cannot do without; indispensable; absolutely necessary
Expresses that something is essential or that one cannot manage without it. Often used with a noun marked by が or は.
Experience is indispensable for this job.
Attaches to the negative stem of a verb (ない-form minus ない) to express obligation or necessity. Equivalent to なければならない but slightly more colloquial.
You cannot live without water.
I have to submit the report by tomorrow.
I must study more.
なければならない is more formal and written, while 無くてはいけない is the slightly more conversational way to say the same obligation.
ないといけない has a similar meaning and register to 無くてはいけない, though 無くてはいけない can sound a bit stronger or more emphatic.
無くちゃいけない is a casual, spoken contraction while なくてはいけない is the more standard, neutral form used in both speech and writing.
なくてはいけない expresses the same obligation as なきゃいけない but is more formal and slightly more emphatic about the necessity.
なくてはいけない conveys the same necessity as ないといけません but uses a different negative-conditional pattern and is slightly more emphatic.
無くてはいけない is the plain form of 無くてはいけません, used in casual speech instead of the polite -ません ending.
Formed from the negative て-form of ない (なくて) + は (topic particle) + いけない (negative potential of 行く, literally 'cannot go'). The literal meaning 'if it is not the case, it won't do' developed into expressions of necessity and obligation.