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Subscript — Definition, Formula & Examples

A subscript is a small number, letter, or symbol written slightly below and to the right of another character. It is used to label or distinguish between similar variables, like x1x_1 and x2x_2.

In mathematical notation, a subscript is an index or identifier placed in a lowered position relative to the baseline of an adjacent symbol, serving to differentiate among members of a set, sequence, or collection of related quantities without altering the mathematical meaning of the base symbol.

How It Works

When you see a variable like a3a_3, the "3" is the subscript. It tells you which specific value of aa you are referring to — in this case, the third one. Subscripts do not mean multiplication; a3a_3 is not the same as a×3a \times 3. You will often encounter subscripts when working with data sets, sequences, or formulas that involve multiple similar measurements. For instance, if you measure the heights of five students, you might label them h1,h2,h3,h4,h5h_1, h_2, h_3, h_4, h_5 rather than inventing five completely different variable names.

Worked Example

Problem: Three test scores are labeled s1=85s_1 = 85, s2=90s_2 = 90, and s3=78s_3 = 78. Find the average of these scores using subscript notation.
Identify the values: The subscripts 1, 2, and 3 tell you which score is which.
s1=85,s2=90,s3=78s_1 = 85, \quad s_2 = 90, \quad s_3 = 78
Write the average formula: Use the subscripted variables in the formula for the mean.
Average=s1+s2+s33\text{Average} = \frac{s_1 + s_2 + s_3}{3}
Calculate: Substitute the values and compute.
85+90+783=2533≈84.3\frac{85 + 90 + 78}{3} = \frac{253}{3} \approx 84.3
Answer: The average score is approximately 84.384.3.

Why It Matters

Subscript notation appears constantly in statistics, physics, and algebra courses whenever you work with lists of data or indexed variables. Understanding subscripts is essential for reading formulas like the mean (xˉ=1n∑i=1nxi\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i) and for writing clear, organized solutions in any STEM field.

Common Mistakes

Mistake: Confusing a subscript with an exponent (superscript). Students read x2x_2 as "x squared" instead of "x sub 2."
Correction: A subscript sits below the baseline and is a label; an exponent sits above and indicates a power. x2x_2 names the second value of xx, while x2x^2 means x×xx \times x.