Distance Off by Two Bearings Calculator
As you steam past a lighthouse or headland on a steady course, two relative bearings taken a known distance apart let you fix how far off you are without any range finder. The two bearings and the run between them form a triangle, and trigonometry gives the distance to the object at the second bearing and the distance off when it comes abeam. Special cases like doubling the angle on the bow and the bow-and-beam bearing fall straight out of the same formula. Enter the two relative bearings and the run distance and this calculator returns both distances.
Two-bearing distance formula
Distance at 2nd bearing = run x sin(A) / sin(B - A)
Distance off abeam = distance at 2nd bearing x sin(B)
A and B are relative bearings from the bow, with B > A
Doubling: if B = 2A then distance at 2nd bearing = run
The two bearings and the straight run between them form a triangle. The law of sines gives the side opposite the change in bearing. Multiplying by sin(B) projects that distance onto the beam.
Running fix notes
- Hold a steady course and speed between the two bearings.
- Bearings are relative to the bow; B must be larger than A.
- Doubling the angle on the bow makes the run equal the distance at the second bearing.
- A bow-and-beam bearing (45 then 90 degrees) makes the run equal the distance abeam.
- Use a charted object whose position you can identify with confidence.
Distance off by two bearings: frequently asked questions
What is the two-bearing distance-off method?
It is a running fix that finds your distance from a fixed object using two relative bearings taken as you pass it, plus the distance you run between the two observations. By forming a triangle from the bearings and the run, trigonometry gives both the distance at the second bearing and the distance off when abeam.
What is the formula for distance off by two bearings?
With first relative bearing A and second relative bearing B (both measured from the bow, B greater than A) and run distance d between them, distance off at the second bearing = d x sin(A) / sin(B - A), and distance abeam = that distance x sin(B). This calculator computes both.
What is doubling the angle on the bow?
It is a special case where the second bearing is twice the first (for example 30 then 60 degrees relative). When the angle on the bow doubles, the distance run between the two bearings equals the distance off the object at the second bearing, a handy mental shortcut needing no tables.
What is a bow-and-beam bearing?
Another special case: take the first bearing at 45 degrees on the bow and the second when the object is abeam at 90 degrees. The distance run between them then equals the distance off when abeam, because sin(45)/sin(45) is 1 and sin(90) is 1.
Why must I keep a steady course and speed?
The method assumes you travel in a straight line at constant speed between the two bearings, so the run distance is the base of a fixed triangle. Any course change or speed change between observations invalidates the geometry and the resulting distance off.
Official sources
- U.S. Coast Guard Navigation Center: Navigation Center.
- NOAA Office of Coast Survey: Nautical Charts.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.