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

QuadrantRangeCardinal Q1000°-090°N to E Q2090°-180°E to S Q3180°-270°S to W Q4270°-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°

Frequently Asked Questions

What is a reciprocal bearing?

The bearing in the exact opposite direction. If you are heading 225° (SW), the reciprocal is 045° (NE). Used to navigate back the way you came.

What is magnetic declination?

The difference between true north and magnetic north at your location. In the western US it is about 10-15° east (add to true bearing for magnetic). In the eastern US it is 10-20° west (subtract).

Ready to run the numbers?

Open Nautical Bearing Converter