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If the words computation and calculation are not perfect synonyms what is the difference between them? Which one describes more accurately what is done by a person computing or calculating something on a piece of paper?

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up vote 16 down vote accepted

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.

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In abstract mathematics one often computes things (not necessarily numbers but more general structures) by proving that they are "isomorphic" to things one already knows well. This need not involve inserting numbers into formulas. In that case, would you say that "computation" is the more appropriate choice? – Rasmus Jan 27 '11 at 21:35
Yes, I think that by invoking a more complex process than mere arithmetic, you're transitioning from "calculation" to "computation". – Chris B. Behrens Jan 27 '11 at 21:57
If that distinction were true (which I don't accept) it would be at odds with, for example, all these usages of I calculate to mean I think. – FumbleFingers Aug 12 '11 at 14:38
@Rasmus: this is a case, I think, where the connotations in abstract mathematics are different from the colloquial ones. For literal uses in colloquial speech, I think @Chris nails it pretty well (though as @FumbleFingers points out, there are figurative uses too). But in maths it’s quite idiomatic to talk about eg “calculating homology groups” or other structures. Computing is also fine, but slightly less common, unless one’s actually talking about algorithms. Comparing google results for eg compute homology, calculate homology shows this difference in usage. – PLL Aug 12 '11 at 16:04
@ChrisB.Behrens So you would always compute a derivative (like d/dx x^2 = 2x), because it's not mere arithmetics? Other people use calculate for derivatives and integrals quite commonly. Actually both "calculate derivative" and "calculate integral" dominate over "compute derivative" and "compute integral" in google hits. – Sampo Smolander Jun 11 '14 at 17:44

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... enter image description here

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).

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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.

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I agree. Computation to me implies following an algorithm whereas calculation is using mathematical operations only. But I think in common usage the terms are virtually synonymous – tinyd Aug 12 '11 at 15:00
This isn't a general distinction in computer science, not least because it's not especially useful. – Marcin Aug 13 '11 at 10:17

For something on a piece of paper, especially a napkin or back of an envelope, I would use calculation. Not accidentally, I think calculation implies something you would do with a calculator; computation something that would require a computer. (Granted, many of today's calculators are much more powerful than the "computers" that were available in the early days of computing.)

The difference is fairly subtle, though, and it is no great crime to use either word in place of the other.

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I concur with other answers. Computation gives the nuance of a longer and more involved process, not strictly numerical.

Historically, computation has been associated with more complex tasks (the word "comput" was used for the theory and long-term calculations of the religious calendars, Easter sunday as a basis for the whole liturgical year in particular).

Computation has also parts of its meaning coming from looking up tables of data, of curves (see also nomography, abaque) or making such tables for others to use (see almanach, ephemerides). Starting mainly in the 17th century, this could be trigonometric and logarithm tables, astronomical or sea level predictions, etc. But we have found large tables of computations in ancient civilisations of Mesopotamia, China, America.

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