Difference between "computation" and "calculation"

Solution 1:

They're pretty close to synonyms, but "calculation" implies a strictly arithmetic process, whereas "computation" might involve applying rules in a systematic way. You would calculate your mortgage payment, and you might compute your actuarial health risk.

All this, IMHO.

Solution 2:

I disagree with other answers attempting to make some subtle distinction between computation and calculation based on the complexity of the operation, or whether it involved a computer. They're probably as close as you can get to the almost mythical true synonyms.

Even with the related verb form computed, I was surprised to find this hasn't become significantly more common since computers became widespread. In fact, calculated continues to dominate...

However, there are "idiomatic" contexts (particularly in casual speech) where only one word is used. For example...

• does not compute sometimes means makes no sense (always in the negative).

• calculate sometimes means think, consider, believe (with no arithmetic involved).

Solution 3:

Speaking as a Computer Science graduate...

A computation may involve executing steps as complex as a Turing-complete program. In other words, something that requires repetition (a loop of some kind) and/or selection (choosing what different operations to do next based on the result of previous ones).

A calculation would simply be a computation that requires neither repetition nor selection.

That might be a bit much for a layman though.