Percentage Decrease Formula

A complete walk-through of the formula, every variable, the algebraic derivation, and ten worked examples.

The Standard Percentage Decrease Formula

The formula is Percent Decrease = ((Original − New) ÷ |Original|) × 100. It returns the relative drop from a starting value to a smaller new value. The result is a positive percentage when the new value is smaller, zero when they are equal, and negative when the new value is larger.

Understanding Each Variable in the Formula

Original is the earlier or larger value: the base of comparison. New is the later or smaller value. |Original| is the absolute value of the original, which protects the formula from sign confusion when the original is negative. The multiplication by 100 converts the decimal fraction into the percentage form most people read. Some sources label these same two inputs Starting Value and Final Value; the arithmetic does not change with the name.

Formula Derivation: Where It Comes From

Begin with the simple subtraction Original − New, which gives the absolute drop. That number alone is not comparable across scales, so divide by the original to express the drop relative to where it started. The result is a fraction between 0 and 1 in the typical case. Multiply by 100 to read it as a percent. The whole derivation is two operations on top of subtraction, which is why the formula generalizes so cleanly to any pair of numbers.

Why the Original Value Is Used as the Base

The question the formula answers is "what fraction of the starting amount was lost?" Only the starting amount can be the denominator for that question to make sense. Using the new value as the base answers a different question, namely how much larger the original was as a multiple of the new value, and it produces a different number. Mixing the two is the most common source of percent-decrease errors, and it is worth checking twice on any calculation that matters.

When the Result Is Negative: What It Means

A negative percent decrease means the new value is larger than the original. The formula has worked correctly; the wording is just inverted. Convert to a percent increase by flipping the subtraction order: ((New − Original) ÷ Original) × 100.

Percentage Decrease Formula in Excel

Use =((A1-B1)/ABS(A1))*100. Place the original in A1 and the new value in B1. Format the cell as a number; do not use the percent format, which would multiply the result by 100 a second time and report values like 2,500% instead of 25%.

Percentage Decrease Formula vs Percentage Change Formula

Percent change is ((New − Old) ÷ |Old|) × 100, which is the same arithmetic with the subtraction order reversed. Percent decrease is the absolute size of a negative percent change. The two are interchangeable as long as you keep track of direction.

10 Worked Examples Using the Formula

1. $200 → $150: ((200 − 150) ÷ 200) × 100 = 25%.
2. $1,000 → $750: 25%.
3. 50 → 40: 20%.
4. $85,000 → $72,000: 15.29%.
5. 12,000 → 10,800: 10%.
6. $4.20 → $3.78: 10%.
7. $340 → $289: 15%.
8. 48,000 → 31,200: 35%.
9. 60W → 8W (LED replacement): 86.67%.
10. $1,000,000 → $750,000: 25%.

Each of these examples uses the same three operations in the same order: subtract, divide by the original, multiply by 100. The formula does not care whether the units are dollars, watts, people, or points on a test. That is the entire appeal of a percentage: it strips away units and leaves a single comparable number.

Common Formula Mistakes

Dividing by the new value instead of the original is the most frequent error, and it produces a number that looks plausible but answers the wrong question. Forgetting to multiply by 100 leaves the answer as a decimal that looks like a tiny percentage, such as reporting 0.25 instead of 25%. Averaging two percent changes from different periods double-counts in unpredictable directions; chain the multipliers instead of adding the percentages. A fourth mistake is rounding intermediate steps too early, which can shift a final answer by a full percentage point on larger numbers.

FAQs About the Formula

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