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Distance Calculator in Degrees

Reviewed by Calculator Editorial Team

This distance calculator in degrees helps you determine the distance between two points on Earth's surface when you know their latitude and longitude coordinates in degrees. The calculation accounts for Earth's curvature and provides results in kilometers or miles.

How to Use the Distance Calculator in Degrees

Using our distance calculator in degrees is straightforward:

  1. Enter the latitude and longitude of the first location in degrees.
  2. Enter the latitude and longitude of the second location in degrees.
  3. Select your preferred unit of measurement (kilometers or miles).
  4. Click "Calculate" to get the distance between the two points.
  5. Review the result and any additional information provided.

The calculator will display the distance between the two points based on the Haversine formula, which is commonly used for geographic distance calculations.

The Formula Explained

The distance between two points on Earth's surface can be calculated using the Haversine formula:

a = sin²(Δφ/2) + cos φ1 ⋅ cos φ2 ⋅ sin²(Δλ/2)

c = 2 ⋅ atan2(√a, √(1−a))

d = R ⋅ c

Where:

  • φ1, φ2 are latitudes of point 1 and point 2 in radians
  • Δφ = φ2 - φ1
  • Δλ = λ2 - λ1 (difference in longitudes in radians)
  • R is Earth's radius (mean radius = 6,371km)

This formula accounts for Earth's curvature and provides an accurate distance measurement between two geographic coordinates.

Assumptions and Limitations

Our distance calculator in degrees makes the following assumptions:

  • Earth is a perfect sphere with a mean radius of 6,371 kilometers.
  • Coordinates are provided in decimal degrees.
  • The calculator uses the Haversine formula for accurate distance calculation.

Note: For very small distances (less than 1km), the difference between the Haversine formula and simpler Euclidean distance calculations becomes negligible.

Worked Examples

Let's look at a practical example to understand how the distance calculator in degrees works.

Example 1: Distance Between New York and London

Coordinates:

  • New York: 40.7128° N, 74.0060° W
  • London: 51.5074° N, 0.1278° W

Using the calculator:

  1. Enter New York coordinates: 40.7128, -74.0060
  2. Enter London coordinates: 51.5074, -0.1278
  3. Select kilometers as the unit
  4. Click "Calculate"

The calculator will display the distance between New York and London as approximately 5,570 kilometers.

Frequently Asked Questions

What is the difference between degrees and radians in distance calculations?

Degrees are commonly used for geographic coordinates, while radians are used in trigonometric calculations. The Haversine formula requires converting degrees to radians before performing the calculations.

Can I use this calculator for air travel distances?

Yes, this calculator provides a good approximation for air travel distances between two points on Earth's surface. However, actual flight paths may vary due to air traffic control and weather conditions.

What is the Earth's mean radius used in the calculation?

The calculator uses a mean Earth radius of 6,371 kilometers, which is the average distance from the Earth's center to its surface.

How accurate is the Haversine formula for distance calculations?

The Haversine formula provides highly accurate results for most practical purposes, especially for distances up to several thousand kilometers.