the daily pages give it.
| Body | GHA | Dec |
|---|
GHA is the Greenwich Hour Angle (how far west of Greenwich the body is) and Dec is its declination (its latitude on the sky). The almanac lists these two for the Sun, Moon and planets; the sidereal hour angle (SHA) is given only for the stars, in the table below. Aries is the reference point on the sky: add a star’s SHA to the GHA of Aries to get that star’s own GHA.
The 57 navigational stars
Their sidereal hour angle and declination for the same moment selected above, sorted by SHA as the almanac lists them. Add a star’s SHA to the GHA of Aries to get its GHA. Every one of these stars is also selectable in the sight-reduction calculator below. (These come from catalog positions carried forward to date, so a few of the fastest-moving stars can differ from the official almanac by an arc-minute or two. The magnitudes are rounded catalog values, for picking out the brighter stars, not the almanac’s own figures.)
| Star | SHA | Dec | Mag |
|---|
Sight reduction: work a sextant sight
Enter the altitude you measured with a sextant, the time, and your DR (dead-reckoning) position, your best estimate of where you are, ideally within about 30 nautical miles. The calculator corrects your reading to a true observed altitude, computes where the body really was, and gives you a line of position by the intercept method.
A note on terms: the classic printed sight-reduction tables (HO-229, HO-249 and the NAO tables) ask for a special assumed position, a whole degree of latitude and a longitude chosen to make the local hour angle a whole degree. This calculator does the trigonometry directly, so you can simply enter your DR or estimated position and it works from there. The two are not the same thing; we use your DR position here.
A worked example, line by line
Suppose that on 21 June 2026 at 14:45:00 UT, from a DR position of 40° N, 70° W, with your eye 2 m above the water and no index error, you bring the lower limb of the Sun down to the horizon and read Hs = 60° 18.5′. The reduction goes:
- Hs 60° 18.5′, the raw sextant angle.
- minus index error (0.0′ here) and minus dip for 2 m of height (about 2.5′) gives the apparent altitude Ha.
- minus refraction (about 0.6′ at this altitude), then plus the Sun’s semi-diameter (about 15.7′ for a lower-limb sight) gives the observed altitude Ho, the true angle to the Sun’s center.
- The almanac gives the Sun’s GHA and Dec for that second; combined with your DR position the navigational triangle gives the computed altitude Hc and the azimuth Zn.
- Ho minus Hc, in minutes of arc, is the intercept in nautical miles: toward the body if Ho is larger, away if smaller. Here it comes out about 10 nautical miles toward the Sun. Plotted from your DR position square to Zn, that is your line of position.
Press Load the worked example above to drop these exact numbers into the calculator and watch every line fill in.
Quick glossary
- Hs
- the raw sextant altitude, straight off the instrument.
- Ha
- apparent altitude: Hs after index error and dip.
- Ho
- observed altitude: the true angle to the body’s center, after refraction and semi-diameter.
- Hc
- computed altitude: the angle you should see from your DR position.
- Zn
- azimuth: the body’s true bearing, clockwise from north.
- IE
- index error: a small fixed bias in the sextant.
- GHA
- Greenwich Hour Angle: how far west of Greenwich the body lies.
- SHA
- sidereal hour angle: a star’s angle west of Aries.
- LHA
- local hour angle: the GHA seen from your own longitude.
- Dec
- declination: the body’s latitude on the sky.
- DR
- dead reckoning: your best estimated position.
Latitude without a full reduction
Two classic shortcuts give latitude on their own, with no plotting. The noon sight uses the Sun at its highest; latitude by Polaris uses the pole star. Both are worked here from the same live positions.
Noon sight: latitude by meridian passage
At local apparent noon the Sun crosses your meridian and reaches its greatest altitude. Measure that maximum altitude and note which way the Sun bore, and latitude follows directly, with no exact time needed.
Latitude by Polaris
From the northern hemisphere, Polaris sits within about a degree of the celestial pole, so its altitude is almost exactly your latitude. This works out the small correction from Polaris’s live position, so you do not need the printed Polaris tables.
Which bodies are well placed right now?
A good star fix needs three or four bodies spread around the horizon, each high enough to clear the haze but not so high that the angle is awkward to measure. This lists the Sun, Moon, planets and the 57 navigational stars currently between 15° and 65° above your horizon, with the altitude and bearing to expect, sorted around the compass for a clean spread.
| Body | Alt (Hc) | Bearing (Zn) | Mag |
|---|
Daily pages: the hourly tables
The heart of the printed almanac is a table of GHA and declination for every whole hour of the day. Pick any date and read or print a clean copy, generated live so it is never out of date.
| UT | Aries GHA | Sun | Moon | Venus | Mars | Jupiter | Saturn | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| GHA | Dec | GHA | Dec | GHA | Dec | GHA | Dec | GHA | Dec | GHA | Dec | ||
How a sextant fix works
Celestial navigation rests on one idea: at any instant a body sits directly over one point on Earth, its geographic position, and your angle up to that body, its altitude, tells you how far away that point is. Measure an altitude of 60° and you are 1,800 nautical miles from the spot beneath the body; measure 40° and you are 3,000 miles off. Every place at that same distance forms a huge circle on the globe, a circle of equal altitude, and you are somewhere on it.
