How Percentage Change Works
A percentage change tells you how much a value increased or decreased relative to a starting point. It’s one of the most used “quick comparison” measurements because it converts different scales into a single unit: percent. Whether you are comparing prices, website traffic, revenue, body weight, stock performance, exam scores, or lab results, percentage change helps you answer the same basic question: How big is the change compared to where we began?
This percentage change calculator supports multiple common needs: you can calculate percent increase/decrease between two values, compute percent difference when there is no clear “original,” reverse a percent change to recover an original value, and apply a percent to a base number (percent-of and add/subtract). These variations look similar, but they solve different real-world problems. Using the correct one prevents the most common mistakes.
The Standard Percent Change Formula
When you have an old value (original) and a new value (final), percent change is:
= (New − Old) ÷ Old × 100%
The sign matters: a positive result means an increase, and a negative result means a decrease. The calculator can display the sign directly (for example, −12.5%), or convert it into words (“Decrease 12.5%”) so it’s easier to interpret in reports.
Example: Percent Increase
Suppose a product price changes from 100 to 125. The absolute change is 25. Divide 25 by the original 100 to express that change relative to the starting point:
That’s a 25% increase. This is one of the clearest use cases for percent change: you have a true baseline (the original price) and want to measure how far the new price moved away from it.
Example: Percent Decrease
If sales drop from 200 to 150, the absolute change is −50. Divide by the original 200:
That’s a 25% decrease. Notice the sign carries the meaning. Many dashboards show decreases as negative values because it makes trends easier to scan quickly.
Why Old = 0 Breaks Percent Change
Percent change uses the old value in the denominator. If the old value is 0, the formula requires dividing by 0, which is undefined. In practice, you have a few options depending on what you’re measuring:
- Use absolute change (New − Old) if a percent doesn’t make sense.
- Pick a different baseline (for example, last non-zero period).
- Use percent difference if you don’t want to treat either value as a baseline.
This calculator will warn you when the old value is zero and will still provide the absolute change so you can keep working.
Percent Change vs Percent Difference
People often say “percent change” when they really need percent difference. Percent difference is used when neither value is a clear original, such as comparing two measurements, two estimates, or two groups. It uses the average of the two values as the reference:
= |A − B| ÷ ((|A| + |B|) ÷ 2) × 100%
Because percent difference doesn’t depend on choosing “old” or “new,” the result is symmetrical: swapping A and B gives the same answer. That makes it useful for comparisons and error reporting.
Quick Comparison Table
| Metric | Best when… | