Which of the following sentences regarding the calculation of something should be preferred?

  1. The calculation of the result by this equation...
  2. The calculation of the result by means of this equation...
  3. The calculation of the result through this equation...
  4. The calculation of the result from this equation...

Moreover, is any of them particularly incorrect?

  • 2 and 3 are good. 1 and 4 sound awkward to me. option 4 says that the answer is already in the equation and you just have to look for it.
    – vickyace
    Commented Jun 11, 2014 at 11:21

3 Answers 3


As a matter of style, I would write "The calculation of the result through the use of this equation". Alternatively I would suggest by the use of.

The correctness of choosing by, by means of, through, or from depend on whether this equation is thought of as a tool, a route to a result, or a process that generates a result. The choice of the phrase through the use of avoids any ambiguity about the nature of equation because it is equally applicable to all of those meanings.


Although not incorrect, probably none of those sentences is common in mathematics. More common choices are:

  1. This equation yields... / The above equation yields... / Equation (1) yields... (in the case of numbered equations)
  2. From this equation one obtains/we obtain... / From the above equation one obtains/we obtain... / From (1) one obtains/we obtain
  3. By plugging the values into ..., one gets/we get

How about, "solving this equation," or "calculating the result of this equation," or "the calculation of the solution to this equation?"

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