Cross-Track Error and Course Correction Calculator
Calculate cross-track error (XTE) and bearing correction to return to a planned course.
Find the angle needed to intercept the original route from your current position.
Cross-Track Error (XTE) Cross-track error measures how far off your planned course you are — perpendicular to the route. Also called: cross-course error, cross-track distance, lateral error. XTE = 0: you are on the planned track. XTE > 0: you are to the right of track. XTE < 0: you are to the left of track.
Formula (Spherical Earth) Given the planned course from waypoint A to waypoint B, and current position P: XTE = asin(sin(d_AP/R) × sin(θ_AP − θ_AB)) Where: d_AP = distance from A to current position P (in radians × R) θ_AP = bearing from A to current position P θ_AB = planned bearing from A to B (planned course) R = Earth’s radius (6,371 km) All angles in radians for the formula.
Along-Track Distance (ATD) ATD = acos(cos(d_AP/R) / cos(XTE/R)) × R How far along the planned track you have effectively traveled.
Intercept Heading To return to track at the next waypoint B: Correction angle = atan2(XTE, distance_to_B) New heading = bearing from P to B.
Practical Navigation GPS devices automatically calculate and display XTE. Alarm threshold: typically set to 0.05–0.5 nm (100–900 m) depending on context. In the open ocean: ±5 nm acceptable. Near reefs/coast: ±0.1 nm critical. XTE alarm allows skipper to focus on other tasks while GPS monitors deviation.
Units Marine navigation: nautical miles (nm). 1 nm = 1.852 km = 1 minute of latitude. Aviation: nm or km. Road navigation: km or miles.