Haversine Formula

Key idea

Great-circle distance between points on Earth.

In depth

The great-circle distance between two points on a sphere is d = 2R arcsin(√(sin²(Δφ/2) + cos φ₁ cos φ₂ sin²(Δλ/2))). It is numerically stable for short distances, so it is used for navigation.

Worked example

London to Paris (about 344 km) can be computed by plugging latitudes and longitudes into the formula.

Real-world uses

• Calculating the distance between two GPS points on Earth in mapping and ride-sharing apps

Common mistake

Entering latitude and longitude in degrees when the function expects radians.

How to learn this

1. Read the key idea and say it in your own words.
2. Work through the worked example, then try a similar problem.
3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

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Related expert topics in Trigonometry

• Half Angle Formulas – Trig of θ/2.
• Power Reducing Formulas – Reduce squares to first powers of cos 2θ.
• Product-to-Sum Formulas – Convert products into sums.
• Sum-to-Product Formulas – Convert sums into products.
• Triple Angle Formulas – sin3θ and cos3θ in terms of θ.
• Trig and Inverse Trig Compositions – Evaluate expressions like sin(arccos x).