ToolJoltTools

Compass Bearing Calculator (Point to Point)

Initial and final bearings between two coordinates — why they differ on a round Earth, plus the compass-rose name of your heading.

0
Initial bearing (°)
0
Final bearing on arrival (°)
0
Compass point
0
Distance (km)

On a sphere, a 'straight line' continuously changes its compass direction: London→New York departs at 288° but arrives heading 232°. Only routes due north-south (or along the equator) keep one bearing — every other constant-bearing path is a rhumb line, longer by design.

Formula

θ = atan2( sinΔλ·cosφ₂, cosφ₁·sinφ₂ − sinφ₁·cosφ₂·cosΔλ ); final bearing = reverse(back-bearing)
References: Movable Type Scripts / Veness, great-circle formulae (Haversine, bearings); Bowditch, The American Practical Navigator (NGA Pub. 9)

⚠️ Great-circle estimates on a spherical Earth (±0.5% vs ellipsoidal) — for surveying, legal boundaries and navigation use geodetic-grade tools and official datums.

Initial and final bearings between two coordinates — why they differ on a round Earth, plus the compass-rose name of your heading.

About Compass Bearing Calculator (Point to Point)

Ask 'which direction is New York from London' and the honest answer is a moving target: the shortest path leaves Heathrow pointing 288° — almost northwest — and lands at JFK pointing 232°, southwest, having swung 56 degrees without ever turning. This calculator computes initial and final great-circle bearings between any two points, names the compass point, and explains the rhumb-line alternative that trades distance for the comfort of a single heading.

How to use Compass Bearing Calculator (Point to Point)

  1. 1Enter — sensible defaults are pre-filled so you see a worked result immediately.
  2. 2Read the live results: .
  3. 3Check the "With your numbers" line to see the formula θ = atan2( sinΔλ·cosφ₂, cosφ₁·sinφ₂ − sinφ₁·cosφ₂·cosΔλ ); final bearing = reverse(back-bearing) substituted step by step.
  4. 4Adjust inputs (or flip the unit toggle) until the scenario matches yours, then copy or share the result.

Why use Compass Bearing Calculator (Point to Point)?

  • Instant, free and private — every calculation runs in your browser, nothing is uploaded
  • Built on the published formula θ = atan2( sinΔλ·cosφ₂, cosφ₁·sinφ₂ − sinφ₁·cosφ₂·cosΔλ ); final bearing = reverse(back-bearing) with sources cited on the page
  • On a sphere, a 'straight line' continuously changes its compass direction: London→New York departs at 288° but arrives heading 232°. Only routes due north-south (or along the equator) keep one bearing — every other constant-bearing path is a rhumb line, longer by design.
  • Switch units, tweak any input and watch every result update live

Frequently asked questions

Why does the bearing change along a 'straight' route?+

Because meridians converge: your heading is measured against local north, and local north's direction shifts as you move across the globe. A great circle is straight in the geodesic sense (no turning on the surface), but the reference grid rotates beneath it. The extreme case makes it obvious: the shortest path between two points at the same high latitude arcs over the pole — departing northeast-ish and arriving southeast-ish, having pointed 'north' in the middle.

What's the difference between great-circle and rhumb-line navigation?+

A rhumb line (loxodrome) holds one constant bearing the whole way — it spirals on the globe but draws straight on a Mercator chart, which is exactly why Mercator invented the projection in 1569. The price: it's longer — London→New York costs ~150 extra km by rhumb. Classic practice splits the difference: compute the great circle, divide into segments, sail/fly each segment as a short rhumb with periodic heading updates. GPS-era autopilots just track the geodesic continuously.

Is this bearing true or magnetic?+

True — referenced to the geographic pole, like all chart work. Your compass reads magnetic, offset by local declination (variation): −15° to +20° across the continental US, 0–25° across India and Europe, changing slowly as the magnetic pole wanders. Convert with: magnetic = true − declination (east declination subtracts). Look up your current local value (NOAA's WMM calculator); aviation and marine charts print it. Forgetting the conversion puts you kilometres off after an hour's travel.

How do I get the bearing for the return trip?+

Not by adding 180° to your outbound INITIAL bearing — that's the classic spherical-trig trap. The correct return initial bearing equals this tool's FINAL bearing reversed: if you arrive in New York heading 232°, you depart back on 52°. The asymmetry vanishes only for short hops (under ~100 km the difference is a fraction of a degree) and pure north-south routes. Swap the points in this calculator and it handles the bookkeeping for you.

Related tools

Related Field tools

Sponsored