Resultant course with current calculator

This resultant course with current calculator combines the vessel's velocity through the water with the current vector and reports the actual course over ground and ground speed. Enter the vessel heading, its speed through the water, the direction toward which the current flows, and the current speed. The calculator resolves both motions into east and north components, adds them, and converts the combined vector back into a nautical bearing and speed. It is useful for navigation exercises, passage estimates, training, simulations, and reproducible API calculations.

Enter headings and speeds with a consistent convention

Treat every direction as a compass bearing measured clockwise from true north: zero degrees is north, ninety is east, one hundred eighty is south, and two hundred seventy is west. The vessel heading describes the direction the bow and through-water velocity point. The current direction must describe where the water flows toward, not where it comes from. That distinction matters because some marine forecasts name a current by its destination while other sources may describe its origin. Convert any source convention before entering the value. Supply vessel speed and current speed in the same unit, such as knots, kilometres per hour, metres per second, or miles per hour. The calculator does not need to know the unit because vector addition preserves it, but mixing knots and metres per second produces a meaningless result. Directions outside the usual range are normalized, so minus ten degrees and three hundred fifty degrees represent the same bearing. Speeds must be non-negative finite values. True headings produce a true course; magnetic headings require consistently magnetic current directions or a separate variation correction.

Understand the vector addition behind the answer

The calculation uses an east-north coordinate system. For a speed v at compass bearing theta, the east component is v times sine theta and the north component is v times cosine theta. This ordering differs from the familiar classroom formula where angles start at the positive x-axis, because nautical bearings start at north and increase clockwise. The vessel components and current components are added independently. The length of that combined vector, found with the Pythagorean theorem, is ground speed. Its direction is recovered with a two-argument inverse tangent using east and north, then normalized into the interval from zero up to but not including three hundred sixty degrees. The response includes the vessel, current, and ground vectors so you can audit signs and reproduce the work. It also returns the course and speed rounded to ten decimal places for stable automation. If equal opposing vectors cancel exactly, ground speed is zero and course has no physical meaning, so the request is rejected instead of inventing a northward bearing for a stationary vessel.

Use the result within the limits of the model

The returned course is an instantaneous course over ground for two constant planar velocity vectors. It is a clean answer for chart-work exercises, short time intervals, simulator inputs, and first-pass passage planning. It does not account for changing tidal streams, wind-driven leeway, steering error, magnetic variation, waves, acceleration, latitude-dependent chart geometry, or obstacles. For a real passage, divide the route into suitable time and location segments, obtain current forecasts for each segment, and recalculate as conditions change. Remember that this calculator answers the forward problem: given a heading through the water, what course over ground results? The inverse problem—choosing a heading that will achieve a desired ground track—requires solving for a correction angle and can be impossible when the cross-current exceeds available boat speed. Keep source data and units beside any saved result, since a number without its bearing convention is easy to misuse. The browser tool uses the same deterministic core as the API. Automated calculations cost $0.002 per successful item, making the output suitable for repeatable lessons, logs, and lightweight navigation software tests.