Learn Finnish: Minun on määrä kylvää vehnä huomenna. - I am meant to sow the wheat tomorrow.

Both structures take a genitive subject (minun) and a verb in the third person singular, followed by the first infinitive (kylvää). The difference is in the meaning: täytyy means you have a direct obligation or necessity (I must), whereas on määrä means there is a schedule, plan, or external expectation (I am meant to or I am scheduled to).

Why is the object vehnä in the nominative case instead of the genitive-looking accusative (vehnän)?

Because on määrä triggers the same object rules as necessive verbs (like täytyy or on pakko). In these structures, a singular total object drops the -n ending and looks exactly like the nominative case. Therefore, we use vehnä instead of vehnän.

Could I say minun on tarkoitus kylvää instead?

Yes, structurally it works exactly the same way. The difference is a slight nuance: on tarkoitus expresses your own personal intention (I intend to sow), while on määrä implies an arrangement, schedule, or something expected of you (I am meant or scheduled to sow).

Doesn't the word määrä usually mean 'amount' or 'quantity'?