Distance Calculator

Distance Calculator: 2D, 3D & Great-Circle Distance

(0, 0) to (3, 4) is 5 units in 2D; NYC (40.71° N, 74.01° W) to London (51.51° N, 0.13° W) is about 5,570 km great-circle. Flat Pythagorean or spherical Haversine, with map pins in Geographic mode.

How distance is computed

Flat coordinates use Pythagoras and inherit your axis units. Lat/lon uses Haversine on a sphere with R = 6,371 km, and the map draws the great-circle arc between pins.

2D worked example:

Point 1: (0, 0), Point 2: (3, 4) →
d = √(3² + 4²) = 5
Same units as x and y.
Geographic worked example:

40.7128° N, 74.0060° W (New York) to 51.5074° N, 0.1278° W (London) is about 5,570 km Haversine. Tokyo to Los Angeles works out near 8,815 km on the same model. The curve looks longer on a Mercator map because flat maps stretch high latitudes.
What this misses:

Road or driving distance, which needs a routing service. Ellipsoidal Vincenty/WGS84 geodesics, usually within ~0.5% of this sphere model on long routes. Geographic mode returns the surface arc, not the chord through the planet.
Also on screen:

DMS and decimal lat/lon stay in sync with draggable markers; all math runs locally in your browser.

Euclidean vs great-circle

Flat coordinates use the Pythagorean theorem. Lat/lon uses Haversine on a sphere (R = 6,371 km).

2D:

d = √[(x₂−x₁)² + (y₂−y₁)²]
Example: Δx = 3, Δy = 4 → d = 5.
3D:

Add (z₂−z₁)² under the radical. Same units as your axes.
Geographic (Haversine):

Shortest surface arc, not a straight line through the planet.
d = 2R × atan2(√a, √(1−a))
with
a = sin²(Δφ/2) + cos φ₁ cos φ₂ sin²(Δλ/2)
(φ, λ in radians). Crow-flies city pairs match flight planning at this precision; survey work may need an ellipsoid solver.

Coordinates and units

Cartesian: right-handed x, y, z; distance inherits those units. Geographic: latitude ±90° (N/S), longitude ±180° (E/W), decimal degrees or DMS. Sphere radius

R = 6,371 km

then convert display to miles or nautical miles as needed.

Distance Calculator FAQ

What is the 3D distance formula?

The 3D distance formula is the Euclidean distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂):

d = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²]

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) space, what you get with the 2D or 3D formula. Geodesic distance (great-circle distance) is the shortest path along the Earth’s surface between two points, an 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 “latitude longitude [city name]” 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.

Points & mode

Current calculation

Using this calculator

Formulas used

Three modes

Choosing a mode

Flat (x, y) or (x, y, z)

Two places on Earth

Using the map

Crow-flies, not driving