Route legs, courses, and totals

Each leg's distance, true and magnetic course, and cumulative distance for a route of waypoints, with leg times and arrival times from a groundspeed and departure time.

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

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.

370.8NM

The route is 370.8 NM in 3 legs.

Legs
From	To	Distance	True course	Final true course	Declination	Magnetic course	Cumulative distance	Leg time	Arrival time
KDEN	KASE	108.9 NM	250 deg	249 deg	7.3 deg	243 deg	108.9 NM	54 min	09:54
KASE	KGJT	77.6 NM	266 deg	265 deg	8.4 deg	258 deg	186.5 NM	39 min	10:33
KGJT	KDEN	184.4 NM	75 deg	77 deg	9.1 deg	66 deg	370.8 NM	1 h 32 min	12:05

Route
Latitude	Longitude	Name
39.8617000 deg	-104.6731000 deg	KDEN
39.2232000 deg	-106.8688000 deg	KASE
39.1224000 deg	-108.5267000 deg	KGJT
39.8617000 deg	-104.6731000 deg	KDEN

Total time
Arrival time
Arrival time (UTC)
Legs

Provenance

Computed by: navigation.route.legs 1.0.0, core 0.1.0
Model: Geodesic (Karney 2013) legs on WGS 84; magnetic declination from WMM2025 at each leg's start
Accuracy: Distances and courses to nanometers; declination per WMM2025 (about ±0.5° typical)
Reference data: version WMM2025 (2024-11-13) of a reference dataset
Notes: None
Cites: Karney, C. F. F., Journal of Geodesy, Algorithms for geodesics; NOAA National Centers for Environmental Information and British Geological Survey, The US/UK World Magnetic Model for 2025-2030: Technical Report

Something look off?

Your values

Showing an example. Change anything.

Waypoints In order: name (optional), latitude, longitude, like KDEN, 39.8617, -104.6731 · one per line: name, latitude, longitude

Import a file KML, KMZ, GPX, GeoJSON, CSV, WKT, or WKB — or drop it on the box. Read on this device.

Legs flown asoptional geodesic (shortest, default) or rhumb (constant course) Date for magnetic coursesoptional Like 2026-09-18; leave empty for true courses only Groundspeedoptional Like 120 kt, for leg times · plain numbers mean kt Ellipsoidoptional wgs84 (default), grs80, clarke1866, intl1924, airy1830, bessel1841, or krassovsky1940

More options 4

Departure timeoptional Local clock time, like 14:30 UTC offsetoptional Of the departure time, like -06:00 or Z Custom semi-major axisoptional With inverse flattening, like 3396190 m (Mars) · plain numbers mean m Custom inverse flatteningoptional Like 169.894; 0 for a sphere

Run many at once from a CSV

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

Model: Geodesic legs (Karney 2013) on WGS 84; magnetic declination from WMM2025

Accuracy: Distances and courses to nanometers; declination per WMM2025 (about ±0.5° typical)

When to use this: Use this to turn a list of waypoints into a flight or voyage plan: the distance and true course of every leg, the running total, and, with a groundspeed and a departure time, how long each leg takes and when you arrive. It is the table a navigation log is filled in from.

Limitations: The legs are geodesics, the shortest way between each pair, so the course changes continuously along one and the figure given is the course leaving the waypoint; a rhumb line holds one heading instead and is the other tool. The time assumes the groundspeed given holds for the whole route, which is a planning figure and not a forecast: wind, climb, and descent are not in it. Courses are true, not magnetic, so a compass needs the variation applied.

Worked example: Denver to Aspen to Grand Junction to Denver at 120 kt. Source: navigation route-geometry scenario: a 4-waypoint route shows true and magnetic courses per leg, with the declination and model.

You enter

Date for magnetic courses: 2026-09-18
Departure time: 09:00
Groundspeed: 120 kt
UTC offset: -06:00
Waypoints: KDEN, 39.8617, -104.6731 KASE, 39.2232, -106.8688 KGJT, 39.1224, -108.5267 KDEN, 39.8617, -104.6731

You get

Total distance: 370.8 NM
Total time: 3 h 05 min
Arrival time: 12:05
Arrival time (UTC): 18:05Z
Legs: 3

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 1.0.0, core 0.1.0. See this tool in the verification report.

Changes

2026-09-19, added: New navigation tools: rhumb lines, cross-track and along-track distance, fly-by turn anticipation, time-speed-distance with arrival times, closest point of approach, and route legs with true and magnetic courses; and the first geometry tool, polygon area on the ellipsoid. Changelog

Checked against: 22 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.
The US/UK World Magnetic Model for 2025-2030: Technical Report, NOAA National Centers for Environmental Information and British Geological Survey, WMM2025, NESDIS/NCEI (December 2024). Section 1.2 (equations 1-25: synthesis, secular variation, and elements).

Terms

UTC: Coordinated Universal Time: The world's civil time standard, kept within 0.9 s of Earth's rotation by leap seconds. Aviation calls it Zulu time, written with a Z. Source: IERS Bulletin C (leap seconds)