GEOGRAPHY & CARTOGRAPHY CALCULATOR
Savi Calculator
A precise tool.
What is the Savi Calculator & How does it work?
The surface of the Earth is approximated as a sphere for many navigation and mapping tasks. The shortest path between two points on this sphere, known as a great‑circle route, follows the intersection of the sphere with a plane that passes through its centre and the two points. This principle underlies airline routing, maritime navigation, and the design of many map projections.
To compute the length of a great‑circle segment, cartographers often employ the haversine formula, which remains numerically stable for small distances. The formula relates the central angle between the points to their latitudinal and longitudinal differences.
Understanding this distance is essential when converting between real‑world scales and map scales. A map’s scale ratio (e.g., 1:50 000) tells how many ground units correspond to a single unit on the map, and the great‑circle distance helps verify that the chosen scale accurately represents the region of interest.
d = 2R arcsinleft( sqrt{ sin^2left(frac{phi_2-phi_1}{2}right) + cosphi_1cosphi_2sin^2left(frac{lambda_2-lambda_1}{2}right) } right)
d = great‑circle distance, R = Earth radius, phi = latitude, lambda = longitude
Parameters
Result
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Frequently Asked Questions
What is a great-circle route?
A great-circle route is the shortest path between two points on the Earth’s surface, following the intersection of the sphere with a plane through its center.
How does the haversine formula work?
The haversine formula calculates the distance between two points on a sphere given their longitudes and latitudes by using spherical trigonometry.
Why is the Earth approximated as a sphere for navigation?
The Earth is approximated as a sphere to simplify calculations for navigation, making it easier to determine great-circle routes.
What are some applications of great-circle routing?
Great-circle routing is used in airline and maritime navigation, as well as in the design of map projections to ensure accurate distance representation.
Can I use this calculator for any location on Earth?
Yes, you can use this calculator for any two points on the Earth’s surface to determine the great-circle distance between them.
How does this calculator differ from other distance calculators?
This calculator uses the haversine formula specifically for spherical geometry, making it suitable for accurate navigation and mapping tasks.
What units can I get the results in?
The results can be obtained in various units such as kilometers, miles, or nautical miles, depending on your preference.
Results are for informational purposes only and do not constitute professional advice.