Holding Pattern Entry Calculator: How It Works

A holding pattern entry calculator works out which of the three standard entry procedures—direct, teardrop, or parallel—you should use when joining a holding pattern, based on your inbound course and the holding radial. You enter your current heading and the holding radial, and the calculator returns the recommended entry type plus the initial heading to fly. This removes the mental trigonometry during a busy arrival, letting you focus on flying the procedure.

Formula

The standard entry determination uses the angular difference between your current heading and the holding radial. The holding radial is the course you fly to the fix (the inbound course). The three sectors are defined as follows:

• Direct entry: your heading is within 90° to the left of the inbound course (i.e., from radial−90° to radial).
• Teardrop entry: your heading is within 90° to the right of the inbound course (i.e., from radial to radial+90°).
• Parallel entry: your heading is in the remaining 180° opposite the inbound course.

In the calculator, the formula uses the heading (H) and the radial (R) in degrees, normalized to 0–360. The entry is determined by:

If R−90 ≤ H < R → Direct

If R ≤ H < R+90 → Teardrop

Otherwise → Parallel

The initial heading for teardrop is R+30° (a 30° offset from the inbound course), and for parallel it is R−30° (a 30° offset to the left). For direct entry, the initial heading is simply R (fly directly to the fix).

Worked Example

Using the default values: your heading is 180° and the holding radial is 090°.

1. Compute the angular difference: 180° − 90° = 90°.
2. Check the sectors: 90° is not less than 90° (for direct), but it is within the teardrop sector (90° to 180°). So the entry is teardrop.
3. Initial heading = radial + 30° = 090° + 30° = 120°.

The calculator returns: Teardrop and initial heading 120°.

How to Use the Calculator

Enter your current heading (the direction you are flying at the moment) and the holding radial (the inbound course to the fix, as published on the chart). The calculator then tells you which entry to fly and the initial heading to turn to. For a direct entry, you simply fly directly to the fix and then turn to the outbound course. For a teardrop, you turn to a heading 30° to the right of the inbound course (i.e., radial+30°) and fly for the outbound time, then turn back to the fix. For a parallel, you turn to a heading 30° to the left of the inbound course (radial−30°) and fly parallel to the inbound course for the outbound time, then turn back to the fix.

When to Use It

This calculator is most useful during instrument flight training, when practicing holds, or when you are being vectored into a hold and want to confirm your entry. It is also handy for flight simulators and for studying for the FAA instrument written exam. However, in real-world IFR operations, ATC will often issue a “direct” entry if they want you to fly straight in, but you must still be able to determine the correct entry yourself.

Common Mistakes

• Using the outbound course instead of the inbound course: The holding radial is always the course you fly to the fix, not the outbound leg.
• Not normalizing headings: If your heading is 350° and the radial is 010°, the calculator may give a parallel entry, but you need to add 360° to the radial to get the correct sector. Most calculators handle this, but be aware when doing it manually.
• Confusing teardrop and parallel: The teardrop is a 30° offset to the right (in the direction of the holding side), while the parallel is a 30° offset to the left (opposite the holding side).
• Forgetting wind correction: The calculator assumes no wind. In real flight, you must adjust your heading to maintain the correct ground track.

Limitations of the Formula

The standard entry formula is based on the assumption that you are approaching the fix from a specific direction and that you turn in the standard direction (right turns for a standard hold). It does not account for wind, which can cause you to drift off course. It also assumes that you are at the correct altitude and speed. The entry type is only a recommendation; ATC may issue a different instruction, and you must follow it.

Frequently Asked Questions

What if my heading is exactly on the boundary between sectors?

If your heading is exactly equal to the radial (or radial−90°), the calculator will treat it as the lower sector (direct or teardrop). In practice, you can choose either entry if you are on the boundary, but it is safer to pick the one that requires less turning.

Does the calculator work for non-standard holding patterns?

No, it assumes a standard pattern with right turns. For left-turn holds, you would reverse the teardrop and parallel offsets.

Can I use this for VFR practice?

Yes, but it is primarily designed for IFR procedures. For VFR, you can still use it to practice holding entries, but you must be aware of airspace restrictions.

Why does the calculator give a parallel entry when I am coming from the opposite direction?

That is correct. If you are approaching the fix from the side opposite the holding side, you need to fly parallel to the inbound course to get onto the correct side before turning back.

What if the holding radial is given as a radial from the VOR, not a heading?

The holding radial is the inbound course, so it is the same as the heading you would fly to the fix in no wind. The calculator uses that value directly.

Alternatives

Instead of using a calculator, you can use the “thumb rule” or a paper E6B. The thumb rule involves holding your thumb over the heading indicator to visualize the sectors. Many pilots also use a simple diagram on a kneeboard. However, a calculator is faster and reduces error, especially when you are busy.

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in hdg | Your heading | deg | 180 | 0
in rad | Holding radial | deg | 090 | 0
out entry | Entry type | - | if(and(hdg>=rad-90,hdg=rad,hdg=rad-90,hdg=rad,hdg