Height equals TCH plus distance times tan θ
A published ILS glideslope is a straight line in space that crosses the landing threshold at the threshold crossing height (TCH) printed on the approach chart, typically about 50 or 55 feet for a 3.00° path in the United States. If x is the distance to the threshold and θ is the path angle,
h = TCH + x tan θ.
At 3.00°, tan θ is 318.4 feet per nautical mile (using 1 NM = 1,852 / 0.3048 ft), so one mile from the threshold on a 50-foot TCH you are about 368 feet above the runway. The same identity inverted is the distance for a given height. A DME located past the threshold reads a slightly larger range than x; entering that offset subtracts it before the tangent is applied. Descent rate on a constant path is groundspeed times feet per nautical mile, divided by 60 — the same identity used on this site’s descent-rate calculator. A visual descent point, by contrast, is a plan-view fix, covered separately on the VDP page.
What the geometry does not capture
The real beam is a hyperbolic locus of a constant-difference signal, approximated as a straight line only near the runway. Terrain, a displaced threshold, and a non-standard TCH all change the number you should fly. Use the published glide path, TCH, and minima; this page does not replace a DA, an RA, or a PAPI. A 3° path at 90 knots is about 478 fpm, a little steeper than the familiar “groundspeed × 5” rule of 450 fpm, which assumes a slightly shallower angle.
Sources
- ICAO Annex 10 and Doc 8168 (PANS-OPS), ILS glide-path angle and threshold crossing height.
- FAA Instrument Flying Handbook and Aeronautical Information Manual (ILS, TCH, and descent rates).
- FAA Order 8260.3 (United States Standard for Terminal Instrument Procedures, TERPS), straight-in approach geometry.
Frequently asked questions
Why is a 3° slope 318.4 ft per NM, not 300?
A 3° angle is a 5.24 percent grade, and one nautical mile is 6,076.12 feet, so the rise is 6,076.12 × tan 3° ≈ 318.4 ft. The “300 ft/NM” memory item is a rough 3-percent stand-in, not the ILS figure.
Should I use DME or distance to the threshold?
The formula uses distance to the landing threshold. If you only have a DME that sits past the threshold, enter the published antenna offset and check “Distance is DME” so the page subtracts it.
Is this a DA or a visual descent point?
No. Decision altitude comes from the approach chart. A VDP is a plan-view point for the missed-approach point; this page only converts a straight path into a height.