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Spherical Coordinate Distance

Find a great-circle distance from decimal degrees or degrees, minutes and seconds.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

The worked inputs demonstrate the selected model; change a known value or leave an editable unknown empty for a supported inverse.

distance=2R asin(√h), R=6,371,000 m

Worked example

Enter these known values and leave the other values blank.

Coordinates in:
Degrees
Latitude
0 deg
Longitude
0 deg
Latitude
0 deg
Longitude
90 deg
Distance
10008 km

Assumptions and limitations

  • This is a spherical-Earth distance using a fixed 6371 km radius, not an ellipsoidal geodesic, route length or elevation-aware measurement.
  • Latitude lies in −90…90 degrees and longitude in −180…180; the shortest central angle is used.

Common questions

What does this model assume?

This is a spherical-Earth distance using a fixed 6371 km radius, not an ellipsoidal geodesic, route length or elevation-aware measurement. Latitude lies in −90…90 degrees and longitude in −180…180; the shortest central angle is used.

How do units and inverse calculations work?

Choose compatible units for each quantity. The model converts quantities internally; supported editable fields can be solved from sufficient independent known values. Display rounding does not change the underlying value.

References

The shortest spherical angle is evaluated with atan2 of the cross-product magnitude and dot product of unit position vectors. This is algebraically the same 6371 km sphere model, while avoiding the captured inverse-haversine loss of roughly half the working digits at antipodes. Both decimal-degree and DMS modes use the stable formula.

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