Distance Calculator: 2D, 3D & Great-Circle Distance
Free distance calculator: distance between two points, distance between two cities. 2D and 3D distance formula, latitude longitude distance, great circle distance. How to calculate distance between two points; air distance between cities; Euclidean and geodesic distance.
What This Calculator Does & Who It's For
Calculator Purpose & Ideal Users
- What You'll Get:2D: Straight-line distanced = โ[(xโโxโ)ยฒ + (yโโyโ)ยฒ]3D: Same with (zโโzโ)ยฒ added under the square root. Geographic: Great-circle (air) distance in km, miles, or nautical miles. Map: In Geographic mode, an interactive map with draggable markers; coordinates stay in sync.
- Ideal Users:Students & geometry: 2D/3D distance formula, coordinate systems. Travel & logistics: Air distance between cities, how far between two cities. Developers & GIS: Distance between two coordinates for apps or scripts. Anyone with two points: Cartesian or decimal degrees.
- Scope & Limits:Geographic mode uses a spherical-Earth formula (R = 6,371 km). Lat ยฑ90ยฐ, lon ยฑ180ยฐ. Accepts decimal degrees or degree-minute-second (DMS). Location data is processed locally; no maps are tracked.
This tool computes the distance between two points in 2D, 3D, or on the Earth (latitude/longitude).
What Is a Distance Calculator? Distance Between Two Points and Two Cities
A distance calculator (or distance between two points calculator) finds the distance between two points or the distance between two cities. In 2D or 3D it uses the Euclidean distance (Pythagorean theorem)โthe straight line distance between two points. For latitude longitude it uses the great circle distance formula (Haversine) for air distance between cities. Use it for the 3D distance formula, distance between two coordinates, or to measure distance on a map. How to calculate distance between two points: enter coordinates (decimal or degree-minute-second) or use the map; result in km, miles, or nautical miles. Free online; all calculations local.
Euclidean vs. Geodesic Distance: Straight Line vs. Great Circle
Euclidean distance is the straight line distance between two points in flat space:
d = โ[(xโโxโ)ยฒ + (yโโyโ)ยฒ]
in 2D, plus (zโโzโ)ยฒ
in 3D. Geodesic distance is the shortest path along the Earthโs surfaceโa curve on a flat map, or great circle distance. For distance between two lat long points, this calculator uses the Haversine formula to compute that arc in km. Driving distance and road routes require a routing service; this tool gives air miles between cities (great-circle) only.Coordinate Systems: Cartesian (X,Y,Z) vs. Latitude Longitude
Cartesian (X, Y, Z): Right-handed axes; result in the same units as your coordinates (meters, feet, etc.). Latitude longitude (decimal degrees): latitude ยฑ90ยฐ (N/S), longitude ยฑ180ยฐ (E/W). Earth distance uses a spherical model:
R = 6,371 km
Great-circle (Haversine) distance in km: d = 2R ร atan2(โa, โ(1โa))
where a = sinยฒ(ฮฯ/2) + cos ฯโ cos ฯโ sinยฒ(ฮฮป/2)
(angles in radians). Enter decimal degrees in Geographic mode or use the map to set points; the tool shows latitude longitude distance in your chosen unit.How to Calculate Air Distance Between Two Cities
To find the shortest distance between two cities (as the crow flies): get the latitude and longitude of both cities (decimal or degree-minute-second), enter them in Geographic mode, or use the map to place markers. The calculator returns the great circle distanceโthe shortest path over the Earthโs surfaceโin km, miles, or nautical miles. Thatโs the same as air distance between cities that flights follow. For driving distance or how far is it between two cities by road, use a routing or maps service; this tool gives straight-line (air) distance only.
Distance Calculator FAQ
? What is the 3D distance formula?
The 3D distance formula is the Euclidean distance between two points (xโ, yโ, zโ) and (xโ, yโ, zโ):
d = โ[(xโโxโ)ยฒ + (yโโyโ)ยฒ + (zโโzโ)ยฒ]
It extends the 2D Pythagorean theorem by adding the z-difference. This distance calculator supports 2D, 3D, and geographic (lat/lon) modes.? How do I find distance on a map?
For distance on a map between two places, use latitude and longitude (decimal degrees). Enter the coordinates of both points, or use the interactive map to click or drag markers. The calculator uses the Haversine formula to compute the great-circle (air) distance. You can display the result in km, miles, or nautical miles.
? Is the Earth a perfect sphere for these calculations?
The Haversine formula assumes a spherical Earth with radius 6,371 km, which is a good approximation for most purposes. For higher precision over long distances, the Vincenty formula uses an ellipsoid (WGS84); the difference is usually under 0.5%. This calculator uses Haversine for clarity and speed; for sub-meter accuracy over thousands of km, use a geodesic library.
? What is the difference between Euclidean and geodesic distance?
Euclidean distance is the straight-line distance in flat (Cartesian) spaceโwhat you get with the 2D or 3D formula. Geodesic distance (great-circle distance) is the shortest path along the Earthโs surface between two pointsโan arc, not a straight line through the globe. For lat/lon, this calculator uses Haversine to compute geodesic distance in km.
? How do I get latitude and longitude for a city?
Search for โlatitude longitude [city name]โ or use a site like OpenStreetMap. Enter coordinates in decimal degrees (e.g. 40.7128, -74.0060 for New York). This calculator also has an interactive map: switch to Geographic mode and drag the markers to set points; the lat/lon fields update automatically.