HesapHanem

Compass Bearing Calculator

Find the bearing and distance from one coordinate to another.

How it is calculated

The tool gives the initial great-circle bearing from point 1 to point 2, plus the distance. With latitudes φ and longitudes λ in decimal degrees (north and east positive), and Δλ = λ₂ − λ₁: y = sin Δλ · cos φ₂, x = cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos Δλ, and bearing = atan2(y, x) normalised to 0–360° clockwise from true north. The result is also named as one of 16 compass points (N, NNE, NE and so on), each 22.5° wide. Distance uses the haversine formula on a spherical Earth of radius 6371 km, shown in kilometres. Because the Earth is treated as a sphere, distances can be off by a fraction of a percent.

Worked example

From Istanbul (41.0082, 28.9784) to Ankara (39.9334, 32.8597): the longitude difference is 3.8813°, and the formulas give an initial bearing of 108.73°. Dividing 108.73 by 22.5 gives 4.83, which rounds to 5, so the compass point is ESE. The great-circle distance is 349.36 km.

Try this example →

Common mistakes

  • Entering south latitudes or west longitudes as positive numbers. West and south need a minus sign.
  • Swapping latitude and longitude. The order is latitude first, then longitude, for each point.
  • Expecting one constant heading for the whole trip. This is the initial bearing; on a long great-circle route the heading changes along the way.
  • Entering degrees, minutes and seconds in the decimal field. Convert them to decimal degrees first.
  • Confusing true north with magnetic north. The bearing is measured from true north, so a compass needs the local magnetic declination applied.

About this calculator

This calculator finds the initial compass bearing and great-circle distance between two latitude/longitude coordinates, using spherical trigonometry (the same formula behind the Haversine distance calculation). The bearing is the compass direction — from 0° (north) to 360° — you'd need to head at the start of the journey to follow the shortest path over the Earth's curved surface.

Pilots, sailors, and navigators use this to plot great-circle routes, since flying or sailing a constant bearing isn't the same as taking the shortest path on a sphere — the true bearing actually changes gradually along a great-circle route. It's also used in orienteering, geocaching, and GIS applications.

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Comments (1)

  • Editorial team

    The way back is not simply the first bearing plus 180 degrees. From London to New York the initial bearing is 288.32 degrees (WNW), but from New York to London it is 51.21 degrees (NE), because a great-circle path curves across the map. The distance, 5,571.49 km both ways, assumes a perfectly spherical Earth, so expect differences of a fraction of a percent from survey-grade figures. Which routes do you plan with it?

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