Haversine Distance Calculator

Calculate distance between coordinates using the haversine formula.

About Haversine Distance Calculator

The haversine formula is numerically stable for short distances, where the simpler spherical law of cosines loses precision through catastrophic cancellation. That stability is why it is the standard choice. Using the law of cosines for nearby points can produce errors of tens of metres or fail entirely, which matters for anything geofenced.

Formula

Haversine Distance

a = sin²(Δlat/2) + cos(lat₁)cos(lat₂)sin²(Δlon/2); distance = 2R·atan2(√a, √(1−a))

haversine: Half the versed sine, a formulation stable for small distances
Δlat, Δlon: Differences in latitude and longitude in radians

Worked example

With the default values below, Haversine Distance Calculator returns Distance of 5,570.222. Change any input above and every figure here is recalculated in your browser.

Inputs used

First latitudeaccepts -90–90 degrees: 51.5074 degrees
First longitudeaccepts -180–180 degrees: -0.1278 degrees
Second latitudeaccepts -90–90 degrees: 40.7128 degrees
Second longitudeaccepts -180–180 degrees: -74.006 degrees

Results

Distance: 5,570.222 km
Distance: 3,461.175 miles
Distance: 3,007.681 nmi
Initial Bearing: 288.33 degrees
Flight Time at 900 km/h: 6.189 h

Step by step

1Values used
2Haversine Distance
3Distance= 5,570.222 km
4Distance= 3,461.175 miles
5Distance= 3,007.681 nmi
6Initial Bearing= 288.33 degrees
7Flight Time at 900 km/h= 6.189 h

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Haversine Distance calculated?

a = sin²(Δlat/2) + cos(lat₁)cos(lat₂)sin²(Δlon/2); distance = 2R·atan2(√a, √(1−a)) The haversine formula is numerically stable for short distances, where the simpler spherical law of cosines loses precision through catastrophic cancellation. That stability is why it is the standard choice.

Why does Haversine Distance matter?

Using the law of cosines for nearby points can produce errors of tens of metres or fail entirely, which matters for anything geofenced.

What values do I need to enter?

This calculator takes 4 inputs: First latitude, First longitude, Second latitude, Second longitude. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.