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Distance off

Distance off a charted object from two bearings and the distance run (the running fix), or from a vertical sextant angle; and turning: rate of turn and wheel-over.

Method

First angle off the bow

Relative bearing, e.g. 45

Second angle off the bow

Same side, e.g. 90

Distance run between

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How it works

Two bearings of one object, a known run between them, steady course, no current: distance at the second bearing = run × sin a₁ / sin(a₂ − a₁), where a₁ and a₂ are the angles off the bow. Special cases: doubling the angle on the bow (e.g. 30° then 60°) gives a distance off equal to the run; the four-point bearing (45° then 90°) gives the distance abeam.

Vertical sextant angle: distance = height / tan(angle), for an object whose base is not below your horizon. Use the charted height corrected for the tide.

Turning: rate of turn (°/min) ≈ 0.955 × speed (kn) / radius (nm). Start the turn (wheel over) a distance of radius × tan(alteration / 2) before the course lines meet, plus the ship's own delay in answering the helm.

For training and cross-checking. Not a substitute for approved navigation equipment, nautical publications and the ship’s own procedures. Calculations run in your browser and nothing you type is stored; a PDF you download is made on our server and not kept.

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