Running Distance Calculator Geo

Haversine Formula:

\[ a = \sin^2(\Delta\phi/2) + \cos\phi_1 \cdot \cos\phi_2 \cdot \sin^2(\Delta\lambda/2) \] \[ c = 2 \cdot \text{atan2}(\sqrt{a}, \sqrt{1-a}) \] \[ \text{Distance} = R \cdot c \]

Latitude 1:

degrees

Longitude 1:

degrees

Latitude 2:

degrees

Longitude 2:

degrees

Distance:

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1. What is the Haversine Formula?

The Haversine formula calculates the great-circle distance between two points on a sphere given their longitudes and latitudes. It's particularly important in navigation and geography for calculating the shortest distance between two points on the Earth's surface.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ a = \sin^2(\Delta\phi/2) + \cos\phi_1 \cdot \cos\phi_2 \cdot \sin^2(\Delta\lambda/2) \] \[ c = 2 \cdot \text{atan2}(\sqrt{a}, \sqrt{1-a}) \] \[ \text{Distance} = R \cdot c \]

Where:

\( \Delta\phi \) — Difference in latitude (radians)
\( \Delta\lambda \) — Difference in longitude (radians)
\( \phi_1, \phi_2 \) — Latitudes of point 1 and point 2 (radians)
\( R \) — Earth's radius (3958.8 miles)

Explanation: The formula accounts for the Earth's spherical shape to calculate the shortest path between two points.

3. Importance of Distance Calculation

Details: Accurate distance calculation is crucial for navigation, route planning, fitness tracking, and various geographical applications. The Haversine formula provides a more accurate result than simple flat-earth approximations.

4. Using the Calculator

Tips: Enter latitude and longitude coordinates in decimal degrees format. Valid ranges: latitude (-90 to 90), longitude (-180 to 180). The calculator returns the distance in miles.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is the Haversine formula?
A: The Haversine formula is very accurate for most practical purposes, typically within 0.5% of the actual great-circle distance.

Q2: Can I use this for running routes?
A: Yes, this calculator is perfect for measuring the straight-line distance between two points on a running route.

Q3: What's the difference between great-circle distance and rhumb line?
A: Great-circle distance is the shortest path between two points on a sphere, while a rhumb line maintains a constant compass bearing.

Q4: How do I convert decimal degrees to degrees-minutes-seconds?
A: Multiply the decimal portion by 60 to get minutes, then multiply the decimal of minutes by 60 to get seconds.

Q5: Can I calculate distance in kilometers instead of miles?
A: To get kilometers, multiply the result by 1.60934, or modify the Earth's radius in the formula to 6371 km.