Surprisingly thin, in many cases.

the classic "knight in shining armour" consists of steel plate which would vary depending on location - the head and chest protected with much thicker steel than the arms or fingers.

As a general summary, based off original harnesses shows the following:

Head: about 2.5mm - 3mm thick.

Breastplate: 3-4mm thick on the centre, thinning down to 1mm at the sides.

Elbow and Knees, about 1.5mm-2mm.

Arms and Legs: around 1mm thick, sometimes less.

Feet and Fingers, about 0.6-0.8mm thick.

Plate armour is made of curved or ridged surfaces, which give a lot of strength and make hits slide off, where a flat surface could easily be dented deeply.

Underneath the metal, a knight would wear clothes called an Arming Doublet or Pourpoint, which in some cases had padding to help absorb impact shock - this would likely add a centimetre or so of thickness in some areas.

In earlier armour (before the 13th Century AD), before full plate was developed, the armour would've been made from maille (chain-mail). As maille is flexible thicker padding was worn - a thick garment called a Gambeson or Aketon, with 1-2cm of padding to absorb impacts, while the chain protected from slashing cuts.

Very thick plate armour was also made, specifically for jousting, often 5,6 or even 7mm thick plates of solid steel, making the armour extremely heavy and immobile. However, this was only used for sport jousting, and not for battles. Confusion between sporting and combat armour however has helped create the myth that knights' armour was incredibly heavy and immobile.