About Pathsphere

A small, inspectable spherical model.

Pathsphere is one free browser-local calculator for the central angle and shorter surface separation between two latitude/longitude pairs on a sphere whose radius you choose. It aims to make the assumptions visible rather than hide a radius or route provider behind a single distance number.

What the tool does

It checks plain decimal coordinate bounds, handles exact pole and longitude-alias conventions, calculates the central angle using an atan2 cross/dot model, and multiplies that angle by the entered radius. Results, notes and JSON are created in your browser. The guide explains numerical conventions and the examples show checks you can repeat.

What a result means

The result belongs to an ideal sphere. It does not choose an Earth ellipsoid, transform datums, account for altitude or terrain, find a route, query your location or guarantee real-world accuracy. The input decimal limits and 12-significant-digit display are software choices, not measurement precision claims. Exact antipodal coordinates give a distance but do not select a unique shortest arc.

Free access and support

The calculator has no fee or account requirement. This source release prepares publisher verification metadata and an ads.txt file, which do not themselves display advertisements. Cloudflare Web Analytics is active through the exact-host manual snippet authorized for this first release. It collects page and performance usage telemetry. The calculator processes your entries locally and does not deliberately add them to analytics events. Advertising and consent-platform loaders remain inactive.

The contact address is an existing shared public forwarding alias used across the owner’s free-tool collection: yardfill.helpful594@aleeas.com. It is not a newly created mailbox. Questions about a result are easier to investigate if you include the five decimal inputs and what you expected. Avoid sending sensitive locations or personal details.

Method sources and corrections

Calculation notes link directly to mathematical references, including MathWorld and Chris Veness’s original-author vector-geodesy discussion. If you find a reproducible problem, use the contact page. A report does not automatically change the live source; calculation and release checks are separate from a browser result.