Percent Change Formula

Percent change measures how much a quantity has increased or decreased relative to its original value, calculated as (new - original)/original × 100%.

The Formula

Percent Change=New−OriginalOriginal×100%

When to use: If a price goes from $50 to $60, the change is $10. Compared to the original $50, that's 1050=20% increase.

Quick Example

Price: $80→$60  ⟹  Change=60−8080×100%=−25% (25% decrease)

Notation

Δ%=New−OldOld×100%; positive means increase, negative means decrease

What This Formula Means

Percent change measures how much a quantity has increased or decreased relative to its original value, calculated as new−originaloriginal×100%.

If a price goes from $50 to $60, the change is $10. Compared to the original $50, that's 1050=20% increase.

Formal View

Δ%=xnew−xoldxold×100% where xold≠0

Worked Examples

Example 1

easy
A jacket originally costs $60 and is on sale for $45. What is the percent decrease?

Answer

25% decrease

First step

1
Find the change: 60−45=15.

Full solution

  1. 2
    Divide by the original value: 1560=0.25.
  2. 3
    Convert to a percentage: 0.25×100=25%.
Percent change is calculated as changeoriginal×100%. A decrease means the new value is less than the original.

Example 2

medium
A town's population grew from 12,000 to 15,000. What is the percent increase?

Example 3

hard
A stock price rises by 20% one year and falls by 20% the next year. If it started at $100, what is the final price and the overall percent change?

Common Mistakes

  • Dividing by the new value instead of the original - the denominator is always the starting amount.
  • Forgetting the sign - new less than original is a decrease (negative), not a positive change.
  • Computing percent change of the difference alone - use new−oldold, not just the difference times 100.

Why This Formula Matters

Percent change is how prices, populations, and scores are compared fairly regardless of size — a $10 rise means more on a $50 item than a $500 one. The classic trap is dividing by the new value or the change itself instead of the original. Recognizing it by "Is a change being compared to the original starting value?" — rather than by familiar numbers — is what lets a student tell it apart from percent of a number and percentages and ratio in a mixed problem set.

Frequently Asked Questions

What is the Percent Change formula?

Percent change measures how much a quantity has increased or decreased relative to its original value, calculated as new−originaloriginal×100%.

How do you use the Percent Change formula?

If a price goes from $50 to $60, the change is $10. Compared to the original $50, that's 1050=20% increase.

What do the symbols mean in the Percent Change formula?

Δ%=New−OldOld×100%; positive means increase, negative means decrease

Why is the Percent Change formula important in Math?

Percent change is how prices, populations, and scores are compared fairly regardless of size — a $10 rise means more on a $50 item than a $500 one. The classic trap is dividing by the new value or the change itself instead of the original. Recognizing it by "Is a change being compared to the original starting value?" — rather than by familiar numbers — is what lets a student tell it apart from percent of a number and percentages and ratio in a mixed problem set.

What do students get wrong about Percent Change?

The procedure for percent change is the easy part; the trap is dividing by the new value instead of the original. Asking "Is a change being compared to the original starting value?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

What should I learn before the Percent Change formula?

Before studying the Percent Change formula, you should understand: percentages, subtraction, division.

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