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Increment — Definition, Formula & Examples

An increment is the amount by which a value increases from one step to the next. If a variable changes from 5 to 8, the increment is 3.

An increment of a variable xx is the change Δx=x2−x1\Delta x = x_2 - x_1, where x1x_1 is the initial value and x2x_2 is the new value. While the term often implies a positive change, an increment can be negative when the value decreases.

Key Formula

Δx=x2−x1\Delta x = x_2 - x_1
Where:
  • Δx\Delta x = The increment (change) in x
  • x1x_1 = The initial value of x
  • x2x_2 = The new value of x

How It Works

To find an increment, subtract the starting value from the ending value. The Greek letter delta (Δ\Delta) is the standard symbol for an increment. For instance, Δy\Delta y means "the increment of yy" or "the change in yy." In a table of values, you can check whether a pattern is linear by seeing if the increment between consecutive yy-values stays constant.

Worked Example

Problem: A temperature rises from 62°F to 75°F. What is the increment in temperature?
Identify values: The initial temperature is 62°F and the new temperature is 75°F.
x1=62,x2=75x_1 = 62, \quad x_2 = 75
Subtract: Apply the increment formula.
Δx=75−62=13\Delta x = 75 - 62 = 13
Answer: The increment in temperature is 13°F.

Why It Matters

Increments are the foundation of slope in algebra — slope is just Δy\Delta y divided by Δx\Delta x. In calculus, making the increment infinitely small leads directly to the concept of a derivative.

Common Mistakes

Mistake: Subtracting in the wrong order (new minus old vs. old minus new)
Correction: Always compute x2−x1x_2 - x_1 (new value minus initial value). Reversing the order flips the sign, which changes the meaning of the result.