Bearing Degrees Calculator

How to Use the Bearing Degrees Calculator

Our bearing degrees calculator provides a simple way to determine the compass bearing between two points. Follow these steps to use the calculator:

1. Enter the latitude and longitude of the starting point in decimal degrees.
2. Enter the latitude and longitude of the destination point in decimal degrees.
3. Click the "Calculate" button to compute the bearing.
4. Review the result, which includes the bearing in degrees and a compass direction.
5. Use the optional chart to visualize the bearing.

The calculator uses the standard trigonometric formula for bearing calculations. You can also find the formula and a worked example below.

What Is a Bearing Degree?

A bearing degree is a measurement of the angle between a reference direction (typically north) and the line connecting two points. Bearings are used in navigation, surveying, and mapping to indicate the direction from one point to another.

Bearings are typically measured in degrees clockwise from north. For example, a bearing of 90° means east, 180° means south, and 270° means west.

How to Calculate Bearing Degrees

Calculating bearing degrees involves using trigonometric functions to determine the angle between two points on a spherical Earth model. Here's a step-by-step guide:

1. Convert the latitude and longitude of both points from degrees to radians.
2. Calculate the differences in longitude (Δλ) and latitude (Δφ).
3. Use the following formula to compute the bearing (θ):

Where:

• φ₁ is the latitude of the starting point in radians
• φ₂ is the latitude of the destination point in radians
• Δλ is the difference in longitude between the two points in radians
• θ is the bearing in radians

Convert the resulting bearing from radians to degrees and adjust to a compass bearing by taking modulo 360 and converting to a positive value if necessary.

Bearing Degrees Formula

The formula for calculating the bearing between two points on a sphere is:

Where:

• θ is the bearing in radians
• φ₁ is the latitude of the starting point in radians
• φ₂ is the latitude of the destination point in radians
• Δλ is the difference in longitude between the two points in radians

To convert the result to degrees and adjust to a compass bearing:

Worked Example

Let's calculate the bearing between two points:

• Starting point: Latitude 40.7128° N, Longitude 74.0060° W
• Destination point: Latitude 34.0522° N, Longitude 118.2437° W

1. Convert coordinates to radians:
   • φ₁ = 40.7128° × π/180 ≈ 0.7107 radians
   • φ₂ = 34.0522° × π/180 ≈ 0.5943 radians
   • Δλ = (74.0060° - 118.2437°) × π/180 ≈ -2.8066 radians
2. Apply the bearing formula:
   θ = atan2(sin(-2.8066) * cos(0.5943), cos(0.7107) * sin(0.5943) - sin(0.7107) * cos(0.5943) * cos(-2.8066))
3. Calculate the numerator and denominator:
   • Numerator: sin(-2.8066) * cos(0.5943) ≈ -0.3826 * 0.8207 ≈ -0.3147
   • Denominator: cos(0.7107) * sin(0.5943) - sin(0.7107) * cos(0.5943) * cos(-2.8066) ≈ 0.7547 * 0.5585 - 0.6561 * 0.8207 * 0.1556 ≈ 0.4209 - 0.8669 ≈ -0.4460
4. Compute θ:
   θ ≈ atan2(-0.3147, -0.4460) ≈ 2.04 radians
5. Convert to degrees and adjust:
   bearing = (2.04 * 180/π + 360) % 360 ≈ (116.06 + 360) % 360 ≈ 116.06°

The bearing from New York to Los Angeles is approximately 116.06°.