Distance Calculator

Calculate the distance between two points in 2D, 3D, or geographic coordinates

Euclidean Distance: Straight-line distance between two points on a plane

Point 1 (x₁, y₁)

Point 2 (x₂, y₂)

Formula: d = √[(x₂-x₁)² + (y₂-y₁)²]

How to Use This Distance Calculator

  1. Choose your calculation type: 2D plane, 3D space, or geographic (lat/long)
  2. For 2D: Enter x and y coordinates for both points
  3. For 3D: Add z coordinates for height/depth dimension
  4. For geographic: Enter latitude and longitude of both locations
  5. Click 'Calculate Distance' to see results and midpoint

Example: Distance from New York (40.7128, -74.0060) to London (51.5074, -0.1278): The Haversine formula gives 5,570 km (3,461 miles). This is the great-circle distance - the shortest path on Earth's surface.

Tip: For GPS coordinates, positive latitude = North, negative = South. Positive longitude = East, negative = West.

Why Use a Distance Calculator?

Distance calculation is fundamental to navigation, geometry, game development, and location-based services. Different formulas apply to flat planes versus Earth's curved surface.

  • Calculating travel distances between cities
  • Finding straight-line distance for 'as the crow flies' comparisons
  • Game development: collision detection and pathfinding
  • Real estate: proximity analysis to schools, shops, transit
  • Logistics: route planning and delivery optimization
  • Science: measuring distances in coordinate systems

Understanding Your Results

Results show distance, midpoint, and for geographic calculations, multiple unit conversions.

2D/3D Distance (units)

Meaning: Straight-line Euclidean distance

Action: Use same units for all inputs - result is in those units

Geographic (km/miles)

Meaning: Great-circle distance on Earth's surface

Action: Actual travel distance will be longer due to roads, terrain

Midpoint coordinates

Meaning: Point exactly halfway between

Action: Useful for meeting points or dividing journeys

Note: Earth's radius varies slightly (equatorial vs polar). This calculator uses mean radius of 6,371 km for calculations.

About Distance Calculator

Distance on a flat plane uses the solve right triangle sides - the square of the hypotenuse equals the sum of squares of the other sides. For Earth's curved surface, the Haversine formula calculates great-circle distance, accounting for spherical geometry. You can also use the determine rise over run to find the rate of change between two points. Great circles are the largest circles on a sphere's surface and represent the shortest path between two points - which is why flight paths often appear curved on flat maps.

Formula

2D: d = sqrt((x2-x1)^2 + (y2-y1)^2) | Haversine: d = 2R * arcsin(sqrt(a))

Euclidean distance extends naturally to 3D by adding (z2-z1)^2. Haversine uses spherical trigonometry with Earth's radius R.

Current Standards: GPS uses WGS84 datum. Aviation uses nautical miles (1 nm = 1.852 km). Haversine assumes spherical Earth - for highest precision, use Vincenty's formula for the ellipsoid.

Frequently Asked Questions

Why do flights take 'curved' paths on maps?

They're actually taking the shortest path! Flat maps distort the spherical Earth. A 'straight' line on a flat map isn't actually the shortest path on Earth's surface. Great circle routes appear curved on Mercator projections but are actually shorter. NYC to Tokyo via Alaska is shorter than going 'straight' across the Pacific on a flat map.

How accurate is the Haversine formula?

It assumes a perfect sphere, giving accuracy within 0.5% - good enough for most purposes. Earth is actually an oblate spheroid (flattened at poles). For geodetic precision (surveying, mapping), use Vincenty's formula, which accounts for Earth's ellipsoidal shape and achieves millimeter accuracy.

What's the difference between distance and displacement?

Distance is the total length traveled along any path - it's always positive. Displacement is the straight-line distance from start to end with direction - a vector. If you walk 3 km north then 4 km east, your distance is 7 km but your displacement is 5 km northeast (by Pythagorean theorem).

How do I find my GPS coordinates?

On iPhone: Compass app shows coordinates. On Android: Google Maps > tap your location > coordinates appear at top. On computer: Google Maps > right-click any location > coordinates appear. Format: decimal degrees (40.7128) or degrees-minutes-seconds (40 42' 46").

Why doesn't Google Maps distance match this calculator?

Google Maps shows driving/walking distance following roads. This calculator shows straight-line distance. Road distance is always longer due to curves, obstacles, and indirect routes. For planning, driving distance matters; for real estate or 'as the crow flies' comparisons, straight-line distance is useful.

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