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Bearing Between Coordinates Calculator

Calculate the initial and final bearing between two coordinates.

About Bearing Between Coordinates Calculator

Bearing along a great circle changes continuously, so the initial and final bearings differ. On long east-west routes that change can exceed ninety degrees, which is why navigators recompute rather than hold a constant heading. The reverse bearing is not simply the initial bearing plus 180 degrees except on meridians and the equator, which is a common navigational trap.

Formula

Bearing Between Coordinates

Bearing = atan2(sin Δlon · cos lat₂, cos lat₁ sin lat₂ − sin lat₁ cos lat₂ cos Δlon)

initial bearing
The direction to set off in, which changes along a great circle
back azimuth
The bearing from the destination back to the origin

Worked example

With the default values below, Bearing Between Coordinates Calculator returns Initial Bearing of 288.330. Change any input above and every figure here is recalculated in your browser.

Inputs used

First latitudeaccepts -90–90 degrees
51.5074 degrees
First longitudeaccepts -180–180 degrees
-0.1278 degrees
Second latitudeaccepts -90–90 degrees
40.7128 degrees
Second longitudeaccepts -180–180 degrees
-74.006 degrees

Results

Initial Bearing
288.330 degrees
Final Bearing on Arrival
231.213 degrees
Compass Direction
West
Reverse Bearing
51.213 degrees
Bearing Change Along the Route
-57.117 degrees

Step by step

  1. 1Values used
  2. 2Bearing Between Coordinates
  3. 3Initial Bearing= 288.330 degrees
  4. 4Final Bearing on Arrival= 231.213 degrees
  5. 5Compass Direction= West
  6. 6Reverse Bearing= 51.213 degrees
  7. 7Bearing Change Along the Route= -57.117 degrees

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Bearing Between Coordinates calculated?

Bearing = atan2(sin Δlon · cos lat₂, cos lat₁ sin lat₂ − sin lat₁ cos lat₂ cos Δlon) Bearing along a great circle changes continuously, so the initial and final bearings differ. On long east-west routes that change can exceed ninety degrees, which is why navigators recompute rather than hold a constant heading.

Why does Bearing Between Coordinates matter?

The reverse bearing is not simply the initial bearing plus 180 degrees except on meridians and the equator, which is a common navigational trap.

What values do I need to enter?

This calculator takes 4 inputs: First latitude, First longitude, Second latitude, Second longitude. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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