What is percent decrease?

Percent decrease measures how much a value has fallen relative to its original amount, expressed as a percentage. It is always positive — for example, if a price drops from $80 to $60, the percent decrease is 25%, not −25%. Percent decrease is commonly used to describe price drops, population decline, weight loss, and any situation where a quantity gets smaller over time.

What is the percent decrease formula?

The percent decrease formula is: Percent Decrease = ((Original − New) / Original) × 100. For example, if a value drops from 200 to 150, the percent decrease is ((200 − 150) / 200) × 100 = 25%. The denominator is always the original (starting) value — dividing by the new value instead is a common mistake that gives a different (incorrect) answer.

What is the difference between percent change and percent decrease?

Percent change is the general term that covers both increases and decreases. It is calculated as ((New − Original) / |Original|) × 100, which produces a positive number for increases and a negative number for decreases. Percent decrease is specifically the magnitude of a negative percent change — it is the same calculation but expressed as a positive value with "decrease" stated explicitly. This calculator shows both: it labels the result "Percent Increase" or "Percent Decrease" based on the direction, and also shows the raw signed change as the absolute change value.

How do you calculate percent increase?

The percent increase formula is: Percent Increase = ((New − Original) / Original) × 100. For example, if a salary rises from $50,000 to $57,500, the percent increase is ((57,500 − 50,000) / 50,000) × 100 = 15%. This is the same formula as percent change — the sign of the result tells you whether the change is an increase (positive) or decrease (negative). Switch to "Find new value" mode in the calculator to go the other direction: enter the original value and the percent increase to calculate the resulting new value.

Example: what is the percent decrease from 100 to 75?

Plugging into the formula: ((100 − 75) / 100) × 100 = (25 / 100) × 100 = 25%. So going from 100 to 75 is a 25% decrease. Equivalently, 75 is 75% of 100, meaning 25% was removed. A quick sanity check: the multiplier is 75/100 = 0.75, or 1 − 0.25, confirming a 25% reduction.

When is percent change negative vs. positive?

Percent change is positive when the new value is greater than the original (an increase) and negative when the new value is less than the original (a decrease). A percent change of 0% means the value did not change. It is undefined when the original value is 0 (you cannot divide by zero). In finance, a stock that goes from $40 to $50 shows +25% change, while one that drops from $50 to $40 shows −20% change — note these are not symmetric because the base (denominator) is different in each case.

What is the difference between percent change and percentage points?

Percent change and percentage points are often confused. If an interest rate rises from 4% to 5%, that is a 1 percentage-point increase, but a 25% percent change (since (5−4)/4 × 100 = 25%). Politicians and media often conflate these — "the unemployment rate fell 2 points" (from 6% to 4%) sounds more dramatic as "a 33% decrease." Always clarify whether a change is in percentage points (absolute) or percent change (relative).

How do I quickly estimate a percent decrease mentally?

For common percentages: a 10% decrease means the new value is 90% of the original (multiply by 0.9). A 20% decrease: multiply by 0.8. A 25% decrease: multiply by 0.75 (or divide by 4/3). A 50% decrease: divide by 2. Example: a $120 item marked 25% off — 120 × 0.75 = $90. For unusual percentages, convert to a decimal first: 37% off means the price is 63% of original (1 − 0.37 = 0.63).

Why is a 50% increase followed by a 50% decrease not back to the original?

This is a common misconception. Starting with 100: a 50% increase gives 150, then a 50% decrease of 150 gives 75 — not 100. The reason is that the base changes. The 50% increase is calculated on 100, but the 50% decrease is calculated on 150 (a larger base), so the decrease in absolute terms is larger. To return to the original after an x% increase, you need to decrease by x/(100+x) × 100%. After a 50% increase, you need a 33.3% decrease to get back.

Percent Decrease Calculator — % Change & New Value

Calculates percent decrease, percent increase, and new value from any percent change.

How to Use This Percent Decrease Calculator

This percent decrease calculator has two modes. In Find % change mode, enter the original value and the new value — the calculator returns the percent change (labeled as increase or decrease), the absolute change, and the multiplier (New ÷ Original). In Find new value mode, enter the original value, choose decrease or increase, and enter the percentage — the calculator returns the new value and the amount added or subtracted.

For sale price calculations — where you want to find the final price after a percentage discount — try our percent off calculator, which is optimized for retail and discount math.

Percent Decrease Formula

The standard percent decrease formula is:

Percent Decrease = ((Original − New) / Original) × 100

The result is always expressed as a positive number when the value goes down. For example, a drop from $200 to $150 gives ((200 − 150) / 200) × 100 = 25% decrease.

Percent Change Formula (General Form)

The general percent change formula handles both directions:

Percent Change = ((New − Original) / |Original|) × 100

A positive result means the value increased; a negative result means it decreased. Using the same example: ((150 − 200) / 200) × 100 = −25% (decrease of 25%).

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Finding a New Value After a Percent Decrease or Increase

To find the new value after applying a percentage change, use the multiplier method:

Percent decrease: New = Original × (1 − Percent / 100)
Percent increase: New = Original × (1 + Percent / 100)

For example, a 30% decrease on 500: New = 500 × (1 − 0.30) = 500 × 0.70 = 350. A 20% increase on 80: New = 80 × (1 + 0.20) = 80 × 1.20 = 96.

Why the Multiplier Method Is Faster

The multiplier approach avoids a two-step calculation (compute the change amount, then add or subtract). Instead, you multiply in one step. This is especially useful for compound percentage changes — for example, two successive 10% decreases on 1,000: 1,000 × 0.9 × 0.9 = 810, not 800 (the changes are not simply additive).

Percent Increase vs. Percent Decrease — Asymmetry

A key concept: percent increases and decreases are not symmetric. A 25% increase followed by a 25% decrease does not return to the original value. Starting with 100: +25% gives 125, then −25% of 125 gives 93.75 — a net loss of 6.25%.

This asymmetry matters in investing and pricing. A stock that drops 50% needs a 100% gain just to break even. Similarly, a store that raises prices 20% and then offers a 20%-off sale ends up at the original price: 100 × 1.20 × 0.80 = 96 — actually 4% below the starting price.

Use our decimal calculator to work through multi-step percentage chains with exact decimal precision.

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Common Percent Decrease Examples

100 → 75: (25 / 100) × 100 = 25% decrease
500 → 350: (150 / 500) × 100 = 30% decrease
80 → 96: (16 / 80) × 100 = 20% increase
1,200 → 900: (300 / 1,200) × 100 = 25% decrease
50 → 75: (25 / 50) × 100 = 50% increase
200 → 200: 0 / 200 × 100 = 0% change (unchanged)

Sources & References

Percent Change — Khan Academy — Khan Academy

Percent Decrease Calculator

Percent Decrease / Increase Calculator