Distance Calculator
Calculate distances between GPS coordinates with high precision
Calculation Results
0.000 km
0.000 km
What Is Distance Calculation and Why It Matters
When we talk about the distance between two places on Earth, we're not usually talking about a straight line through the planet. Instead, we mean the shortest path along the surface. This path is known as a great-circle or geodesic distance. It's the fundamental concept behind flight paths and maritime routes, representing the most efficient way to travel on a sphere.
This calculator specializes in these types of calculations, providing tools for various applications:
- Aviation & Maritime: Pilots and sailors use great-circle routes to save fuel and time on long journeys.
- GIS (Geographic Information Systems): Analysts use these distances to understand spatial relationships, proximity, and network analysis.
- Logistics & Planning: Estimating travel distances for supply chains or event planning.
- Education & Hobbies: Understanding geography, planning hikes, or tracking personal travel data.
It's crucial to distinguish this from driving distance, which follows road networks and is always longer than the great-circle distance.
How We Calculate Distances — Haversine and Alternatives
Because the Earth is a sphere (or more accurately, an oblate spheroid), we can't use simple planar geometry like the Pythagorean theorem for long distances. We need spherical trigonometry.
The Haversine Formula (Default)
The Haversine formula is a widely used and reliable method for calculating great-circle distance. It's particularly well-conditioned for small distances and avoids issues with floating-point precision that can affect other formulas. The core equations are:
a = sin²(Δφ/2) + cos φ₁ ⋅ cos φ₂ ⋅ sin²(Δλ/2)
c = 2 ⋅ atan2(√a, √(1−a))
d = R ⋅ c
Here, φ is latitude, λ is longitude, Δ represents the difference, R is the Earth's radius (approx. 6,371 km), and d is the final distance. This calculator shows you the step-by-step substitution for full transparency.
Spherical Law of Cosines
This is a simpler formula but can suffer from rounding errors at small distances. It's often used for its mathematical elegance:
d = R ⋅ acos( sin φ₁ ⋅ sin φ₂ + cos φ₁ ⋅ cos φ₂ ⋅ cos(Δλ) )
Equirectangular Approximation
For very short distances where the Earth's curvature is negligible, a faster approximation can be used. It essentially treats the latitude/longitude grid as a plane. It's less accurate but computationally cheaper.
Vincenty's Formulae (High Precision)
For geodetic-level accuracy, Vincenty's formulae are used. They model the Earth as an ellipsoid, accounting for its equatorial bulge. This adds significant complexity for a tiny increase in accuracy (up to 0.5%) that is unnecessary for most non-scientific applications.
Entering Coordinates — Tips and Common Mistakes
Correctly formatting your coordinates is the most important step. Here are the two primary formats this tool accepts:
- Decimal Degrees (DD): This is the most common format used in digital mapping. Positive values for North latitude and East longitude; negative values for South and West. Example:
51.5074, -0.1278for London. - Degrees, Minutes, Seconds (DMS): The traditional format. You can use various separators. Examples:
51° 30' 26" N,0 7 40 W, or-0 7 40. The tool's parser is flexible.
Common Mistakes:
- Switching Latitude and Longitude: Always remember: Latitude (North/South) comes first, then Longitude (East/West).
- Incorrect Signs: Forgetting the negative sign for Southern latitudes or Western longitudes is a frequent error.
- Out of Range: Latitude must be between -90 and +90. Longitude must be between -180 and +180.
Polyline and Path Distances
A polyline is a series of connected straight-line segments defined by ordered points. This tool's "Polyline Path" mode calculates the total length of such a path by summing the great-circle distances of each individual segment. This is useful for:
- Measuring the length of a hiking trail or flight path with multiple waypoints.
- Calculating the perimeter of a geographic area by providing the vertices and selecting the "closed loop" option.
The results table provides a breakdown of each segment's length, the cumulative distance at each point, and the bearing from one point to the next. This allows for detailed analysis of the path's characteristics.
Frequently Asked Questions
- 1. What Earth radius does the calculator use?
- By default, it uses the WGS-84 mean radius of 6371.0088 kilometers, which is a standard for many applications. Other radii can be selected in advanced options when available.
- 2. What is a bearing?
- The initial bearing (or forward azimuth) is the compass direction you would travel from the starting point to the destination, measured in degrees from true North (0° to 360°).
- 3. Can I upload a file with coordinates?
- Yes, the Polyline mode supports client-side parsing of simple CSV (lat,lon) or GPX files. The processing is done in your browser, and no data is sent to a server.
- 4. Why is my calculated distance different from Google Maps?
- This calculator provides the shortest possible path on the Earth's surface (a great circle). Google Maps and other services provide driving, walking, or transit distances that follow actual routes and are almost always longer.
- 5. How does the map visualizer work without an internet connection?
- The visualizer is not a true map with tiles. It's an SVG (Scalable Vector Graphic) that uses a simple mathematical projection (Equirectangular) to plot your coordinates onto a 2D plane. It's a visual aid, not a navigational chart.
- 6. What is "Rhumb Line" distance?
- A rhumb line is a path of constant bearing. On a Mercator projection map, it's a straight line, but it's not the shortest distance on a sphere (except along the equator or meridians). Great circles are shorter but require continuous bearing adjustments. This tool focuses on the shortest (great-circle) path.
- 7. Is my data saved?
- No. All calculations are performed on your device. The tool does not use cookies or servers to store your input. Your privacy is fully respected.
- 8. Can I use this for legal or land surveying purposes?
- Absolutely not. Land surveying requires specialized, high-precision equipment and ellipsoidal models (like Vincenty's) to account for the Earth's exact shape and local variations. This tool is not accurate enough for such purposes.
