Speed Over Ground with Current Calculator
Speed over ground (SOG) is what GPS reads and what governs your true progress along a passage. It combines the speed your boat makes through the water with the current beneath you. Enter your speed through the water and heading, plus the current set (the direction it flows toward) and drift (its speed), and this tool resolves both into north and east components, adds them, and returns your resultant speed over ground and course over ground. Use it to estimate arrival times, allow for foul tides, and pick a heading that holds your intended track.
Speed over ground formula
Boat east = STW * sin(heading)
Boat north = STW * cos(heading)
Cur east = drift * sin(set)
Cur north = drift * cos(set)
E = boat east + cur east
N = boat north + cur north
SOG = sqrt(E^2 + N^2)
COG = atan2(E, N) in degrees, normalised to 0 to 360
Each velocity is split into east and north components using its true bearing, where bearings are measured clockwise from north. The components are summed and the resultant magnitude is the speed over ground; its direction is the course over ground. The track offset is the difference between course over ground and the steered heading.
Worked example
A boat makes 6 knots through the water on a heading of 090 degrees true. The current sets toward 180 degrees true (south) at 2 knots. Boat components: east = 6, north = 0. Current components: east = 0, north = -2. Sum: E = 6, N = -2. SOG = sqrt(36 + 4) = sqrt(40) = 6.32 knots. COG = atan2(6, -2) = 108.43 degrees true. The cross-current pushes the track 18.43 degrees south of the heading.
Speed over ground: frequently asked questions
What is the difference between speed through water and speed over ground?
Speed through the water (STW) is how fast your hull moves relative to the water around it, as read by a paddle-wheel or impeller log. Speed over ground (SOG) is how fast you move relative to the seabed, as read by GPS. They differ whenever a current is flowing: a favourable current adds to your SOG, a foul current subtracts from it, and a cross-current pushes you off course.
How is speed over ground calculated from current?
Your boat's velocity through the water and the current's velocity are each vectors (a speed and a direction). Speed over ground is the magnitude of their vector sum. This calculator resolves each velocity into north and east components, adds them, then takes the resultant magnitude for SOG and the arctangent of the components for course over ground (COG).
What is set and drift?
Set is the compass direction the current flows toward, in degrees true. Drift is the current's speed, usually in knots. Together they form the current vector. Tide tables and current atlases published by NOAA give predicted set and drift for many waterways.
Why does my course over ground differ from my heading?
A cross-current carries the boat sideways while it moves forward, so the actual track over the ground (course over ground) is offset from the direction the bow points (heading). The angle between them is the set and drift effect; navigators correct for it by steering an upstream heading.
Official sources
- NOAA Tides and Currents: predicted current set and drift.
- NOAA Office of Coast Survey: nautical charts and navigation.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.