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Conversions

Great Circle Distance (Haversine)

km between two lat/lon points. Free online Great Circle Distance (Haversine) for conversions — instant, accurate results, mobile-friendly, no signup needed.

Great-circle distance between two lat/lng points.
Distance (km)
5,570.22218

Derivation

  1. ├── 01Givenlat1 = 40.7128, lon1 = -74.006, lat2 = 51.5074, lon2 = -0.1278
  2. ├── 02Formula12742 × asin(√(c))
  3. └── 03Compute Distance (km)5,570.22218
Did you know?

The haversine formula (1805) lets sailors compute great-circle distance from latitude/longitude without a calculator — just a log table.

§01What is

Understanding the Great Circle Distance (Haversine)

The Great Circle Distance (Haversine) computes Distance (km) from 4 inputs: lat 1, lon 1, lat 2, lon 2. km between two lat/lon points.

Quick calculators for the math that shouldn’t need a notepad — instant, accurate, private to your browser. The Great Circle Distance (Haversine) sits in that toolkit — it km between two lat/lon points. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

12742 × asin(√(c))

Where

lat1
Lat 1
lon1
Lon 1
lat2
Lat 2
lon2
Lon 2
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Lat 1 = 40.7128, Lon 1 = -74.006, Lat 2 = 51.5074, Lon 2 = -0.1278.

  1. 01Start by noting the input — Lat 1: 40.7128.
  2. 02Start by noting the input — Lon 1: -74.006.
  3. 03Start by noting the input — Lat 2: 51.5074.
  4. 04Start by noting the input — Lon 2: -0.1278.
  5. 05Substitute these values into the formula: 12742 × asin(√(c))
  6. 06Compute Distance (km): the calculator returns 5570.22.
  7. 07Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Great Circle Distance (Haversine) Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Lat 1 halved

lat1 = 20.3564 (from 40.7128)

Keep every other input at its default and halve the lat 1. See how distance (km) responds.

  1. 01New Lat 1: 20.3564
  2. 02Baseline Distance (km): 5570.22
  3. 03New Distance (km): 7145.28
  4. 04Distance (km) increases by 28.3% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Lat 1 doubled

lat1 = 81.4256 (from 40.7128)

Keep every other input at its default and double the lat 1. See how distance (km) responds.

  1. 01New Lat 1: 81.4256
  2. 02Baseline Distance (km): 5570.22
  3. 03New Distance (km): 4102.84
  4. 04Distance (km) decreases by 26.3% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Lon 1 halved

lon1 = -37.003 (from -74.006)

Keep every other input at its default and halve the lon 1. See how distance (km) responds.

  1. 01New Lon 1: -37.003
  2. 02Baseline Distance (km): 5570.22
  3. 03New Distance (km): 3045.26
  4. 04Distance (km) decreases by 45.3% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Lon 1 doubled

lon1 = -148.012 (from -74.006)

Keep every other input at its default and double the lon 1. See how distance (km) responds.

  1. 01New Lon 1: -148.012
  2. 02Baseline Distance (km): 5570.22
  3. 03New Distance (km): 9299.32
  4. 04Distance (km) increases by 66.9% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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