iPhone 6 - Battery Problem...?

I have an iPhone 6 which until 2 days ago was working ok. Here's what happened:

I noticed that the battery percentage had dropped suddenly from about 50% to 3%. A minute later the phone died.

I've been able to restart it, but it will switch itself off and reboot at random. I'm trying to charge it (using the correct charger and lead that came with the phone originally) but the battery percentage stays at 1% the whole time.

I've carried out a "battery recalibration" process but it didn't change anything. I've also performed a factory reset but that didn't change anything either.

This phone is a few years old, and I'm assuming that the most likely cause is that the battery is dying/dead and needs to be replaced. Is this likely to be the case?

Thank you.