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# Equations

Most papers include some equations. Make sure to properly format and reference your equations.

## Numbering

Equations are typically numbered. In general, equation numbers should be given in parentheses and placed on the right-hand side of the page.

Example 1. Equation numbering Then, is expressed as

(1)

## Equation references in text

Equations should be referenced in the text as "Eq. (X)", "equation (X)", or "(X)" (check guidelines).

Example 2. Equation reference format: Eq. (X) …​ is shown in Eq. (1). …​ are shown in Eqs. (1) and (2). …​ are shown in Eqs. (1)-(5). For some journals, "Equation (X)" is required at the start of a sentence. Also note that some journals prefer "eq. (X)" and "eqs. (X)" (check guidelines).
Example 3. Equation reference format: equation (X) …​ is shown in equation (1). …​ are shown in equations (1) and (2). …​ are shown in equations (1)-(5).
Example 4. Equation reference format: (X) …​ is shown in (1). …​ are shown in (1) and (2). …​ are shown in (1)-(5). Note that "Equation" is often used at the start of a sentence (check guidelines). Equation (1) is used to …​

## Variable definitions

Make sure that you define all variables in an equation. Definitions usually come after the equation and are introduced by the word "where". Note that "where" is not indented and is not followed by a comma.

Example 5. Example of "where"
Comma where, x is the …​ where x is the …​
Indentation The expression can be written as:

• where is the …​ The expression can be written as:

where is the …​

## Punctuation

Depending on your target journal, equations may require punctuation.

Example 6. Equation punctuation
Period The matrix is expressed as
Comma The sum is expressed as

where n is the number of …​

## Common phrases

Some common phrases used with equations are shown below.

Example 7. Common phrases Substituting Eq. (1) into Eq. (5) yields …​ Taking the derivative of Eq. (3) with respect to time and substituting the result into Eq. (7) yields …​