Azimuth Calculator (Bearing Between Two Points)

An azimuth is a direction expressed as an angle measured clockwise from north: 0° is north, 90° east, 180° south and 270° west. Surveyors, navigators, hikers with a map and compass, radio amateurs aiming antennas and anyone pointing a satellite dish use azimuths because a single number is more precise than “south-south-west”.

Between two points on Earth the relevant azimuth is the direction of the great circle – the shortest route over the globe. You start out on the initial azimuth, but unless you travel along a meridian or the equator the direction slowly changes, so the calculator also gives the final bearing on arrival and the back azimuth, which is the direction you would set off in to return.

Enter both points as decimal degrees or degrees, minutes and seconds. All bearings are relative to true north; to use them with a magnetic compass, add or subtract the local magnetic declination shown on your map or by NOAA’s declination calculator.

How to use the Azimuth Calculator

1. Coordinates in
2. Starting point – latitude — Positive north, negative south
3. Starting point – longitude — Positive east, negative west
4. Starting point – latitude degrees
5. minutes
6. seconds
7. N / S
8. Starting point – longitude degrees
9. minutes
10. seconds
11. E / W
12. Destination – latitude — Positive north, negative south
13. Destination – longitude — Positive east, negative west
14. Destination – latitude degrees
15. minutes
16. seconds
17. N / S
18. Destination – longitude degrees
19. minutes
20. seconds
21. E / W
22. Earth radius

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

How it works

The calculator converts both points to radians and applies the spherical forward-azimuth formula, normalising the result to 0–360°. The distance comes from the haversine formula and the back azimuth is the azimuth from the destination back to the start.

Worked example

From London (51.5074° N, 0.1278° W) to Rio de Janeiro (22.9068° S, 43.1729° W): Δλ = −43.0451°. The numerator sin Δλ · cos φ₂ = −0.6825 × 0.9211 = −0.6287 and the denominator cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos Δλ = 0.6224 × (−0.3892) − 0.7827 × 0.9211 × 0.7310 = −0.7693. atan2(−0.6287, −0.7693) = −140.7°, i.e. an azimuth of about 219.3°. The great-circle distance is about 9,277 km, and the final bearing on arrival is 205.3°, so the back azimuth is 25.3°.

Compass points and azimuths

Tips

• Use decimal degrees (negative for south and west) or the degrees–minutes–seconds fields.
• Great-circle distances assume a spherical Earth (error under 0.5%).
• Every field has its own unit menu.
• Everything is calculated in your browser.

Common mistakes to avoid

• Swapping latitude and longitude.
• Forgetting the minus sign for southern and western coordinates.
• Mixing magnetic and true north for bearings.

Inputs explained

What each result means

• Compass direction = mod(round([Azimuth (initial bearing)]÷22.5), 16)
• Back azimuth (from the destination to the start) = mod([Final bearing on arrival] + 180, 360)
• Great-circle distance = 2×[Earth radius]×atan2(sqrt([a]), sqrt(1 – [a]))
• Azimuth in NATO mils = [Azimuth (initial bearing)]÷360×6400
• Azimuth in gradians = [Azimuth (initial bearing)]÷0.9