Sextant Basics

Part of Cartography & Surveying

How a sextant works, how to build a simplified version, and how to use it to measure celestial altitudes for latitude and navigation.

Why This Matters

The sextant is the instrument that made reliable ocean navigation possible and remains the most precise hand-held tool for measuring angles to celestial bodies. By accurately measuring the altitude of the sun, moon, or stars above the horizon, a navigator can determine latitude to within a few kilometers — enough to safely navigate across seas and between continents.

Even without ocean navigation, the sextant serves important terrestrial purposes. It can measure horizontal angles between distant landmarks (useful in triangulation), determine local time from the sun’s position, and verify compass accuracy. These capabilities make it a high-value instrument for any community aspiring to regional or long-distance coordination.

A sextant is among the most precision-requiring instruments in the surveyor’s toolkit. A good improvised sextant can achieve results within a degree of accuracy — adequate for latitude measurement but not for professional survey work. Understanding its principles is essential for anyone serious about celestial navigation.

Principle of Operation

The sextant’s key insight is using a double reflection to bring an image of a distant celestial body into alignment with the horizon, while simultaneously measuring the angle of the mirror tilt needed to do so.

The geometry: A mirror tilted at angle θ reflects a ray of light through an angle of 2θ. By measuring how much the mirror must be tilted to bring a reflected image into coincidence with a direct-view image, the sextant measures the angle between the two objects in the original scene.

In practice: one mirror (the index mirror) rotates with the measuring arm. A second half-silvered mirror (the horizon glass) is fixed. Light from a star reflects off the index mirror, then off the horizon glass, reaching the eye. Light from the horizon passes directly through the unsilvered half of the horizon glass to the eye. When the star image coincides with the horizon, the angle on the instrument’s scale equals the star’s altitude above the horizon.

Why double reflection matters: It eliminates the error from hand-holding or ship motion. Because both the star image and the horizon pass through the same optical path, small movements of the instrument affect both images equally — the alignment is preserved even if the instrument moves. This allows accurate measurements on a moving ship, which a simple clinometer cannot achieve.

The Sextant’s Parts

Frame: A rigid triangle of metal (brass, aluminum) or dense wood with a curved arc at the base.

Arc: The curved bottom edge of the frame, graduated in degrees (a sextant measures angles up to 120°, though the arc spans 60° of actual arc — hence the name).

Index arm (alidade): A rotating arm pivoting at the arc’s center, with a vernier scale for reading fractions of a degree at the point where it intersects the arc.

Index mirror: A flat mirror mounted perpendicular to the plane of the frame on the index arm. Rotates with the arm.

Horizon glass: A fixed half-silvered mirror at the frame’s front. The left half reflects (to receive the index mirror’s reflected image); the right half is clear (to see the horizon directly).

Telescope or sighting tube: Mounted to view through the horizon glass. Not strictly necessary but greatly improves accuracy.

Shade filters: Dark glass filters for sun observations, preventing eye damage. Critical for solar sights; improvise with smoked glass or multiple layers of film.

Building a Simplified Sextant (Davis Quadrant)

A Davis quadrant (named for its inventor but the principle predates him) uses a different geometry but achieves similar results with simpler construction:

1. Arc: Cut a quarter-circle (90°) of hardwood or metal, 20–30 cm radius. Graduate the arc in degrees.
2. Shadow vane: A flat piece of wood or metal with a small hole, mounted to cast a shadow or project a point of light. Slides along the arc and clamps at readings.
3. Horizon vane: A second vane with a horizontal slit, fixed at the pivot point.
4. Reading: Slide the shadow vane until the sun’s spot of light (projected through a small hole in the shadow vane) falls on the horizon slit in the horizon vane. Read the angle from the arc.

Accuracy: A well-made Davis quadrant is accurate to about 0.5–1.0 degree. Sufficient for latitude measurements but not for longitude by lunar distance.

For stars and planets (which cannot project light through a vane), a cross-staff or astrolabe works better than a Davis quadrant.

Taking a Sight

Solar noon (latitude) sight:

1. Face south (northern hemisphere) or north (southern hemisphere) — the direction of the sun at noon.
2. About 20 minutes before expected solar noon, begin observing. Move the index arm to bring the sun’s reflected image down to the horizon.
3. Watch as the sun climbs: advance the index arm to keep the image at the horizon.
4. At noon, the sun stops climbing and begins to descend. The maximum reading (when the sun appears to touch the horizon and then begins to rise away from it) is the altitude at noon.
5. Note this maximum reading.
6. Latitude = 90° − noon altitude + solar declination for that date.

Star sights:

1. Choose a bright star at reasonable altitude (30°–60° is ideal — too low and atmospheric refraction distorts the reading; too high and matching the horizon is awkward).
2. In twilight, when both stars and the horizon are visible simultaneously, take the sight.
3. Set the arm to the expected altitude, find the star’s reflection, bring it to the horizon, and record the exact reading and time.

Multiple sights: Take at least three sights, discard outliers, and average the remaining readings. A single sight can be significantly off due to horizon distortion, wave action, or timing error.

Corrections Applied to Raw Readings

A raw sextant altitude requires several corrections before giving true altitude:

Index error: Check with the index arm at zero — the horizon should appear as an unbroken line through both halves of the horizon glass. Any visible step is the index error. Add or subtract it from all readings.

Dip of horizon: At sea, the horizon dips below the true horizontal because the observer is elevated above sea level. Correction = −0.97 × √(height above sea level in meters) in arc minutes. On land, use the actual horizon or a spirit level horizon instead.

Refraction: Atmospheric refraction lifts celestial bodies slightly above their true positions, especially near the horizon. Correction is approximately −1/tan(altitude) arc minutes for small angles, reducing to nearly zero above 45°. Tables give exact values; approximate rule: subtract 34’ at 0° altitude, 5’ at 10°, 1’ at 30°.

Semi-diameter (sun and moon): A sextant sight of the sun typically measures the lower limb (bottom edge) to the horizon. The center of the sun is one semi-diameter above the lower limb (about 16’ of arc). Add the semi-diameter to get true altitude of center.

Applying all corrections transforms the observed altitude into the true altitude needed for navigation calculations.

Maintenance and Care

Keep the mirrors flat and clean. Even small scratches on the index mirror introduce angle errors. Clean with a soft dry cloth; never use abrasive materials. Store the instrument cushioned against shock; a single drop can misalign mirrors permanently.

Check calibration (index error) before every use. With careful maintenance, a well-made sextant remains accurate indefinitely.