Azimuth Calculator

How to use this azimuth calculator

What this calculator does

This calculator turns two geographic coordinate pairs into two navigation quantities: the Azimuth, or initial clockwise bearing from true north at the starting point, and the Distance, measured along the shortest great-circle path on a spherical Earth. It is useful for quick orientation, route checks, field planning, map work, and educational geodesy. It does not account for roads, terrain, magnetic declination, local obstructions, or the small ellipsoidal corrections used by high-precision geodetic software. For survey-grade work, compare the result with a geodetic inverse calculation such as the National Geodetic Survey inverse-position documentation.

When to use it

• Estimate the direction and straight-over-Earth distance from one city, waypoint, or field location to another.
• Check whether a mapped destination lies generally north, southeast, west, or another compass direction from a known point.
• Validate coordinate data before transferring a bearing into a navigation or GIS workflow.
• Explore how latitude and longitude changes affect initial bearing and great-circle distance.

How to calculate

The calculator opens with a complete demonstration from London to Rio de Janeiro, so the results and a validated example Excel workbook are available immediately. To calculate another route:

1. Replace the Starting point Latitude and Starting point Longitude with your origin coordinates.
2. Replace the Final point Latitude and Final point Longitude with your destination coordinates.
3. Read the live Azimuth and Distance. No Calculate button is required; valid edits update the model automatically.
4. Select Download Excel to export the current, validated coordinates and results as a real XLSX workbook. Select Reset to clear the demonstration and all calculated state. After Reset, Excel export stays disabled until all four required coordinates are valid again.

Input guide

Starting point Latitude is required decimal degrees from – 90 to 90. Positive values are north of the equator and negative values are south. A realistic example is 51.50. Increasing latitude moves the origin north and can change both bearing and distance. Enter a period as the decimal separator; a value such as “51,5” is rejected rather than silently reinterpreted.

Starting point Longitude is required decimal degrees from – 180 to 180. Positive values are east of the prime meridian and negative values are west. The demonstration uses 0. Changing longitude rotates the origin around Earth and therefore changes the east-west component of the bearing and usually the distance.

Final point Latitude follows the same – 90 to 90 decimal-degree rule and is also required. The demonstration uses – 22.97. A common mistake is to omit the minus sign for a southern latitude, which places the destination in the opposite hemisphere.

Final point Longitude is required from – 180 to 180 decimal degrees. The demonstration uses – 43.18. West longitudes are negative in this calculator. The U.S. Geological Survey documents the standard decimal-degree ranges of latitude – 90 to 90 and longitude – 180 to 180, matching the validation used here.

Output guide

Azimuth is an initial bearing in degrees from 0° up to but not including 360°, measured clockwise from true north. Approximately 0° means north, 90° east, 180° south, and 270° west. It is an estimate from the spherical great-circle model and should not be treated as a magnetic-compass heading unless magnetic declination is handled separately. Distance is the great-circle surface distance in kilometers. Zero distance occurs only when both coordinate pairs are the same; in that case an azimuth is geometrically undefined, so the calculator reports a clear same-point state instead of inventing a direction.

Worked example

With the startup values 51.50°, 0° and – 22.97°, – 43.18°, the latitude change is – 74.47° and the longitude change is – 43.18°. The Haversine calculation gives a central angular separation of about 1.4580 radians. Multiplying by the spherical Earth radius used here, 6,371 km, produces 9,289.05 km. The initial-bearing equation gives – 140.65° before normalization; adding 360° produces the displayed 219.35°, which points generally southwest. These same startup coordinates and canonical numeric results are used by the on-screen display and the first-open XLSX export.

Learn more

Azimuth and distance are part of geodesy, the science of measuring and understanding Earth's geometry. NOAA's National Geodetic Survey offers a concise explanation of what geodesy measures and why coordinates need a consistent reference framework. This calculator deliberately uses the simpler spherical approximation, which is appropriate for quick estimates but not a replacement for precision ellipsoidal geodesics.