The 1-in-60 rule
One degree of angular offset subtends about one unit of arc in sixty units of distance (the exact factor is 1 radian ≈ 57.3°, so the rule is slightly conservative). Off-course distance is
offset ≈ distance × degrees / 60 (rule), offset = distance × sin(degrees) (exact).
Five degrees off at 30 NM is 2.5 NM by the rule and 2.61 NM exactly. The same identity, inverted, tells you how many degrees of heading change will take out a known offset.
Time to the station
If a bearing (or ADF relative bearing) changes by D degrees in t minutes, the estimated time to the station is tts = 60 t / D minutes, and the distance is groundspeed × that time. This is the classical off-course / timed-turn estimate; it assumes a reasonably constant groundspeed and a station that is not far off the beam geometry you flew.
DME slant range
DME measures the slant range to the facility, not the horizontal distance. If you are h feet above the facility,
horizontal NM = √( DME² − (h / 6,076.12)² )
The difference is noticeable close in and high — for example at 1 NM of height and 2.0 NM DME, the horizontal distance is √3 ≈ 1.73 NM, not 2.0.
Lead radial
To roll out on a course, start the turn about one turn radius before the course. The lead angle from a station is atan(radius / distance). Radius comes from TAS and bank, or from a standard-rate turn (see also the turn radius calculator).
Sources
FAA Pilot’s Handbook of Aeronautical Knowledge (1-in-60, Chapter 16); FAA Instrument Flying Handbook (VOR, DME, time to the station, lead radial); AIM navigation.
Frequently asked questions
When is the 1-in-60 rule close enough?
For the small angles of everyday tracking (a few degrees), it is within a tenth of a mile or so of the exact sine at typical VOR distances. At large intercept angles, use the sine, which this page also shows.
Does DME slant range matter on a typical ILS?
Usually not at glideslope intercept distances. It matters when you are close to a DME facility and high above it — crossing a VORTAC at 6,000 ft AGL, for example — or when you are using DME to identify a close-in fix.
Is time-to-station still useful with GPS?
It is still a good cross-check, and it is the identity many oral exams expect. With GPS, the direct range and time figures are on the box; this math is how you would estimate them from a VOR or ADF bearing change alone.