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by the formula vs according to the formula

Both phrases are correct and commonly used in English. They can be used interchangeably to introduce a formula or method. The choice between 'by the formula' and 'according to the formula' is a matter of personal preference or style.

Last updated: March 19, 2024 • 2734 views

by the formula

This phrase is correct and commonly used in English to introduce a formula or method.

This phrase is used to indicate that the following information or calculation is based on a specific formula or method.

Examples:

Calculate the area of the triangle by the formula A = 1/2 * base * height.
Solve the equation by the formula provided in the textbook.
Find the solution by the formula given in the manual.

Show examples from the web [+]

Distance Formula: Given the two points (x1, y1) and (x2, y2), the distance between these points is given by the formula: Don't let the subscripts scare you.
In a certain sequence, the term xn is given by the formula xn=2∗xn−1−12∗xn−2 for all n≥2. If x0=3 and x1=2, what is the value of x3? (A) 2.5
\begin{displaymath}f(x) = h \circ g(x. The derivative of the composition is given by the formula. \begin{displaymath}\Big(f \circ g(x)\. Another way to write this ...
Find the common ratio for the sequence given by the formula, 2. The formula indicates that 3 is the common ratio by its position in the formula. A listing of the ...

Alternatives:

using the formula
with the formula
applying the formula
following the formula
based on the formula

according to the formula

This phrase is correct and commonly used in English to introduce a formula or method.

This phrase is used to indicate that the following information or calculation is based on a specific formula or method.

Examples:

Calculate the area of the triangle according to the formula A = 1/2 * base * height.
Solve the equation according to the formula provided in the textbook.
Find the solution according to the formula given in the manual.

Alternatives:

by the formula
using the formula
with the formula
applying the formula
following the formula

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