bearing calculator

What Is a Bearing?

A bearing is a direction, measured clockwise from north, usually from 0° to 360°. It is commonly used in navigation, surveying, hiking, aviation, and mapping. For example, a bearing of 90° points due east, 180° points due south, and 270° points due west.

When you enter two coordinates in this tool, the calculator returns the initial bearing from the first point to the second point along a great-circle route on Earth.

How This Bearing Calculator Works

Inputs

• Start latitude/longitude: your origin location.
• Destination latitude/longitude: where you want to go.
• Format: decimal degrees (negative for south and west).

Outputs

• Initial true bearing in decimal degrees.
• Bearing in DMS (degrees, minutes, seconds).
• Compass direction (N, NE, E, etc.).
• Reciprocal bearing for the opposite direction.
• Great-circle distance in kilometers and miles.

Formula Used

The calculator uses the standard spherical trigonometry formula for initial bearing:

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

Where φ is latitude, λ is longitude, and all trig calculations are done in radians. The final angle is normalized to a 0° to 360° range.

True, Magnetic, and Grid Bearing

True Bearing

Measured from true north (geographic north). This calculator returns a true bearing.

Magnetic Bearing

Measured from magnetic north (what a compass points to). To convert from true to magnetic bearing, apply local magnetic declination.

Grid Bearing

Used on map grid systems (like UTM). Depending on your map projection, grid north can differ slightly from true north.

Example Use Case

Suppose you want to travel from New York City (40.7128, -74.0060) to Los Angeles (34.0522, -118.2437). Enter those coordinates and calculate. You will get the initial heading needed at departure, plus a reciprocal direction and an estimated great-circle distance.

Common Input Mistakes

• Swapping latitude and longitude values.
• Forgetting negative signs for west longitudes or south latitudes.
• Using degrees-minutes-seconds directly instead of decimal degrees.
• Expecting magnetic bearing without applying declination.

When a Bearing Calculator Is Useful

• Planning long-distance routes in GIS or mapping software.
• Creating waypoints for outdoor navigation.
• Checking directional alignment in surveying tasks.
• Teaching navigation fundamentals in schools and training programs.

Quick FAQ

Is this the same as direction of travel the whole time?

Not exactly. On a curved Earth, your heading can change along a great-circle path. The calculator gives the initial heading at the starting point.

Can I use this for short distances?

Yes. It works for short and long distances, though at very short ranges small coordinate errors can cause noticeable bearing changes.

Does this account for terrain or roads?

No. It is a geometric calculation over Earth’s surface, not a route planner.