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In order to answer this question, there are a few factors that need to be considered.

First, we need to know the approximate size of Mr. Sponge Bob. Unfortunately, Bikini Bottom doesn't seem to use standard measurements so we can only estimate by proxy. The only decent approximation of Sponge Bob's relative size comes from his brief escapade at shell beach in his full length animated film. Judging from screen captures of Sponge Bob being held by hero and all-around swell guy David "The Hoff" Hasselhoff, I would estimate that he was no more than 4 inches tall and approximately 1/2 inch thick.

Given the only available data on sponge growth gives an approximate rate of 0-7 centimeters per year (or 2.75590 inches a year), Spongebob could not be less than 2 years. If we take an average and assume he grew consistently at 1.378 inches per year, that would make him 2.9 years old at the time the movie was filmed.

But.

He's a kitchen sponge, so lets call it 17 years (he drives and has a job) and call it a night.

Actually, as seen on his drivers license, he is 23 years old.

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15y ago

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