It can all depend how long they can grow. On PC, you can trigger their age by selecting from 1 day to around 70 days of a child to live.
Otherwise on the Playstation, you can trigger their age and they can live up to a certain amount.
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3 Days( sim time) But they don't turn into adults, just children. --JBiebzx :D
It takes three Sim days for the baby to turn into a child.
It takes about a week (in sim time)
If you are talking about The Sims 2, below the picture of the your Sim there will be a little bar, on the bar there will be how many days it will take until that Sim grows up.
Only the baby can grow up. Which is 3 days. The boy or girl Sim(child sim) can't grow up.