Distance Calculator

Subtract the coordinates to get the horizontal and vertical differences, square both, add them, and take the square root. That's the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). For (2, 3) and (7, 11), the differences are 5 and 8, the squares are 25 and 64, and the square root of 89 is about 9.43. The 2D mode above does this instantly and plots the triangle so you can see where the numbers come from.

Yes, it's the Pythagorean theorem in disguise. The two points sit at the ends of a right triangle's hypotenuse, the horizontal difference is one leg, and the vertical difference is the other. The theorem says the hypotenuse squared equals the sum of the squared legs, so the distance is the square root of that sum. The plot in the 2D mode draws those two legs as dashed lines, and that's exactly the triangle you're solving.

It's the same idea with one more term. Take the differences along x, y, and z, square all three, add them, and take the square root: d = sqrt(dx^2 + dy^2 + dz^2). A point 3 units over, 4 units up, and 5 units deep is sqrt(9 + 16 + 25) = sqrt(50), about 7.07 units away. It works because you're applying the Pythagorean theorem twice, once across the floor and once up the height.

You can't use the flat formula, because latitude and longitude wrap around a sphere. The standard method is the haversine formula, which converts both points to angles, finds the central angle between them through Earth's center, and multiplies it by Earth's mean radius, about 6,371 km. That gives the great-circle distance, the shortest path along the surface. The GPS mode here runs the whole calculation and reports kilometers, miles, and nautical miles.

It's the shortest route between two points along the surface of a sphere, the path an aircraft would ideally fly. A great circle is any circle around Earth whose center is Earth's center, like the equator. On a flat map these routes look curved, which is why flights from New York to London arc up near Greenland. A line that looks straight on a flat map is usually longer in reality than the great-circle route.

Within about 0.5% for almost any pair of points, which is plenty for planning and general use. The error comes from treating Earth as a perfect sphere when it's really slightly flattened at the poles, with about 21 km between the polar and equatorial radius. Surveying tools use ellipsoid methods like Vincenty's formula to shrink the error to millimeters, but for distances between cities, hikes, or waypoints, haversine is the standard choice.

No, and it's worth knowing why. This tool returns the straight-line or great-circle distance, sometimes called 'as the crow flies'. Roads bend around terrain, water, and property lines, so real driving routes typically run 20% to 40% longer than the straight line. The straight-line figure is still useful as a lower bound, for range checks, and for anything that really does travel in a straight line, like radio signals and flight planning.

A nautical mile is 1,852 meters, about 1.15 land miles, and it's the unit ships and aircraft use. It was defined so that one nautical mile equals one minute of latitude, 1/60 of a degree, which makes chart navigation clean: a degree of latitude is 60 nautical miles. Speed in knots is just nautical miles per hour, so an aircraft doing 300 knots covers 300 nautical miles of great-circle distance in an hour.