Marine Navigation Distance and Bearing Calculator
Route positions
Route calculation
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Great-circle vs. rhumb-line route
A great circle is the shortest path between two positions on a spherical Earth. Except along a meridian or the equator, its true course changes as the vessel advances, so the calculator reports both departure and arrival bearings.
A rhumb line, or loxodrome, crosses every meridian at the same angle. Its one constant true course is convenient to plot on a Mercator chart, but it is normally longer over substantial east–west distances.
How to use this calculator
- Enter departure latitude and longitude as signed decimal degrees.
- Enter destination latitude and longitude in the same format.
- Choose the primary distance unit and calculate.
- Compare shortest-path great-circle values with the constant-course rhumb line.
- Plot and verify an actually navigable track using current official information.
Calculation method
Coordinates are converted to radians. The great-circle central angle δ uses the numerically stable haversine form:
a = sin²(Δφ/2) + cos φ₁ cos φ₂ sin²(Δλ/2)
δ = 2 atan2(√a, √(1−a))
distance = R × δ
The rhumb calculation uses the shortest wrapped longitude difference and the Mercator latitude difference Δψ. Both use mean Earth radius R = 6,371,008.8 m.
Reading the bearings
- Bearings are degrees true, clockwise from true north: 000° is north, 090° east, 180° south, and 270° west.
- The great-circle initial bearing is the course at departure; its final bearing is the forward course on arrival.
- The rhumb bearing remains constant only in the spherical/Mercator model.
- No magnetic variation, compass deviation, leeway, current correction, or steering error is applied.
Frequently asked questions
How is marine distance calculated from latitude and longitude?
This tool treats Earth as a sphere with a mean radius of 6,371,008.8 meters. It uses the haversine central angle for great-circle distance and a Mercator latitude difference for rhumb-line distance.
What is the difference between a great-circle route and a rhumb line?
A great circle is the shortest spherical path, but its bearing usually changes. A rhumb line has one constant true course, but it is generally longer except in special cases such as travel along the equator or one meridian.
Are the bearings true or magnetic?
They are degrees true, measured clockwise from true north. Apply appropriate, current local magnetic variation and vessel-specific compass deviation separately when relevant.
Does the calculated route avoid land, shallow water, and hazards?
No. It is a mathematical line between coordinates and knows nothing about land, charted depths, obstructions, traffic schemes, restricted areas, weather, or currents.
Why might another navigation app give a slightly different distance?
This page uses a spherical mean-Earth model. Another system may solve on the WGS 84 ellipsoid, measure a plotted multi-leg route, use a chart projection, or round differently. The difference becomes more noticeable on long or high-latitude routes.
What happens near the 180° meridian?
The calculator wraps longitude difference to the shorter direction across the international date line. A route from 179°E to 179°W therefore uses a 2° longitude difference, not 358°.
Why can a bearing be undefined?
Coincident positions have no travel direction. Exactly antipodal positions have infinitely many equal-length great circles, so there is no unique initial bearing. The tool identifies these cases rather than presenting a misleading course.
Are my coordinates uploaded or tracked?
No. Calculations run locally in the browser, and this tool does not send, store, or attach entered coordinates to analytics events.
Assumptions and navigation limits
- Earth is modeled as a sphere, not the WGS 84 ellipsoid. This is suitable for a convenient estimate, not precision geodesy.
- Distance is converted using the international nautical mile of exactly 1,852 meters. Bearings are rounded for display while calculations retain full floating-point precision.
- Latitude must be strictly between 90°S and 90°N because longitude and rhumb-line course are singular at the poles.
- Initial/final great-circle bearing and a rhumb course describe ideal mathematical lines, not a heading to steer continuously in real conditions.
Safety disclaimer: This educational calculator is not an electronic chart display, route planner, collision-avoidance system, or substitute for current official charts, notices, forecasts, position verification, legal requirements, and competent navigational judgment.
Methodology and sources
Last reviewed: August 1, 2026. Route terminology, spherical-navigation context, geodesic inverse-problem definitions, the mean Earth radius, and marine units were checked against: