Does it need to be "calculated"? In most process systems, if something happens in less than 1 second, then it probably isn't real. And solenoid valves are faster than that.
The response time of a pneumatic system has got rather more to do with the pipe layout, air pressure, chest size of the actuator and the spring characteristics than the response time of the solenoid valve.
Based on the lack of information accompanying your question, along with no definition of exactly what you mean by reponse time, there is no way to tell you how to calculate it, since there are too many unknown variables.
In general, always consult the manufacturer of the valve(s) in question. They will have the detailed information you seek. In the event the valve is manufactured as a copy or low cost alternative to someone elses product, and they lack the testing sophistication to provide this information in detail (a not at all uncommon occurrence in the present marketplace), and you still wish to employ their solenoid valve, then you must resort to empirical testing.
This is not necessarily a bad thing, and is commonly done. Be aware though that the validity of the data so obtained regarding accuracy, repeatability, and so forth of the response times you obtain from your tests will be based on the quality of those tests and your testing setup/procedures, along with the number of units tested since there could be a unit to unit difference that is significant for your application.
I take issue with a line in one of the posts saying in effect that generally if something happens in a process in less than one second it is not "real" in terms of an overall pneumatic (or otherwise) system. Anyone involved in automated machinery, or many processes employing solenoid valves, or involved in programming/debugging their controls will attest that things that happen in tiny fractions of a second can be all too "real".
Good Luck!
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"The more I learn, the more ignorant I realize I am."
You don't get good specs on closure of solenoids because of the physics.
recall F=m*a, force = mass times acceleration. so how much mass you have to move is different is every application.
second the force if variable because it depends on the time the current flowing and the engagement of the solenoid plunger. and the current is will depend on the power source.
Have the manufacture take the first wild guess build a mock-up and test.
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No matter how much you know....God knows more
My own experience has mainly involved "small" integrated solenoid valve assemblies with ports ranging from 1/16" to 1", and whether controlling a liquid or compressible gas, and whether piloted or direct acting, and AC or DC, the manufacturer's data was quite complete and accurate.
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"The more I learn, the more ignorant I realize I am."
You normally doesn't have to calculate it, but read in even in the brochures.
If you are in a time critial process, you may still want to do some measurements before the final assembly. In this case, It may be required the use of a pressure transducer and some sort of datalogger, to measure how much time the output pressure increases to a determined value.
As the other people have written, also consider your system response, time to fill the lines, etc. If you must be fast, you must keep lines and connections at a minimum and as close as possible.