This **azimuth calculator** is used to find the **horizontal angle** between a **reference direction** and a line from an observer to a **point of interest**.

θ = atan2(sin(Δλ) * cos(φ2), cos(φ1) * sin(φ2) – sin(φ1) * cos(φ2) * cos(Δλ))

Imagine you’re standing at the center of a

compass rose. If you’re facingnorthand turn90°to your right (east), the azimuth would be90°. Similarly,southwould be180°, andwestwould be270°.

## Azimuth Calculator

Starting Point | End Point | Latitude 1 | Longitude 1 | Latitude 2 | Longitude 2 | Azimuth |
---|---|---|---|---|---|---|

New York | London | 40.7128°N | 74.0060°W | 51.5074°N | 0.1278°W | 51.3° |

Tokyo | Sydney | 35.6762°N | 139.6503°E | -33.8688°S | 151.2093°E | 188.7° |

Cairo | Cape Town | 30.0444°N | 31.2357°E | -33.9249°S | 18.4241°E | 181.1° |

Anchorage | Miami | 61.2181°N | 149.9003°W | 25.7617°N | 80.1918°W | 120.2° |

Rio de Janeiro | Moscow | -22.9068°S | 43.1729°W | 55.7558°N | 37.6173°E | 48.6° |

Los Angeles | New Delhi | 34.0522°N | 118.2437°W | 28.6139°N | 77.2090°E | 87.5° |

Berlin | Beijing | 52.5200°N | 13.4050°E | 39.9042°N | 116.4074°E | 74.1° |

Buenos Aires | Lima | -34.6037°S | 58.3816°W | -12.0464°S | 77.0428°W | 306.2° |

Nairobi | Johannesburg | -1.2864°S | 36.8172°E | -26.2041°S | 28.0473°E | 198.5° |

Madrid | Lisbon | 40.4168°N | 3.7038°W | 38.7223°N | 9.1393°W | 248.9° |

Moscow | Tokyo | 55.7558°N | 37.6173°E | 35.6762°N | 139.6503°E | 152.5° |

Dubai | Cairo | 25.276987°N | 55.296249°E | 30.0444°N | 31.2357°E | 333.1° |

Seattle | Vancouver | 47.6062°N | 122.3321°W | 49.2827°N | 123.1207°W | 337.5° |

Hanoi | Bangkok | 21.0285°N | 105.8542°E | 13.7563°N | 100.5018°E | 192.1° |

San Francisco | Mexico City | 37.7749°N | 122.4194°W | 19.4326°N | 99.1332°W | 152.9° |

## Azimuth Calculation Formula

The formula for calculating azimuth depends on the given information and the **coordinate system** used. One common method uses **latitude** and **longitude** coordinates:

**Azimuth = atan2(sin(Δλ) * cos(φ2),
cos(φ1) * sin(φ2) - sin(φ1) * cos(φ2) * cos(Δλ))**

Where:

- φ1, λ1 =
Latitudeandlongitudeof the starting point- φ2, λ2 =
Latitudeandlongitudeof the end point- Δλ =
Differencein longitude (λ2 – λ1)

This formula yields results in **radians**, which can be converted to **degrees** by multiplying by (**180/π**).

**Example**: Starting point: **40°N**, **75°W**

End point: **42°N**, **70°W**

**Convert**to radians**Apply**the formula**Convert**result to degrees

The resulting azimuth would be approximately

58.3°, indicating anortheasterly direction.

## How to Calculate Azimuth

**Determine coordinates**: Identify the**latitude**and**longitude**of both the starting point and the destination.**Convert to radians**: If using degrees, convert all values to**radians**.**Apply the formula**: Use the azimuth calculation formula mentioned earlier.**Interpret the result**: Convert the output to degrees and adjust if necessary to ensure it falls within the**0-360° range**.

**Example**:

Let’s calculate the azimuth from New York City (40.7128°N, 74.0060°W) to London (51.5074°N, 0.1278°W).

**Convert to radians:**

**φ1 = 40.7128 × (π/180)****λ1 = -74.0060 × (π/180)****φ2 = 51.5074 × (π/180)****λ2 = -0.1278 × (π/180)**

**Calculate** Δλ = **Δλ = λ2 – λ1**

**Apply** the formula

The azimuth from New York to London is approximately

51.3°, indicating anortheastern direction.

## What is the Azimuth 0 to 180?

**0°**:**Due North****45°**:**Northeast****90°**:**Due East****135°**:**Southeast****180°**:**Due South**

The azimuth range from **0° to 180°** covers half of the **compass rose**, representing directions from **due north** through **east** to **due south**.

If a ship captain receives a bearing of

67°to a lighthouse, they know the lighthouse is in theENE (East-Northeast)direction, falling within the0-180° azimuth range.

## How to Convert Degrees to Azimuth

Converting degrees to azimuth often involves **adjusting the angle** to fit the **0-360° azimuth scale**.

**N45°E**=**45° azimuth****S30°W**=**210° azimuth**(180° + 30°)**N80°W**=**280° azimuth**(360° – 80°)

To convert from a **quadrant system**:

- Identify the
**quadrant**(NE, SE, SW, NW) - Use the appropriate formula:
**NE**: Azimuth = Angle**SE**: Azimuth = 180° – Angle**SW**: Azimuth = 180° + Angle**NW**: Azimuth = 360° – Angle

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