Is there a way to objectively measure

pain? Like, if you hit your finger with a hammer you suffer 5.7 units of pain?

Step 1) Ask the test subject to scream as loud as he can and measure it in decibels.
Step 2) Whack the subject with various objects and record how loud he screams in each case.
Step 3) Divide the numbers from step 2 by the number from step 1.  Voila!  Instant pain-meter.