CPA / TCPA

Closest Point of Approach distance and time from own-ship and target course+speed. The core radar plotting relationship for COLREG compliance.

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This calculator requires JavaScript to compute its result. The formula, symbols, and regulatory sources are shown in the Formula section below.

Formula, assumptions, and limits

\text{CPA} = |r_0 + v_\text{rel} \cdot t_\text{CPA}|, \quad t_\text{CPA} = -\frac{r_0 \cdot v_\text{rel}}{|v_\text{rel}|^2}

Symbol	Meaning	Unit
$r_0$	Current relative position vector	nm
$v_\text{rel}$	Relative velocity = target − own	kn
$CPA$	Closest Point of Approach distance	nm
$TCPA$	Time to CPA	min

Source: IMO Resolution A.823(19) - ARPA performance; COLREGS Rules 7–8

Closest Point of Approach distance and time from own-ship and target course+speed.