True Wind Calculator (Sailing)

A sailboat's wind instruments read apparent wind — the wind actually felt onboard, which combines the true wind (the wind blowing over the water if the boat were standing still) with the headwind created by the boat's own motion. Treating apparent wind as a vector and subtracting the boat's velocity vector (boat speed, pointing dead ahead) recovers the true wind vector: trueWindX = AWS·cos(AWA) − boat speed, trueWindY = AWS·sin(AWA), then true wind speed = √(trueWindX² + trueWindY²) and true wind angle = atan2(trueWindY, trueWindX) — the standard sailing-navigation decomposition, verified via web search against published true-wind references, and algebraically identical to the textbook law-of-cosines relation TWS² = AWS² + BS² − 2·AWS·BS·cos(AWA).

Apparent wind angle and boat speed are both entered exactly as read off the boat's own instruments/knotmeter (0° is dead ahead, 180° is dead astern), so nothing here is looked up or assumed — only computed from what the sailor already has in front of them.

A well-known consequence of this geometry: as boat speed increases, the apparent wind angle always sits forward of (smaller than) the true wind angle — the reason a fast boat feels like the wind has 'moved forward' even when the true wind direction hasn't changed at all.