VMG (Velocity Made Good) Calculator

Velocity Made Good Formula

Signed VMG = boat speed × cos(angle); use radians inside the cosine function.

Choose the Reference Axis

Velocity made good is a projection of travel speed onto a chosen direction. In wind-axis mode, positive values mean progress toward the wind and negative values mean progress away from it. In waypoint mode, positive values mean closing on the waypoint and negative values mean moving away along that reference. Zero means no instantaneous component along the selected axis. The reference choice changes the interpretation, not the cosine arithmetic.

Use Consistent Speed and Direction Data

For the wind-axis calculation, use speed and course through the water relative to the wind axis. If you use heading as an approximation to travel direction, leeway can change the actual projection. For waypoint closure, use speed over ground and the angle between course over ground and the waypoint bearing. Mixing through-water speed with a ground-track angle can give a misleading answer when current is present.

Three Solve Modes

VMG mode needs boat speed and angle. Speed mode rearranges the equation to VMG ÷ cos(angle). Angle mode uses acos(VMG ÷ speed), with a result between 0 and 180 degrees. The angle gives the size of the separation from the reference and does not distinguish port from starboard. Inputs can use degrees or radians and knots, miles per hour, kilometers per hour, or meters per second. Changing a unit converts the entered quantity. Supported speed magnitude is at most 1,000 knots.

Indeterminate and Impossible Inputs

At 90 degrees, the projection is zero regardless of boat speed, so VMG alone cannot determine speed there. At zero boat speed, angle cannot be recovered from VMG. A supplied VMG magnitude cannot exceed the boat-speed magnitude in angle mode. A positive VMG paired with an angle greater than 90 degrees would require negative speed in speed mode, so that sign-inconsistent combination is rejected. Zero speed is valid in direct VMG mode.

Worked Projection Example

A boat speed of 6 knots at a 60-degree reference angle gives 6 × cos(60°) = 3 knots of positive VMG. The cross-axis speed magnitude is approximately 5.196 knots. At 120 degrees, the same speed gives -3 knots along the selected reference. The boat is still moving at 6 knots in both examples; only the direction of progress along the axis has changed.

Compare Complete Sailing Scenarios

A smaller angle does not necessarily produce more VMG if the boat slows while achieving it. For an arithmetic illustration, 6 knots at 45 degrees gives about 4.243 knots of VMG, while 7 knots at 60 degrees gives 3.5 knots. These are supplied scenarios, not predictions for a named boat or wind strength. To estimate an achievable optimum, use appropriate measured performance or a boat-specific polar and the actual conditions.

Result Details and Limits

The result includes signed VMG, boat speed, angle, cross-axis magnitude, and the signed projection percentage. Cross-axis magnitude omits which side of the reference the boat travels on. A single projection does not account for a future tack, changing waypoint bearing, waves, acceleration, or changing current. Wind VMG and waypoint progress may differ even at the same instant, and neither is an arrival-time forecast by itself.

Reference Table

Sources

Garmin, GNX Wind Owner’s Manual: Velocity Made Good, and Waypoint VMG and Wind VMG support guidance, accessed 2026. US Sailing, Speed Guide Explanation, accessed 2026. Vector projection and inverse trigonometric identities.