Converting mb (pressure) to altitude, and sites where this is useful

Mick West

Administrator
Staff member
When studying contrails, you quite often come across diagrams and charts where instead of the altitude in feet or meters, we are given a pressure value in mb (millibars, sometimes also labeled hPa, which is exactly the same unit)

For example, on the excellent site earth.nullschool.net, we have:


Converting between mb and altitude is a slightly complex formula*​ you can't do in your head. Here's a spreadsheet that does it for a variety of values:
Source: https://docs.google.com/spreadsheets/d/1nDolj1BIv4HcyLYMA32_53S8-BKPu29Fc4cfYK_lC1s/edit?usp=sharing

20161022-100215-18cax.jpg

But in order to more easily use the various sites that use mb/hPa, it's useful to remember a few things.

It's not exact. Pressure varies with the weather, so the conversion is only an approximation. It's generally good to within about 100 feet though.

Higher pressure is lower altitude. So the smaller the mb, the higher we are in feet.

1000 mb is about sea level. The international standard is 1013.2, but "about 1000" is easier to remember.

300 mb is about 30,000 feet. An easy one to remember, most contrails in temperate areas like the US (excepting Alaska) happen above 30,000 feet, so pressure under 300 mb is generally where contrails will form. However, they can form at higher pressure (lower altitude). The key factor is really temperature.

250 mb is about 34,000 feet. This is a very typical cruise altitude. It's also the only cruise altitude that earth.nullschool.net gives as an option. It's a little harder to remember than 300/30000, but it's a nice round number for the middle of the cruise altitude range.

150 mb is about 44,000 feet. This is a useful upper range for possible commercial planes, which will rarely fly about that level.

100 mb is about 52,000 feet. Pretty much a hard limit for the majority of planes, so you can usually discount any mb that's in two digits

Other than nullschool, a great place to use this is NASA's contrail forecast page:

http://cloudsgate2.larc.nasa.gov/cgi-bin/site/showdoc?docid=33&cmd=latest

Here the range is 400mb (23,500 feet) to 125mb (48,000 feet). The color indicates the likely altitudes where contrails will from. Notice the difference between north and south. Lots of green over the US, indicating around 250mb (34,000 feet), the sweet spot contrail altitude.

And of course you will see it a lot on weather charts, for example:

source: http://weather.rap.ucar.edu/upper/
This is a 500mb RH and temperature chart. The green indicates above 70% RH, but since it's only 500mb (around 18,000 feet) we know immediately most of this area will not be cold enough. However look at the -40 line near the top, it's possible some areas of Alaska could see low altitude contrails today.

Regarding units, we are discussing atmospheric pressure here, and most people will be familiar with this as the pressure at ground level, and using the change in that pressure to forecast changes in the weather (higher pressure is clear, lower pressure means rain, very roughly). So you might have seen a barometer like this:

Notice there are two scales, the outside one goes from 28 to 31, and represents inHg (inches of mercury). The inside one goes from 950 to 1050, and represents mb (millibars).

Different units are used both in different situations, and in different parts of the world. In aviation we use inHG (the 28-31 range) to use in calibrating altimeters. In meteorology we more commonly use mb (millibars). But in countries that use the metric system (most of the world) it's common to use the term hPa (hectopascals), which is exactly the same thing as a millibar.

There's one more common unit used, millimeters of mercury, or mmHg, which is just a metric version of inHg, but unlike the mb/hPa, the units are different. Here's all three units on one Barometer:


And where does this "inches/mm of mercury" come from? Well early barometers use a three foot long glass tube inserted into a reservoir of mercury. Not very practical.



* Formula to convert from millibars to feet:
LaTeX:
\[(1-(millibars/1013.25)^{.190284}))*145366.45\]
(1-(millibars/1013.25)^.190284))*145366.45
 
Last edited:

WeedWhacker

Senior Member
I find the handy way is to (for example) copy/paste and then print your part above...in about the middle...and use as a handy reference. (Starting with "1000 mb is about sea level". Of course, the accepted "standard atmosphere" is 1012.3, but "1000" is close enough, of course, for this purpose).
 

Mick West

Administrator
Staff member
I find the handy way is to (for example) copy/paste and then print your part above...in about the middle...and use as a handy reference. (Starting with "1000 mb is about sea level". Of course, the accepted "standard atmosphere" is 1012.3, but "1000" is close enough, of course, for this purpose).
1013.2, I was confused, remembering the standard 29.92 inHg, as 992 mb. Niner niner! Fixed it in the OP.
 

TWCobra

Senior Member
I had a word to the creator of the "Earth" website about including data from around 38000 feet. he was receptive but said it would take a bit of time.
 

