Nautical Bearing Converter Formula

Understand the math behind the nautical bearing converter. Each variable explained with a worked example.

Use the Nautical Bearing Converter

Formulas Used

Quadrant

nautical_quadrant = value <= 90 ? 1 : (value <= 180 ? 2 : (value <= 270 ? 3 : 4))

Reciprocal Bearing

reciprocal = value < 180 ? value + 180 : value - 180

Magnetic (West US, -14° decl.)

magnetic_approx = value + 14 > 360 ? value + 14 - 360 : value + 14

Variables

VariableDescriptionDefault
valueBearing from North (°)(°)225

How It Works

Nautical Bearings

Three-Figure Bearing

Bearings are always given as three digits measured clockwise from north: 000° to 360°.

Quadrants

| Quadrant | Range | Cardinal | |---|---|---| | Q1 | 000°-090° | N to E | | Q2 | 090°-180° | E to S | | Q3 | 180°-270° | S to W | | Q4 | 270°-360° | W to N |

Reciprocal Bearing

The opposite direction: add 180° (or subtract if over 180°). Used to find the return course.

Worked Example

Analyze bearing 225°.

value = 225
  1. 01Quadrant 3 (180°-270°): Southwest
  2. 02Reciprocal = 225 - 180 = 045° (Northeast)
  3. 03Approximate magnetic (-14° West US) = 239°

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