The general rule is: double a single consonant following a single vowel with a short-vowel sound; don't double anything else. (The doubled consonant is a cue that the vowel sound should remain short.)

So:

• cut has a short 'u' and a single 't': therefore cutter.
• program has a short 'a' and a single 'm': programmer.
• read has a long 'e' sound from 'ea': reader
• head has a short 'e' sound but it comes from a double-vowel 'ea', so header.

Of course, this being English, there will be exceptions.

The general rule is: double a single consonant letter following a single vowel letter with a short vowel sound; don't double anything else. (The doubled consonant is a cue that the vowel sound should remain short.)

So:

• cut has a short 'u' and a single 't': therefore cutter.
• program has a short 'a' and a single 'm': programmer.
• read has a long 'e' sound from 'ea': reader
• head has a short 'e' sound but it comes from a double-vowel 'ea', so header.

Of course, this being English, there will be exceptions.