I dont think there is currently a way to measure pain objectively. It would need to deal with measuring signals sent to the brain by nerve cells. But I dont think its entirely understood how this works. There is conventionally different types of pain though.

https://www.mydr.com.au/pain/pain-and-how-you-sense-it/#:~:text=When%20we%20feel%20pain%2C%20such,and%20the%20pain%20is%20perceived.