Intercept a moving target

The course to steer, the time, and the meeting point for reaching a target that is moving on a steady course and speed, or why it cannot be reached.

Planning and education aid. Not for primary navigation. Full disclaimer

Experimental: not yet fully verified. How results are checked

Computing your own values needs JavaScript and WebAssembly. The worked example below was computed when this page was built, and the documentation under "How we got this" applies.

36.87°

Steer 36.87° to meet the target in 37.43 min, after 23,109.398 m.

Time to intercept
Your run
Meeting latitude
Meeting longitude

Provenance

Computed by: navigation.route.intercept 1.0.1, core 0.1.0
Model: On WGS 84, the target runs its geodesic course: T(t) = direct(T0, course, v_T·t). The intercept is the first t where the geodesic range from you to T(t) equals v·t. Steps of f(t) ÷ (v + v_T), with f = range − v·t, never pass the first root because f changes no faster than v + v_T; a Newton step that brackets the root finishes it by regula falsi. You steer the geodesic to the meeting point
Accuracy: Solves to a millimeter of range for steady courses and speeds; real targets turn and change speed
Notes: 1 shown with the answer
Cites: Karney, C. F. F., Journal of Geodesy, Algorithms for geodesics

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Your values

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Paste a coordinateany notation

Your latitude Decimal degrees, north positive, like 40.6413 · plain numbers mean degrees Your longitude Decimal degrees, east positive, like -73.7781 · plain numbers mean degrees Your speed Over the ground, like 20 kt · plain numbers mean kt Target latitude Decimal degrees, north positive, like 40.6413 · plain numbers mean degrees Target longitude Decimal degrees, east positive, like -73.7781 · plain numbers mean degrees Target course True, like 090 deg · plain numbers mean degrees Target speed Over the ground, like 12 kt · plain numbers mean kt

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How we got thisFormula, worked example, sources, and proof

Model: On WGS 84, the target runs its geodesic course: T(t) = direct(T0, course, v_T·t). The intercept is the first t where the geodesic range from you to T(t) equals v·t. Steps of f(t) ÷ (v + v_T), with f = range − v·t, never pass the first root because f changes no faster than v + v_T; a Newton step that brackets the root finishes it by regula falsi. You steer the geodesic to the meeting point

Show your work

Time to meet
the first t with range(t) = your speed × t
20.0 kt against a target at 12.0 kt = 37.43 min
Course to steer
the geodesic azimuth to the meeting point
to 40.16639°, -69.83723° = 36.87°

The same steps an agent gets from the MCP server with explain: true.

Accuracy: Solves to a millimeter of range for steady courses and speeds; real targets turn and change speed

Worked example: 20 kt pursuer, target 10 NM north running east at 12 kt. Source: Worked in the plane first (t = 10 ÷ √(20² − 12²) = 0.625 h) and refined on the ellipsoid; checked by running both to the meeting point. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Your latitude: 40 deg
Your longitude: -70 deg
Your speed: 20 kt
Target course: 90 deg
Target latitude: 40.1665 deg
Target longitude: -70 deg
Target speed: 12 kt

You get

Course to steer: 36.87°
Time to intercept: 37.43 min
Your run: 23,109.398 m
Meeting latitude: 40.1663856°
Meeting longitude: -69.8372314°

Review: Not yet independently reviewed by a geodesist.

Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.1, core 0.1.0. See this tool in the verification report.

Changes

2026-09-23, fixed: Short distances lost their meaning: a 0.859 m geodesic showed as 0.001 km. Distances in the navigation tools (version 1.0.1) still show to the meter in kilometers, but a short one now keeps three significant digits, down to the millimeter, so it shows as 0.000859 km. Differences such as the rhumb line's extra distance keep fixed decimals. Values are unchanged. Changelog

Checked against: 17 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

Algorithms for geodesics, Karney, C. F. F., Journal of Geodesy, Vol. 87, No. 1. pp. 43-55.

Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.