Both of these adjectives seem to mean "correct", but I do not understand the difference.
Here's the difference in usage.
- The short form of an adjective like правильна (-льно, -лен, -льны) is limited to cases where a quality of something (usually put in nominative case) is declared directly:
Эта формула правильна (English: this expression is correct).
- The complete form правильная (льное, льный, -льные) can be used in this sense, too:
Эта формула - правильная. Это правильная формула. (This is a correct expression.)
But unlike the short form, it can also be used for any reference to something having that quality:
Я нашёл правильную формулу. (I've found the correct expression.)
As you can see, правильна has a meaning close to "является правильной" (is correct).
"Правильная" answers to "какая?", "правильна" - to "какова?". Basically they have the same meaning, but they are used in different cases.
For example, "правильная формула" is "the correct formula", and "формула правильна" is "the formula is correct".
Questions "как/каков?", "какова?", "каково?" (don't confuse it with "какого?"), or, to be more exact, answers to them, are mostly used with a definite object or subject of conversations. Like when you asking "how is/was the [something]"?.
Как порыбачили? Каков улов? - How was the fishing? How is the catch?
However, it is more likely to see in literature. In speaking, "какой" is more common.
There is no such word "правильна".
If you read it somewhere most probably it is phonetic description of speaking non-Russian (or even Russian from some region) "правильно"
Ha! Shame on me! I'm a Russian and I feel myself like Haruka Kano in "日本人の知らない日本語" (I don't know English translation).
"Правильна" - using on the end of sentence.
"Правильная формула" but "Формула правильна".
Also: "Формула правильна" have categorical tone:
"I insist that this formula is correct!"
"No!This is correct formula!"