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Great-circle bearing and distance calculator

The reverse bearing is not “plus 180”

On a plane the reverse direction is the forward one plus a hundred and eighty. On a sphere the meridians converge towards the poles, so the same arc leaves its two ends at different angles. On a transatlantic path the difference reaches twenty degrees and more — enough to miss with a narrow beam.

distance
The long path is the same arc round the other side of the globe; on the low bands it is often the working one
What to enter
Your locator
The other station's locator
Short path
Distance
Bearing to the other station
Reverse bearing (from their end)
Long path
Distance
Bearing

📐 The formulas​

Distance (haversine):

a = sin²(Δφ/2) + cos φ₁ · cos φ₂ · sin²(Δλ/2)
d = 2R · asin(√a)

Bearing:

θ = atan2( sin Δλ · cos φ₂,
           cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos Δλ )

The reverse bearing is computed with the same formula and the points swapped — not as θ + 180°.

Long path:

distance = 40030.2 − d       bearing = θ + 180°

Check points:​

  • (0°, 0°) → (0°, 1°): 111.195 km, bearing 90°
  • (0°, 0°) → (0°, 90°): 10,007.5 km
  • Kyiv → London: 2133 km, bearing 285.0°, reverse 81.0°
Where this calculator stops:
  • The Earth is taken as a sphere of radius 6371 km. Against an ellipsoid (Vincenty's formula) the difference is up to 0.5 %, which is immaterial for radio
  • A locator names a cell, so the distance is only accurate to its size: at six characters, a few kilometres
  • For points close together the bearing becomes unstable, and the calculator warns you
  • A real radio path does not follow the great circle: the ionosphere bends the signal, especially on long paths

🎯 In practice​

  • Aiming a directional antenna at the other station.
  • Choosing between short and long path on the low bands.
  • Working out distance for VHF contests, where the score depends on kilometres.
Practical advice:
  1. With a narrow beam (a 20 m Yagi) a few degrees already shows — use the bearing, not “roughly westwards”.
  2. On 160 and 80 metres the long path often works better than the short one, especially along the grey line.
  3. The reverse bearing tells you where the other station's antenna is pointing.
  4. On paths over the pole the bearing can look strange — check yourself on a globe, not on a flat map.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Great-circle bearing and distance calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/others/great_circle (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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