KnotWise includes five celestial navigation calculators covering full sight reduction for the sun and stars, latitude from the meridian altitude of the sun, compass checking against the sun's azimuth and estimated position from multiple position lines. All five run fully offline, use a built-in astronomical ephemeris and are available on every plan — including Free.
How the celestial calculators work
All five calculators share the same astronomical foundation: a built-in ephemeris computes Greenwich Hour Angle (GHA) and declination for the sun and the 57 navigational stars, accurate to better than 0.1 arc minute for any date within 50 years of J2000.0. No internet connection is required.
Sight reduction uses the St. Hilaire intercept method. You enter a sextant altitude, an assumed position and a UTC time; the calculator runs the standard correction chain and computes intercept and azimuth.
Every input is manual — sextant readings, index error, height of eye, limb selection, optional pressure and temperature. The calculator makes no assumptions about your data source. All formulas and intermediate values are shown on screen.
Sun Sight Reduction
The standard daytime sight. You sight the sun's lower or upper limb with a sextant, record the altitude and UTC time, and the calculator reduces the sight to a position line.
| Input | Source |
|---|---|
| Date and UTC time | Chronometer or GPS time signal |
| Sextant altitude (Hs) | Sextant reading |
| Index error (IE) | Sextant check at sea horizon |
| Height of eye | Measured at the observation position |
| Limb (lower / upper) | Your choice at the moment of observation |
| Assumed position (AP) | DR position or whole-degree AP |
| Pressure and temperature (optional) | Barometer and thermometer for non-standard atmosphere |
The calculator applies the full correction chain — index error, dip, refraction (with optional pressure and temperature correction), semi-diameter — and computes the observed altitude (Ho). It then runs the intercept against your assumed position, giving Hc, azimuth (Zn) and intercept (a) in nautical miles toward or away.
Star Sight Reduction
The procedure is identical to the sun sight, with one difference: you select the star from a dropdown. The calculator supplies SHA and declination from its internal table of 57 navigational stars (HO 249), precession-corrected to the current epoch. GHA Aries is computed from date and time.
No semi-diameter or parallax correction applies — stars are point sources at effectively infinite distance.
Best results come from morning and evening twilight, when the horizon is sharp but stars are visible. Take three or more stars at well-distributed azimuths for a strong fix.
Noon Sight
The simplest and most robust method in celestial navigation. At the moment of meridian passage (local apparent noon), the sun is due north or south and at its maximum altitude for the day. The maximum altitude gives latitude directly — no intercept, no assumed position required.
| Input | Notes |
|---|---|
| Date | For declination lookup |
| Meridian altitude (Hm) | Maximum observed altitude after corrections |
| Observer hemisphere | North or south |
| Declination of the sun | Computed automatically, can be overridden manually |
Practical tip: take several altitudes during the 10 to 15 minutes before estimated meridian passage. Use the highest reading — that is your meridian altitude. The calculator handles all four hemisphere cases (observer and sun on the same or opposite sides of the equator).
Compass Check via Azimuth
A practical way to verify your compass at sea using the sun. Take a compass bearing to the sun at a known position and time. The calculator computes the sun's true azimuth from the ephemeris, applies your chart variation to derive the expected magnetic bearing, and reports the total compass error against your observed bearing.
| Input | Source |
|---|---|
| Date and UTC time | Chronometer or GPS time signal |
| Position | GPS or DR |
| Local variation | Chart, current epoch |
| Observed compass bearing | Hand bearing compass or steering compass |
The calculator reports the total compass error — combined variation and deviation — as a single value with direction (high or low). Compare this against the variation alone to isolate the deviation contribution.
Most accurate when the sun is low — within roughly an hour of sunrise or sunset. High sun altitudes amplify small errors in azimuth calculation.
Estimated Position
Assembles two to four position lines into an estimated position. Each line is defined by its assumed position, intercept and azimuth — the outputs of the preceding sight reductions.
The calculator plots all position lines on an SVG diagram and marks the fix. With three or more lines, it shows the cocked hat and marks its centroid as the estimated position.
Three crossing angles tightly grouped indicate a strong fix. A wide cocked hat indicates one or more sights with significant error — review IE, dip, time accuracy and limb selection on the offending sight before discarding.
Shared features across the celestial cluster
All five calculators carry the same UI elements: an expandable formula panel showing the working, a source note specifying that almanac data should come from the Nautical Almanac or Nautisches Jahrbuch, and a coordinate format toggle. Inputs are kept only for the current session — to preserve a sight, use Export PDF or Save to Logbook.
Accuracy and limits
- Ephemeris: Better than 0.1 arc minute for any date within 50 years of J2000.0. Sufficient for practical navigation by any reasonable measure.
- Refraction: Uses the Bennett formula, with optional pressure and temperature correction for non-standard atmosphere. Standard atmosphere assumed when these fields are blank.
- Sea horizon: Dip correction assumes a sea horizon. Sights taken with a mountain horizon or artificial horizon require manual adjustment.
- Limb selection: Lower limb adds the semi-diameter, upper limb subtracts. Errors here propagate as roughly 16 arc minutes to the position line.
- Single sight: Any single sight is a position line, not a fix. Reduce two or more sights at different azimuths and combine with the Estimated Position calculator.
Frequently asked questions
Do I need an internet connection?
No. The astronomical ephemeris is computed locally — no satellite, no data connection, no API call.
Can I use my own almanac data instead?
Yes. Every celestial calculator accepts manual override of GHA and declination. If you prefer to work from Reeds, the Nautisches Jahrbuch or HO 249 directly, enter the values yourself — the calculator skips the internal lookup.
Which navigational stars are supported?
All 57 stars from HO 249, with SHA and declination corrected for current-epoch precession.
Why doesn't my intercept match my GPS position exactly?
A sight reduction produces a position line — a line of position perpendicular to the sun's azimuth at the intercept distance from your assumed position. To produce a fix, you need at least two crossing position lines. Check index error, dip and the accuracy of your sextant chronometer first — small errors propagate quickly. A 4-second time error shifts the position line by approximately 1 nautical mile near the equator.
Can I save a sight reduction to my logbook?
Yes. Save to Logbook creates a new entry pre-filled with the reduction summary — inputs, Ho, Hc, intercept and azimuth — ready for you to add narrative before saving.
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