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.
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
⚠️ 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)
- 1Enter — sensible defaults are pre-filled so you see a worked result immediately.
- 2Read the live results: .
- 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.
- 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.
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