Running Fix Position Calculator
With a single landmark you can still fix your distance off by taking two bearings on a steady course and noting the distance run between them. The two relative bearings and the run between them form a triangle that the law of sines solves for your distance off the object at the second bearing, and for the distance off when the object is abeam. Enter the two relative bearings (measured from the bow) and the distance run to get your distances.
Running-fix formula
A = first relative bearing, B = second relative bearing, D = run
Distance off at second bearing = D * sin(A) / sin(B - A)
Distance off when abeam = distance off at second bearing * sin(B)
When B equals 2A (doubling the angle on the bow), the distance off at the second bearing equals the run D.
Worked example
- First bearing 30 degrees, second 60 degrees, run 4 nm.
- Distance off at second bearing = 4 * sin(30) / sin(30) = 4.00 nm.
- This is the doubling-the-angle case, so the distance off equals the run.
- Distance off when abeam = 4 * sin(60) = 3.46 nm.
Running fix: frequently asked questions
What is a running fix?
A running fix finds your position from two bearings of the same object taken at different times, advancing the first line of position along your course by the distance run between the bearings. From the two relative bearings and the run between them you can solve the triangle for your distance off the object at the second bearing.
What is the running-fix formula?
Using relative bearings A (first) and B (second) measured from the bow, and the distance run D between them, the distance off when abeam or at the second bearing follows from the law of sines. Distance off at the second bearing = D * sin(A) / sin(B - A). The angle between the two lines of position is B minus A.
What is the special doubling-the-angle case?
When the second relative bearing is twice the first (for example 30 degrees then 60 degrees), the distance run between the bearings equals the distance off the object at the second bearing. This handy special case is called doubling the angle on the bow, and the calculator confirms it when B equals 2A.
What inputs do I need?
You need the relative bearing to the object at the first observation, the relative bearing at the second observation, and the distance run (speed times time) between them. Relative bearings are measured from the bow, so an object 30 degrees off the bow is a relative bearing of 30 degrees.
Official sources
- NOAA Office of Coast Survey: coastal navigation and charts.
- NIST: unit conversions (nautical mile).
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.