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What's the difference between formula and method?

Their definitions given by a dictionary are pretty similar to mine: a set of actions taken in order to achieve something.

My understanding is that formula is more specific than method like we need to do what when and how. Is my understanding correct?

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    In what context?? If you look at a recipe for pancakes, the "formula" is the measurements of the ingredients, while the "method" is the the way they are combined and cooked.
    – Hot Licks
    Apr 6 '20 at 11:30
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    Formula usually doesn't change, but method does.
    – Ram Pillai
    Apr 6 '20 at 12:01
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The relevant Merriam-Webster definition adds a well-considered caveat:

formula ... 4:

a customary or set form or method allowing little room for originality

  • All her books were written according to a familiar formula.

[bolding mine]

So a formula is an established method.

Other well-known senses of formula must also inform this usage at the subtext level: the chemical usage, the mathematical usage, the high-tech ('Formula 1' etc) usages. These put the word into the formal / qualified / adept / more sophisticated register. A complex series of steps is quite strongly implied.

While method can probably almost always be used in place of this sense of formula (with broadening, and loss of the connotations mentioned), formula is often the better choice. But by the same token, of course, often inappropriate.

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