What fomula use for calculating pressure altitude?

Question

I'm having some trouble making my calculations of pressure altitude match those in apps and text books.

I'm using the formula from Wikipedia:

(29.92 - altimeter setting) * 1000 + airport elevation

In the app I'm using, the altimeter setting is currently reported as 29.70 with an airport elevation of 22. Using the above formula I would assume:

(29.92 - 29.70) * 1000 + 22 = 242

Yet the app is telling me it is 229

Even more confusing, when looking at the Airman Knowledge Testing Supplement for Sport Pilot, Recreational Pilot, Remote Pilot, and Private Pilot (FAA-CT-8080-2H), figure 8, page 2-8, the pressure altitude for altimeter 29.7 is listed as 205. I assume this is using an airport elevation of 0, but then I would expect the answer to be:

(29.92 - 29.7) * 1000 + 0 = 220

So my questions are:

1. Which answer is correct? Wikipedia, the app or appendix 2?
2. Why are there 3 different answers?

Answer 1

The formula from wikipedia is a rough estimation. Think of it as a rule of thumb. It's useful if you need numbers for rough calculations. However, the exact formula is as shown below:

According to that formula, I calculated pressure altitude difference for 28.92 and it's 938 feet, as opposed to 1000 feet. Additionally, as you can tell from the formula, the relationship is not a constant linear value. So difference of 1 inch of HG is not always 938 feet, it's changing.

So, the FAA guide is accurate. And I would say your app is accurate enough also, however probably omitting some numbers after decimal, hence the small difference. Of course, you need to add field elevation on top of those numbers as well.