WeedWhacker

Senior Member
I had a word to the creator of the "Earth" website about including data from around 38000 feet. he was receptive but said it would take a bit of time.
I think it's an "uphill battle" of a sort, the "Sisyphean" task (related to the ancient Greek myth of "Sisyphus") to explain to those who have not actually experienced high altitude flight. No disrespect to many learned people, but it DOES require (beyond the study from books and other materials) a bit of additional practical experience as well.

(Noting: We pilots, all, who have flow to such altitudes ALSO studied the concepts beforehand, but "learned" the most from the actual experience. Along, of course, with some mentoring).
 

Ross Marsden

Senior Member
The reason it would "take a bit of time" is that the modeled data is distributed in the format of data on certain standard pressure levels. These are (in the upper levels) ... 500, 400, 300, 250, 200, 150, 100, 70, 50 hPa.
The creator of "earth" has selected a sub set of those.
To create another level, a non-standard one, he would need to find the pressure level of 38000 feet in the ISA and then interpolate the wind and other data from the available pressure levels to the new one.

Now, this brings up the matter of height, altitude and flight level.
Above a certain transition altitude / flight level aircraft are required to set the altimeter subscale to 29.92 inHg or (1013.25 hPa) so that the aneroid altimeter then indicates altitude as a "flight level". It may read 35000 ft or F350 but the plane is not flying 36,000 feet above the ground. It is flying on the 300 hPa pressure surface which is generally not level in relation to the earth's surface. The 36000 feet is the height of 300 hPa in the International Standard Atmosphere which is ground referenced to 0 feet at 1013.25 hPa.

http://en.wikipedia.org/wiki/International_Standard_Atmosphere
 

Trailblazer

Moderator
Staff member
Above a certain transition altitude / flight level aircraft are required to set the altimeter subscale to 29.92 inHg or (1013.25 hPa) so that the aneroid altimeter then indicates altitude as a "flight level". It may read 35000 ft or F350 but the plane is not flying 36,000 feet above the ground. It is flying on the 300 hPa pressure surface which is generally not level in relation to the earth's surface. The 36000 feet is the height of 300 hPa in the International Standard Atmosphere which is ground referenced to 0 feet at 1013.25 hPa.

http://en.wikipedia.org/wiki/International_Standard_Atmosphere
Are you sure you have the right numbers there, @Ross Marsden? 300 hPa is not close to 36,000 ft.
 

Ross Marsden

Senior Member
Are you sure you have the right numbers there, @Ross Marsden? 300 hPa is not close to 36,000 ft.
Sorry, as Mick said, 300 hPa is approximately 30,000 feet F300.

Here is the corrected part of that paragraph:
It may read 30000 ft or F300 but the plane is not flying 30,000 feet above the ground. It is flying on the 300 hPa pressure surface (approximately) which is generally not level in relation to the earth's surface. The 30,000 feet is the approximate height of 300 hPa in the International Standard Atmosphere which is ground referenced to 0 feet at 1013.25 hPa.
 

JFDee

Senior Member
Above a certain transition altitude / flight level aircraft are required to set the altimeter subscale to 29.92 inHg or (1013.25 hPa) so that the aneroid altimeter then indicates altitude as a "flight level".
A little addendum: there is a good reason why 'flight levels' (pressure altitudes) are important in aviation.

If you set your altimeter before take-off to match the actual elevation, it will give you the altitude correctly only if you stay in the region surrounding your airfield and the weather does not change during your flight. This is because the altimeter is basically a barometer - any variation of the prevailing air pressure during flight will be reflected and will make your altitude reading inaccurate.

Now imagine two planes having taken off at two airfields a hundred miles apart. Each has set the altimeter correctly at take-off, but the air pressure between the two areas is different. If those planes meet in the middle, they might have a problem.
If they intended to be at the same level according to their altimeter, they will not. More importantly, if they intended to keep a vertical distance from each other, they can't be sure to maintain that distance - which can be dangerous.

If everyone sets their altimeter to a commonly agreed fixed base value when travelling, the actual altitude reading will most likely be inaccurate and variable with conditions, but it will make sure that all relative measurements are correct. So if you get the reading of 6000 ft you may actually be at 5880 ft, but the vertical distance to annother plane that reads 5500 ft is still 500 ft because the other plane is actually at 5380 ft.

(Obviously you shouldn't do that when flying closer to the ground or during take-off and landing.)
 

Ross Marsden

Senior Member
I should have said that aneroid altimeters are carefully made and calibrated to exactly model the International Standard Atmosphere.
 
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