Destination point from bearing and distance calculator

This destination point from bearing and distance calculator solves the direct navigation problem on a spherical Earth. Enter a starting latitude and longitude, an initial bearing measured clockwise from true north, and a non-negative travel distance. The calculator converts the path length to an angular distance, applies the standard great-circle trigonometric equations, and returns a normalized destination coordinate. It accepts meters, kilometers, statute miles, and nautical miles, and it can use a custom spherical radius for classroom models or other worlds.

Enter a valid start point, bearing, and distance

Begin with the latitude and longitude of the departure point in decimal degrees. Latitude must be between negative ninety and positive ninety, while longitude must be between negative one hundred eighty and positive one hundred eighty. Positive latitude means north and positive longitude means east.

Supply the initial bearing in degrees clockwise from true north: zero points north, ninety points east, one hundred eighty points south, and two hundred seventy points west. Bearings outside one complete turn are allowed because the calculator normalizes them into the interval from zero up to, but not including, three hundred sixty. A bearing of four hundred five degrees therefore describes the same initial direction as forty-five degrees.

Distance must be zero or greater. Select m for meters, km for kilometers, mi for statute miles, or nmi for nautical miles; kilometers are used when the unit is omitted. These checks are deliberate.

A negative distance, infinite value, missing coordinate, or latitude beyond a pole produces an invalid input error rather than a plausible-looking but misleading coordinate. For ordinary Earth calculations, leave the radius at its default mean value. Set a custom positive radius only when a lesson, simulation, or specification explicitly calls for a different sphere.

Understand the spherical trigonometry

The calculation models travel along a great circle, the intersection of a sphere with a plane through its center. First, the start latitude, start longitude, and normalized bearing are converted from degrees to radians. The chosen distance is converted to meters and divided by the spherical radius, producing the angular distance of the journey.

Destination latitude comes from an arcsine expression that combines the start latitude, angular distance, and cosine of the initial bearing. Destination longitude adds an atan2 expression to the start longitude. Using atan2 is important because it preserves the quadrant and remains meaningful when the route approaches a meridian, crosses the antimeridian, or heads toward a pole.

Small floating-point overshoots are clamped before arcsine, and the final longitude is wrapped to the familiar range from negative one hundred eighty through less than positive one hundred eighty degrees. The response also includes the normalized initial bearing, converted distance in meters, radius used, and a method label. No network request, random source, clock, or mutable state participates, so identical inputs produce identical output.

Interpret the result and choose the right model

A zero-distance request returns the starting coordinate after normal longitude normalization. Routes that cross the antimeridian wrap cleanly instead of returning a longitude beyond the conventional map range. The initial bearing describes the direction at departure; on most great-circle routes, the direction changes as the traveler moves, so it should not be mistaken for a constant compass heading or an arrival bearing.

This distinction matters at high latitudes and over long distances. The spherical solution is an excellent fit for educational work, approximate planning, visualization, games, simulations, and systems whose stated contract uses a mean Earth radius. It is not a replacement for an ellipsoidal geodesic solver when centimeter or meter accuracy affects surveying, legal boundaries, precision aviation, or safety-critical operations.

Earth is not a perfect sphere, and the difference grows with route geometry and distance. Likewise, use a rhumb-line calculation if the intended path follows a constant bearing throughout rather than only at departure. When chaining several legs, feed each returned destination into the next request and supply the next leg's own initial bearing.

Preserve the radius and unit conventions across all legs so results remain internally consistent and auditable.