Calculate Distance Between Two Locations

Distance Formulas:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \quad \text{(2D Euclidean)} \] \[ d = 2R \cdot \arcsin\left(\sqrt{\sin^2\left(\frac{\Delta\phi}{2}\right) + \cos\phi_1 \cdot \cos\phi_2 \cdot \sin^2\left(\frac{\Delta\lambda}{2}\right)}\right) \quad \text{(Haversine)} \]

Calculation Type:

Point 1 X-coordinate:

units

Point 1 Y-coordinate:

units

Point 2 X-coordinate:

units

Point 2 Y-coordinate:

units

Distance Result:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Is Distance Calculation?

Distance calculation measures the spatial separation between two points. In mathematics and geography, different formulas are used depending on the coordinate system and the nature of the space (Euclidean plane vs. spherical Earth).

2. How Does The Calculator Work?

The calculator provides two methods for distance calculation:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \quad \text{(2D Euclidean Distance)} \] \[ d = 2R \cdot \arcsin\left(\sqrt{\sin^2\left(\frac{\Delta\phi}{2}\right) + \cos\phi_1 \cdot \cos\phi_2 \cdot \sin^2\left(\frac{\Delta\lambda}{2}\right)}\right) \quad \text{(Haversine Formula)} \]

Where:

2D Euclidean: \( x_1, y_1, x_2, y_2 \) — Cartesian coordinates
Haversine: \( \phi_1, \lambda_1, \phi_2, \lambda_2 \) — Latitude and longitude coordinates
R — Earth's radius (6371 km)
Δφ, Δλ — Differences in latitude and longitude

Explanation: Euclidean distance calculates straight-line distance in flat space, while Haversine calculates great-circle distance on a sphere (Earth).

3. Types Of Distance Calculations

Details:

2D Euclidean Distance: Used for flat surfaces, Cartesian coordinates, and mathematical applications
Great-circle Distance: Used for geographical coordinates, calculates shortest path between two points on a sphere
Manhattan Distance: Sum of absolute differences of coordinates
Minkowski Distance: Generalized distance metric

4. Using The Calculator

Tips:

Select calculation type (2D Euclidean or Geographic)
For 2D: Enter x,y coordinates in any consistent units
For Geographic: Enter latitude (-90° to 90°) and longitude (-180° to 180°) in decimal degrees
Results show distance in appropriate units (units for 2D, km/miles for geographic)

5. Frequently Asked Questions (FAQ)

Q1: When should I use Euclidean vs. Haversine distance?
A: Use Euclidean for flat surfaces and mathematical coordinates. Use Haversine for geographical coordinates on Earth's surface.

Q2: How accurate is the Haversine formula?
A: Haversine is very accurate for most practical purposes, assuming a spherical Earth. For extreme precision, Vincenty's formulae account for Earth's ellipsoidal shape.

Q3: Can I use this for navigation purposes?
A: This provides straight-line (great-circle) distance. Actual travel distance may differ due to routes, terrain, and transportation networks.

Q4: What coordinate systems are supported?
A: 2D Euclidean uses Cartesian coordinates. Geographic uses WGS84 decimal degrees (standard GPS coordinates).

Q5: How do I convert degrees to decimal degrees?
A: Decimal degrees = degrees + (minutes/60) + (seconds/3600). For example: 40°45'30" = 40 + 45/60 + 30/3600 = 40.7583°