To pin down where, you need to know exactly where the body was. That is what the almanac gives: the Greenwich Hour Angle and declination place the body’s geographic position for the second you took the sight. Subtract your longitude from the GHA to get the local hour angle, and a little spherical trigonometry on the navigational triangle gives the altitude and bearing you should have measured from an assumed position.
The intercept method
You almost never measure exactly the altitude you computed, and that difference is the whole trick. Compare your observed altitude (Ho) with the computed altitude (Hc) for your assumed position. If you measured higher than computed, you are closer to the body than you assumed; if lower, farther. One minute of arc of difference equals one nautical mile, the intercept. Step that many miles from your assumed position, toward the body if you measured high or away if you measured low, and draw a line square to the body’s bearing. That line of position is where you are. Take a second body, or wait and take the same one from a different bearing, and the crossing lines give a fix. This is the method of Marcq Saint-Hilaire, the backbone of modern celestial navigation.
The corrections
A raw sextant reading needs a few corrections before it becomes a true altitude. Index error removes a small bias in the instrument. Dip allows for your height above the water, which pushes the horizon below true level. Refraction removes the bending of light by the atmosphere, which lifts every body slightly. For the Sun and Moon you sight the lower or upper edge rather than the center, so a semi-diameter is added or removed. The Moon also sits close enough that its direction shifts with your position on Earth, an effect called parallax; this calculator folds that in automatically by computing the altitude from your own DR position.
Why there are no v, d, HP or SD columns
Open the printed almanac and you will see extra columns of v and d next to the Moon and planets, a Horizontal Parallax (HP) for the Moon, and a semi-diameter (SD). Those exist so that, working by hand, you can interpolate the hourly figures to the exact second and add parallax and semi-diameter from a table. This page does not need them: it computes each body’s position for the precise instant you enter, and the sight-reduction tool builds parallax and semi-diameter straight into the result. The columns are not missing by accident; the live method makes them unnecessary.
- Time. Always work in UT, not local clock time. The sky turns about a quarter of a minute of arc every second, so a four-second error in your time moves the line of position roughly a nautical mile.
- Dip. Do not forget your height of eye; from a few metres up it can be several minutes of arc.
- The right limb. For the Sun and Moon, match the limb you actually brought to the horizon, lower or upper, or the semi-diameter goes the wrong way.
- Signs and hemispheres. Keep north latitude and longitude straight, and watch the index-error sign, on the arc or off.
- One line is not a fix. A single sight gives a line of position only. Cross two or three from different bearings, or run one up with your course, to get a position.
Always current, by design
The printed almanac is published a year at a time. Here the positions are generated on the fly from a high-precision astronomical model, so any date you choose, past or future, is computed fresh and is never stale. You can cross-check the figures against the live sky on Today in the Sky or the Live Orrery.
Frequently asked questions
What is a nautical almanac and what is it used for?
A nautical almanac is a table of the positions of the Sun, Moon, planets and stars for every hour of the year, given as Greenwich Hour Angle (GHA) and declination. Navigators use it with a sextant to find their position at sea: you measure a body's altitude, look up where that body was at that instant, and work out a line of position. This page generates the same figures live for any date, so they are never out of date.
What is sight reduction and the intercept method?
Sight reduction is the arithmetic that turns a sextant altitude into a line of position. The intercept method compares your observed altitude of a body with the altitude you would expect at an assumed position. If the body is higher than expected you are nearer to it, if lower you are farther; the difference in minutes of arc is a distance in nautical miles. Drawing that distance toward or away from the body, square to its bearing, gives a line you are somewhere on. Cross two or more lines for a fix.
How accurate is this, and can I rely on it at sea?
The positions come from a precise astronomical model and agree with the official almanac to about a tenth of a minute of arc for the Sun and planets, within an arc-minute or two for the navigational stars, and to about an arc-minute for the Moon. It is excellent for learning, practice and planning. It is not a certified navigational publication, however, and a phone or website can fail. Anyone navigating at sea must carry the official Nautical Almanac and the proper tables and not rely on a website.
Keep exploring
How Celestial Navigation Works
The interactive companion to this tool: the circle of equal altitude, the fix, and the intercept method.
LiveToday in the Sky
Where the Sun, Moon and planets are right now, and the next events, from your location.
CalculatorSunrise & Sunset
Rise, set and twilight times, the other half of the daily-page tables.
InteractiveThe 88 Constellations
The star charts behind the navigational stars, drawn from real positions.