Position fixes — Running Fix and waypoint navigation

KnotWise includes two position-fixing calculators that complement GPS-based navigation. The Running Fix derives a position from two bearings of the same object taken at different times. The Waypoint calculator gives bearing, distance, cross-track error and ETA to a destination. Both work offline and are available on every plan.

Running Fix

A classic technique for fixing position when a single landmark or buoy is visible but no second landmark is available. You take a bearing, run a known distance on a known course, take a second bearing of the same object, and compute the position at the second observation.

KnotWise offers three modes via tabs at the top of the calculator. Each represents a special case with progressively simpler input.

General method

Works with any two bearings. Uses the sinus law on the triangle formed by the first bearing (advanced), the course-and-distance vector and the second bearing.

The output is the distance from the object at the second observation. With object coordinates entered, the calculator returns the full fix position. A crossing-angle indicator shows whether the geometry is reliable.

Double Angle on the Bow

A special case where the relative bearing to the object doubles between the two observations — for example, 30° relative, then 60° relative. Under this condition, the distance to the object at the second observation equals the distance run. No trigonometry is required; the result follows directly from the geometry of the isosceles triangle.

Useful when you can choose your observation times. Take the first bearing at any convenient relative angle, then mark off twice that angle on your compass and wait until the bearing reaches the second value.

Bow and Beam (Four-Point Bearing)

A further special case where the first bearing is taken at 45° relative (four points off the bow) and the second is taken when the object is exactly on the beam — 90° relative. Under this condition, the distance off at the beam equals the distance run between the two bearings.

The simplest of the three modes and the most popular in traditional pilotage. Useful for offshore objects passing abeam during a coastal passage.

Bearing convention

All three modes require bearings to be true bearings. If you read bearings from a compass, convert them first — KnotWise includes a Compass Correction calculator for this purpose. Distance run must come from the ship's log or GPS, consistent with the course recorded.

Waypoint and XTE

Computes bearing, distance and cross-track error from your current position to a waypoint, with optional ETA if you supply a speed. Useful for setting a course to a destination, checking how far you have drifted from your intended track, or estimating arrival.

The output is bearing to the waypoint, distance to the waypoint, cross-track error relative to the start-to-waypoint track, and ETA if speed is supplied. Both rhumb line and great circle results are shown — for short distances they are identical to within a fraction of a mile.

Shared features across the position-fix cluster

Both calculators offer the coordinate format toggle (degrees-minutes or decimal degrees) and an expandable formula panel. The Running Fix includes an SVG diagram showing the bearings, the course vector and the resulting fix. Inputs are session-only — use Export PDF or Save to Logbook to preserve a calculation.

Accuracy and limits

• Crossing angle: A Running Fix is reliable when the angle between the first (advanced) and second bearings is between 30° and 150°. Outside this range, small bearing errors produce disproportionately large position errors. The calculator displays a warning when the angle crosses these thresholds.
• Drift: The basic Running Fix assumes constant course and speed between observations. Wind, current and leeway are not accounted for. If significant drift is suspected, use the Current Triangle calculator to compute the effective ground track first.
• Bearing accuracy: Hand bearing compass readings on a moving vessel typically carry ±2° to ±5° error. Steering compass readings are no better. This is the dominant source of error in most Running Fixes.
• Waypoint distance: Rhumb line and great circle differ measurably for distances above roughly 600 nautical miles or at high latitudes. For ocean passages, use the great-circle figure.

Frequently asked questions

Why must bearings be true?

The Running Fix is a geometrical construction on the chart. True bearings correspond directly to chart geometry; magnetic and compass bearings include offsets that vary with location and vessel and would distort the triangle. Convert to true first using the Compass Correction calculator, then enter the result here.

What does «crossing angle» mean?

It is the angle between the first bearing (advanced forward to the time of the second observation) and the second bearing. A narrow crossing angle — below 30° — means the two position lines are nearly parallel; small bearing errors then produce large fix errors. A near-perpendicular crossing angle around 90° gives the most reliable fix.

Why does my Running Fix differ from GPS?

Three likely sources, in order of frequency: bearing accuracy, drift between observations (wind, current, leeway not accounted for), and distance run accuracy. A 2° bearing error at 10 nautical miles is 0.35 nautical mile of position error.

Can I use my chartplotter waypoints?

Inputs are manual. Read the waypoint coordinates from your chartplotter or paper chart and enter them in the calculator. Direct integration with chartplotters is not part of the current calculator scope.

Is the rhumb-line or great-circle distance more accurate?

Both are exact for their respective tracks. A rhumb line is a constant-course track; a great circle is the shortest path. For short distances they agree. For ocean passages, plan your route along the great circle but steer along rhumb-line segments between intermediate waypoints.