Bound noun used mainly in formal or written contexts; not a standalone word for everyday 'thought'. Often appears in compounds like 思考 (thought process) or 参考 (reference).
The character 考 includes the meaning of thinking.
report on one's investigation into ...
Suffix used in academic or formal titles, e.g., 〜考 meaning 'a study of ...' or 'thoughts on ...'. Not productive in everyday speech.
Rare, archaic suffix used in formal or literary contexts to refer to one's late father, e.g., 先考. Not used in modern conversation.
The title of his thesis was 'A Study of Ancient Japanese History'.
I have seen '先考' (deceased father) inscribed on a tombstone.
考え is the natural standalone word for 'a thought' or 'an idea' in everyday speech, whereas 考 alone is rarely used outside formal compounds or titles.
The kanji 考 originally depicted an old person leaning on a stick, associated with 'aged' and later extended to 'think' or 'consider'. The reading こう is the on'yomi.
reconsideration; rethinking; review
historical investigation; study of historical evidence
careful consideration; deliberation; thinking over carefully
study; discussion; research article; academic paper
examination; test; assessment
consideration; thought; rethinking
long thought; lengthy consideration; pondering for a long time
one's late father
consideration; deliberation; thinking over
miscellaneous studies; collected investigations
misunderstanding; mistaken idea
momentary thought; brief consideration · one's humble opinion; one's thoughts
foolish thought; stupid idea · (one's own) thought; (one's own) idea
surmising; speculation; conjecture
deceased father of the current emperor
deceased grandfather; deceased father and grandfather · distant ancestor; forefather
one's own thoughts; personal opinion; personal view