Case 1
- Start latitude
- 52.52°
- Start longitude
- 13.405°
- End latitude
- 48.1351°
- End longitude
- 11.582°
504.415km
Open with these valuesHaversine Distance Calculator
504.415km
Result: 504.415 kmEnter two pairs of decimal degrees and read the great-circle distance: the shortest path over the curved surface of the Earth. Berlin to Munich is 504.415 km. This is a straight line, not a route — the drive is about 585 km, because roads bend around everything the crow flies over.
The numbers at a glance
Held fixed: Start latitude 52.5200 °, Start longitude 13.4050 °, End latitude 48.1351 °.
| End longitude (°) | Result (km) |
|---|---|
| 0.0000 | 1,066.963 |
| 5.0000 | 769.679 |
| 10.0000 | 544.053 |
| 11.5820Your value | 504.415 |
| 15.0000 | 500.518 |
| 20.0000 | 675.416 |
Worked examples
Case 2
- Start latitude
- 51.5074°
- Start longitude
- -0.1278°
- End latitude
- 48.8566°
- End longitude
- 2.3522°
343.556km
Open with these valuesCase 3
- Start latitude
- 40.7128°
- Start longitude
- -74.006°
- End latitude
- 34.0522°
- End longitude
- -118.2437°
3,935.746km
Open with these valuesHow it's calculated
d = 2·R·asin(√(sin²(Δφ/2) + cos φ₁·cos φ₂·sin²(Δλ/2))), R = 6371 km
- StepEnter the start latitude and longitude in decimal degrees.
- StepEnter the end coordinates the same way; south and west are negative.
- ResultRead the great-circle distance in kilometres.
What this number means
A sphere of radius 6371 km
The formula models the Earth as a sphere of exactly 6371 km, the mean radius the cited source works with. The planet is flattened instead — about 6378 km at the equator against 6357 km pole to pole — so a small residual error is built in.
Decimal degrees in, radians handled inside
Type 13.405, never 13° 24′ 18″ and never a radian value. All four fields take decimal degrees and the formula converts them itself, so pre-converted input would not be slightly off but meaningless.
Up to about 0.5 % off an ellipsoidal method
Against a method that uses the real ellipsoid, such as Vincenty, the result can differ by up to roughly 0.5 % depending on where the line runs. Over 500 km that is a good two kilometres — irrelevant for flight distances and radius searches, not acceptable for surveying.
A straight line, not a route
Berlin to Munich is 504.415 km as the crow flies against roughly 585 km by road. Read the figure as a lower bound for any journey.
Commonly misread
Southern latitudes and western longitudes go in as positive numbers.
South and west are negative: Los Angeles sits at −118.2437, Sydney at −33.8688. Drop the minus and the point lands on the wrong side of the planet.
504 km of air line means roughly 504 km of driving.
Roads bend around mountains, lakes and borders, so the Berlin to Munich drive runs about 585 km. The great-circle figure is the shortest distance there is, never the one travelled.
The result is exact — it is a formula, after all.
The formula is exact on a sphere, and the Earth is not one. Its flattening leaves a deviation of up to roughly 0.5 % against an ellipsoidal calculation.
Reference table
| Start lat, lon — end lat, lon | Route | Distance |
|---|---|---|
| 51.5074, -0.1278, 48.8566, 2.3522 | London → Paris | 343.556 |
| 52.52, 13.405, 48.1351, 11.582 | Berlin → Munich | 504.415 |
| 40.7128, -74.006, 34.0522, -118.2437 | New York → Los Angeles | 3935.746 |
| -33.8688, 151.2093, 35.6762, 139.6503 | Sydney → Tokyo | 7825.819 |
| 0, 0, 0, 90 | Equator, a quarter of the way round | 10007.543 |
| 90, 0, -90, 0 | North Pole → South Pole | 20015.087 |
Questions
What is the haversine distance between two points?
It is the great-circle distance — the shortest path between two points measured over the curved surface of a sphere. The formula takes both latitudes and longitudes and returns that arc. Berlin to Munich comes out at about 504.415 km.
Is this the same as driving distance?
No. This is the as-the-crow-flies line over the Earth's surface, while real roads curve around mountains, lakes and borders. The Berlin to Munich drive is roughly 585 km against a 504 km straight line, so treat the result as a lower bound.
Which Earth radius does the calculator use?
The mean radius of 6371 km, the usual value for spherical-Earth work. Because the Earth is flattened at the poles — about 6378 km at the equator against 6357 km pole to pole — the result can differ from an ellipsoidal method by up to roughly 0.5 %.
Can I enter negative latitudes and longitudes?
Yes. Latitude runs from −90 at the South Pole to +90 at the North Pole, with south negative; longitude runs from −180 to +180, with west negative. Zero is valid too and marks the equator and the prime meridian.
How do I get the distance in miles?
Multiply the kilometre figure by 0.621371. Berlin to Munich is 504.415 km, which is about 313.43 miles — the same great-circle path, only the unit changes.
Sources and last check
Information, not professional advice.