Compass Bearing Calculator
Calculate the compass bearing and great-circle distance between two coordinates, with true, magnetic, final and back bearings.
Bearing between two coordinates
Decimal degrees (50.06639) or DMS (50°03'59"N) — updates as you type.
Fill in all four coordinates to see the bearing.
- Initial bearing (true)
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- Compass point
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- In degrees, minutes, seconds
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- Quadrant bearing
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- Final bearing (on arrival)
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- Back bearing (return)
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- Magnetic bearing
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- Great-circle distance
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Degrees to compass point
Already have a bearing? Convert it to a compass point, a quadrant bearing and mils.
- Compass point
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- Quadrant bearing
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- Back bearing
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- NATO mils
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How it works
The initial bearing (also called the forward azimuth) is the great-circle course you steer the
moment you leave the first point. It uses the standard spherical formula
θ = atan2( sin Δλ · cos φ₂ , cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos Δλ ), normalised
to 0–360°. Because a great circle constantly changes its compass direction, the calculator also
shows the final bearing — the course you are on when you arrive, computed as the reverse
bearing from the destination plus 180°. The back bearing is simply the initial bearing plus
180°, the direction you would sight to look back at where you started.
Distance uses the haversine formula with a mean Earth radius of R = 6371 km, so results are
spherical approximations and can differ from ellipsoidal (WGS-84 / Vincenty) figures by up to
about 0.5%. All bearings are true bearings, measured clockwise from true north. Enter your
local magnetic declination (east positive, west negative) and the magnetic bearing — what your
handheld compass will actually read — is shown too, using
magnetic = true − declination. The compass point uses the 16-point rose, with each
point covering 22.5°: 9° is N, 247.5° is WSW.
Everything is arithmetic done in your browser with plain JavaScript. No coordinates leave your device, there is no sign-up, no tracking of what you enter and no ads.
Frequently asked questions
How is the compass bearing between two coordinates calculated?
It uses the spherical forward-azimuth formula θ = atan2(sin Δλ · cos φ₂, cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos Δλ), normalised to 0–360°. Distance uses the haversine formula with a mean Earth radius of 6371 km. For Land's End to John o' Groats that gives an initial bearing of 009°07′11″ over 968.9 km.
Why do the initial and final bearings differ?
A great circle is the shortest path over a sphere, but its compass direction changes as you travel. The initial bearing is the course you set on departure; the final bearing is the course you are on when you arrive. The back bearing is different again — it is simply the initial bearing plus 180°, the direction you sight to look back at your start point.
What is the difference between a true and a magnetic bearing?
A true bearing is measured clockwise from true north; a magnetic bearing is what a handheld compass reads, measured from magnetic north. They differ by the local magnetic declination. Enter your declination (east positive, west negative) and the calculator applies magnetic = true − declination for you.