CPA & TCPA Calculator – Closest Point of Approach for Radar Plotting

⚙️ How to Use

Use this tool for collision avoidance training and maneuvering board practice. Choose your input mode based on available data.

Mode A: Radar Plot

When to use: Use this mode when you are performing manual plotting from raw radar observations and need to deduce the target's true motion from two successive relative positions.

Select Mode A to practice manual radar plotting.

Enter Own Ship Course and Speed.

Provide two timed observations (Bearing and Range) of the target.

The calculator will recover the Target's True Course and Speed, then solve the relative motion triangle.

Mode B: ARPA Direct Vector

When to use: Use this mode when you already have the target's true course and speed from your ARPA or AIS and want to quickly calculate CPA, TCPA, and BCR.

Select Mode B if you already have the target's True vector from AIS or ARPA.

Input Own Ship and Target Course & Speed.

Input the instantaneous Bearing and Range to the target.

Note: This tool is for training and educational purposes only. Never rely on it for actual navigation or collision avoidance. Always comply with the COLREGs and use certified equipment.

📖 Definitions

CPA (Closest Point of Approach)

The minimum distance between your vessel and a target, assuming both maintain current course and speed.

TCPA (Time to CPA)

The time remaining until the CPA is reached. A negative TCPA means the CPA has already passed.

BCR (Bow Crossing Range)

The distance from your vessel to the point where the target's relative track crosses your heading line.

BCT (Bow Crossing Time)

The time at which the target will cross your heading line.

DRM & SRM

Direction of Relative Movement and Speed of Relative Movement define the apparent motion of the target relative to your own ship.

📐 Worked Example

Let's solve a simple crossing situation:

Own Ship: COG 000°T, 10 kn
Target: Bearing 045°T, Range 10 NM
Target Vector: COG 270°T, 10 kn

1. Both ships are closing at a 90° angle. Own ship moves North, target moves West.

2. The relative velocity resolves to a relative speed (SRM) of 14.1 knots (√2 × 10).

Result:

CPA = 7.07 NM

TCPA = 30.0 min

BCR = +10.0 NM (Target crosses ahead)

Complete Guide to CPA & TCPA in Radar Plotting

Maintaining a proper lookout and accurately assessing collision risks are the most fundamental duties of any Officer of the Watch (OOW). Utilizing marine radar and Automatic Radar Plotting Aids (ARPA) allows navigators to calculate two absolutely critical metrics: the Closest Point of Approach (CPA) and the Time to Closest Point of Approach (TCPA). Our professional CPA & TCPA Calculator streamlines these complex relative motion calculations to help you swiftly verify target vectors and avoid dangerous close-quarters situations at sea.

Understanding CPA and TCPA

The Closest Point of Approach (CPA) is defined as the absolute minimum distance that will eventually exist between your own ship and a target vessel, assuming both vessels strictly maintain their current true courses and true speeds. It is essentially the predicted closest passing distance.

The Time to Closest Point of Approach (TCPA) simply represents the amount of time remaining until that exact moment of CPA occurs. A negative TCPA value indicates that the target vessel has already passed its closest point and the distance between the two ships is now actively increasing.

How Relative Motion Works on a Maneuvering Board

When you plot a target on a radar screen or a traditional maneuvering board, you are dealing with relative motion. Because your own vessel is also moving forward, the target's apparent movement across the radar screen (the Direction of Relative Movement, or DRM) differs from its actual true course over the water.

Speed of Relative Movement (SRM): How fast the target appears to be approaching your center point.
Bow Crossing Range (BCR): The distance at which the target will eventually cross ahead of your vessel's bow.
Collision Course: If the target's relative bearing remains constant and the range is actively decreasing, the CPA will be zero, meaning a collision is imminent.

Practical Example: Assessing a Collision Risk

Consider a practical scenario. You are steaming on a true course of 090° at 15 knots. Your ARPA system acquires a target ship on your starboard bow. The ARPA data shows the target has a CPA of exactly 0.5 Nautical Miles and a TCPA of 12 minutes.

Based on standard company Standing Orders, a CPA of 0.5 NM is considered unacceptably close (most commercial fleets mandate a minimum CPA of 1.0 to 2.0 NM depending on open sea or coastal waters). Because the TCPA is 12 minutes, you have a brief window to take substantial action. As the give-way vessel under the COLREGs, you execute a bold course alteration to starboard, successfully opening the CPA to a safe 2.5 Nautical Miles. This calculator lets you instantly verify such maneuvers without relying solely on the bridge ARPA.

⚓ CPA & TCPA Calculator – Closest Point of Approach for Radar Plotting

Calculation Mode

Own Ship Data

Target 1