Azimuth Calculator - Calculate Bearing Between Coordinates

What is an azimuth calculator?

An azimuth calculator finds the compass bearing between two points on Earth's surface, given their latitude and longitude. The result is an angle called the azimuth, measured in degrees clockwise from true north. A bearing of 0° points north, 90° points east, 180° points south, and 270° points west.

Understanding azimuth

Azimuth is a number from 0° to 360° that describes a direction. It works like a clock face laid flat on the ground, with 0°/360° at the top pointing to true north.

Any angle between these points describes an in-between direction. Surveyors, pilots, sailors, and hikers all use azimuth to describe direction of travel without ambiguity.

Azimuth formula

The calculator finds the initial bearing from a starting point to a destination point using the forward azimuth formula from spherical trigonometry. This formula treats Earth as a sphere and accounts for its curvature, which matters over long distances.

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

Where:

• φ₁ = latitude of the starting point, in radians
• φ₂ = latitude of the destination point, in radians
• Δλ = destination longitude minus starting longitude, in radians
• α = the resulting azimuth

The atan2 function returns an angle that can be negative or greater than 360°, so the calculator adds or subtracts 360° as needed until the result falls between 0° and 360°.

How to calculate azimuth: step by step

1. Convert both latitudes and both longitudes from degrees to radians.
2. Find the difference in longitude, Δλ, between the two points.
3. Compute the two parts of the formula, often called y and x.
4. Take the arctangent of y divided by x using atan2, which picks the correct quadrant.
5. Convert the result from radians back to degrees.
6. Add 360° if the result is negative, so it falls between 0° and 360°.

Example: New York City to Los Angeles

• Starting point: 40.7128°N, 74.0060°W (New York City)
• Destination: 34.0522°N, 118.2437°W (Los Angeles)
• Result: about 273.7°, which falls in the West (W) range

Even though Los Angeles lies south and west of New York, the great-circle bearing points slightly north of due west, because the shortest path over a curved Earth is not a straight line on a flat map.

Example: London to Paris

• Starting point: 51.5074°N, 0.1278°W (London)
• Destination: 48.8566°N, 2.3522°E (Paris)
• Result: about 148.1°, which falls in the Southeast (SE) range

Azimuth vs. bearing

The words azimuth and bearing are often used for the same thing, but they differ slightly. Azimuth is always measured clockwise from true north, giving one number from 0° to 360°. A bearing can instead be written as a quadrant bearing, measured from north or south toward east or west, such as N45°E or S30°W. Azimuth avoids this extra step and is the standard used by this calculator.

Uses of azimuth

• Navigation. Ships and aircraft use azimuth to plot great-circle routes, the shortest path between two points on a sphere.
• Land surveying. Surveyors record azimuth to mark property boundaries and build maps.
• Astronomy. Azimuth, paired with a vertical angle called altitude, tells a telescope where to point in the sky.
• Solar energy. Installers use azimuth to orient solar panels toward the sun.
• Hiking and orienteering. Hikers combine an azimuth with a compass and map to walk a straight course without GPS.

True north vs. magnetic north

This calculator returns azimuth measured from true north, the direction toward Earth's geographic North Pole. A magnetic compass instead points toward magnetic north, which sits in a different location and drifts slowly over time. The angle between true north and magnetic north at a given place is called magnetic declination. Anyone using a magnetic compass alongside this calculator's results needs to add or subtract the local declination first.

Frequently asked questions

What is the difference between azimuth and heading? Azimuth is the bearing from one point to another, measured clockwise from true north. Heading is the direction a vehicle or vessel is actually pointed at a given moment, which can drift from the planned azimuth because of wind, current, or steering corrections.

Can I use GPS coordinates in this calculator? Yes. Enter the latitude and longitude in decimal degree format, such as 40.7128 rather than 40°42'46"N. Most GPS devices and map apps can display coordinates in decimal degrees.

What is a back azimuth? A back azimuth is the bearing from the destination point back to the starting point. On a flat map, it equals the forward azimuth plus or minus 180°. On a curved Earth this shortcut is often inaccurate, sometimes by tens of degrees over long distances, because the shortest path curves rather than running straight. For the New York-to-Los Angeles example above, the forward azimuth is 273.7°, but the true back azimuth from Los Angeles to New York is about 65.9°, not the 93.7° that adding 180° would suggest. The exact back azimuth comes from running the same formula with the start and destination points swapped.

Does the calculator adjust for magnetic declination? No. It returns true azimuth, measured from true north. A compass user must apply local magnetic declination separately.

Can azimuth be negative or greater than 360°? No. The calculator normalizes every result to a value between 0° and 360°, wrapping negative angles around by adding 360°.

Why do the starting and destination points need to be different? When the two points are identical, the direction between them is undefined, so the calculator rejects that input rather than showing a meaningless 0°.