When discussing properties studied using first-principles methods like density functional theory (DFT), I often come across the terms "calculated" and "computed" to describe the obtained results. While both terms seem to be used interchangeably, I wonder if there is a subtle difference in their connotations.

Could someone shed light on the nuances between "calculated" and "computed" when discussing properties obtained through first-principles approaches? Is there a preferred term or any specific context where one is more appropriate than the other?

  • $\begingroup$ DFT isn’t an ab initio (first principles) method $\endgroup$ Commented Dec 23, 2023 at 6:55
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    $\begingroup$ @isolatedmatrix That's wrong. It depends. DFT is (can be) one of the first principles methods as you could derive all its ingredients directly from the Kohn-Sham equation (aka Schrodinger equation version using Kohn-Sham orbitals) without using any fitting empirical data. $\endgroup$ Commented Dec 23, 2023 at 7:08
  • $\begingroup$ @HighPerformanceRangsiman fair point. In practice, though, that’s very rarely done nowadays. $\endgroup$ Commented Dec 23, 2023 at 7:11
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    $\begingroup$ @isolatedmatrix You can refer to this discussion about whether DFT is ab initio or not chemistry.stackexchange.com/q/33764/50844, in any case that's not related to what I am asking $\endgroup$ Commented Dec 23, 2023 at 7:12
  • $\begingroup$ @isolatedmatrix This site also has the question Can DFT be considered an ab initio method? $\endgroup$
    – Anyon
    Commented Dec 23, 2023 at 18:07

3 Answers 3


In my opinion, you use calculate (and calculated) to refer to the process of using mathematical methods or formulas.

E.g. I want to calculate the total electronic energies of a benzene molecule

And, you use compute to refer to the action of mathematical operation, for example, using electronic devices (like computers) or software.

E.g. DFT is used to compute the total electronic energies of a benzene molecule

All in all, grammatically, calculate and compute are interchangeable.


I have been thinking about this, and calculate(d) seems to be used when you’re emphasising the results, e.g.: We calculated the frequencies of methane. or The frequencies were calculated at B3LYP level of theory.

On the other hand, compute(d) seems to be used more when emphasising the technical (not theoretical) method. For example: We computed the frequencies for methane using our algorithm/program. or The frequencies were computed on a Mac Mini with a M1 chip.

I suspect, however, that the two words are entirely interchangeable now. I imagine that the term ‘compute(d)’ became used when computers started being used to run the calculations, to distinguish between calculations which were solved by hand. I suspect that the reason people rarely write ‘compute(d)’ nowadays is because the involvement of a computer is assumed implicitly.


I will give my own opinion and understanding of using those terms and how I have been using them in my own work. First of all both "calculated" and "computed" are commonly used when referring to properties studied using first-principles methods. In practice, the choice between "calculated" and "computed" may come down to personal preference or the specific context in which the term is used. Both terms are widely accepted and understood in the scientific community.

However, if I want to emphasize a specific aspect, there can be a subtle difference:

  1. Calculated: The term "calculated" often implies a more deliberate and intentional process. It suggests that the property or result has been determined through a systematic and well-defined calculation method, such as DFT. It conveys the idea that the value or property has been obtained by performing specific calculations based on theoretical principles.
  2. Computed: On the other hand, "computed" generally suggests a more general process of obtaining a result or property through numerical or computational methods. It indicates that the property has been derived or evaluated using computational techniques, which may include not only theoretical calculations but also numerical simulations or data analysis.
  • $\begingroup$ That makes sense, but have you ever come across an example of the word ‘computed’ being used before the introduction of computers in this kind of work? (I’m not being sarcastic, I’m genuinely interested) $\endgroup$ Commented Dec 25, 2023 at 7:28
  • $\begingroup$ @isolatedmatrix, the term "computed" and its root word "compute" predate the invention of modern computers as devices. The word has its origins in Latin (it is derived from the Latin word "computare," which means "to calculate" or "to reckon." The term "computare" is a combination of "com-" (meaning "together" or "with") and "putare" (meaning "to reckon" or "to think")) and has been used in the English language for centuries to describe mathematical calculations and the act of reckoning or determining results. $\endgroup$ Commented Dec 25, 2023 at 7:45
  • $\begingroup$ I am aware of that. That’s not what I asked. $\endgroup$ Commented Dec 25, 2023 at 8:38
  • $\begingroup$ @isolatedmatrix, I don't have a 'Yes' or 'No' to your question, I didn't go through all the work that has been done in this field to decide whether this term has been used before 'computers' or not, but by knowing that the term itself is not new, it just makes me unable to distinguish between the two terms solely based on what you have suggested. However, thank you for your reply. $\endgroup$ Commented Dec 25, 2023 at 9:03
  • $\begingroup$ Again, I didn’t ask whether it had ever been done, in the entire history of the field, just whether you had come across one. As I said, I wasn’t trying to be sarcastic, I wasn’t trying to argue or make you seem ignorant in any way, I genuinely wanted to know whether the term had been used earlier in this context. I’ll assume the answer is ‘no’ and leave it at that. $\endgroup$ Commented Dec 25, 2023 at 17:28

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