Low Side Pressure fluctuation

I am trying to diagnose an AC problem and have a basic question. When I connect my pressure guage/recharge line to the low side port, the pressure reading is not steady, but varies from a low of about 20 psi when the compressor is running to about 50 psi when the compressor is off. Is this normal?

If it keeps going off on low pressure, it’s low on charge or there’s some other fault in the system. What’s the high side pressure?
Add some leak finder dye along with refrigerant, run the system for a few days, then use a blacklight to find the leak.

It’s not normal and sounds like the system is low on refrigerant.
Twenty is way too low with the compressor engaged and 50 is way too low with the compressor off and the pressure stabilized.

With the compressor off you should show around 115 PSI and around 30-35 PSI with the compressor engaged; depending on various factors of course.

That’s normal, but for a low system.
The fluctuation is normal because the low-side is technically a suction line, it leads BACK to the compressor, so the compressor is sucking in that refrigerant.
Don’t worry about the pressure with the compressor off. Charge until the system runs 35-45psi with the compressor running. Continue to monitor the pressure. It should not leak down. If you have to add a can any more often than every 12 months, have it repaired.