A reliable formula cannot exist, because the relationship between PO2 and SpO2 is not linear. However you can use one useful threshold.

PaO2/FiO2, also known as P/F index, amounting to 285 could be equivalent to SpO2/FiO2 428. 

Few months ago I read a paper about SpO2/FiO2 ratio. If I can find it I will send you

Here are the papers!

Please note that the third link goes to free full text paper.

Enjoy yourself

marco

http://www.ncbi.nlm.nih.gov/pubmed/24362445

http://www.ncbi.nlm.nih.gov/pubmed/17573487

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3776410/

Thank you very much Marco.

The most of calculations are very bad algebraically invertible, but always it is possible to use Newton method, because the function sO2 from pO2 is monotone.

Very simple empirical recalculation at fixed conditions:

Severinghaus, J. W. (1979). "Simple, accurate equations for human blood O2 dissociation computations." Journal of Applied Physiology 46(3): 599-602.

Only oxygen with structural hemoglobin changes:

Monod, J., et al. (1965). "On the nature of allosteric transitions: a plausible model." Journal of Molecular Biology 12(1): 88-118.

With pH,CO2 and temperature dependences based on physical chemistry:

Mateják, M., et al. (2015). "Adair-based hemoglobin equilibrium with oxygen, carbon dioxide and hydrogen ion activity." Scandinavian Journal of Clinical & Laboratory Investigation: 1-8.

With pH, CO2 and DPG based on empirical tanh function:

Siggaard-Andersen, O. and M. Siggaard-Andersen (1990). "The oxygen status algorithm: a computer program for calculating and displaying pH and blood gas data." Scandinavian Journal of Clinical and Laboratory Investigation 50(S203): 29-45.

Dash, R. K. and J. B. Bassingthwaighte (2010). "Erratum to: Blood HbO2 and HbCO2 dissociation curves at varied O2, CO2, pH, 2, 3-DPG and temperature levels." Annals of Biomedical Engineering 38(4): 1683-1701.

Article Adair-based hemoglobin equilibrium with oxygen, carbon dioxi...

Pandharipande paper not bad for this

http://www.ncbi.nlm.nih.gov/pubmed/?term=Crit+Care+Med+2009+Vol.+37%2C+No.+4+pandharipande

A formula cannot exist, because the relationship between PO2 and SpO2 is not linear. Oxymeter is calibrate for a single value : PaO2 60mmHg = SpO2 90%+/-5% aproximativement.

Yes, I know that the relationship is sigmoid and not linear between P02 and Sp02. But thank you for your answer. And also, thanks for the great many articles that everyone has posted. Particularly the Journal of Intensive Care article concenring acute lung injury. It appears that one can use non-invasively the Sp02/Fi02 formula mentioned in that article, and it correlates very strongly with Pa02/Fi02 quotients, provided that the  Sp02

Why do you need to do this? It seems a strange thing to do when measuring it is easy? Will depend on CO, Temp, pH, 23DPG. 

There is no easy way to do it.

Ben Piper's statement that the SO2-pO2 relationship depends on CO is invalide! It is, of course, CO2 (or more accurately: the actual pCO2), not CO, that shifts the oxyHb dissociation curve!

Typo yes CO2. Auto correct is a pain.

I disagree with Ben Piper. Auto correct is NOT a pain. It's funny.

Pheraphs when CO (cardiac output) is low, really oxyHb dissociation curve changes !!!

smile

I don't think anyone has done any better that Severinhaus' equations.

John W. Severinghaus. Simple, accurate equations for human blood O2 dissociation computations. J. Appl. Physiol: Respirat. Environ. Exercise Physiol. 46(3):599-602, 1979. revisions, 1999, 2002, 2007

Hey John Feiner, absolutely awesome article (Severinghaus)! That is exactly what I was looking for, and should serve as an excellent reference for all future work. Thanks for recommending it.

Glad I could help.  I use these formulas all the time to create oxyhemoglobin dissociation curves for teaching and other purposed.  Created user defined functions in Excel to make it easier.  Severinghaus is still alive and well.

Please share with us these Severinghaus' papers !!

I can send you all five papers that I wrote here a week ago (including Severinghaus), just write me a email to marekmatfyzcz . 

Aoa. Dear Sir. While during cardiac catheterization I sent ABG.s of pulmonary artery which did not show spo2 while it showed po2 86mmhg. How I can estimate or calculate spo2?

 I guys! 

Have been following your chat. I was wondering of someone has the conversion on excel. I'm getting crazy trying to put the Severinghaus formula with SaO2 (from the pulse oximeter) and I get weird PaO2 values.

Thanks a million!

I have put the formulas in the user defined function in Excel.  I am happy to share this.

I have tried to describe the functions on the sheet.  You will have to enable macros.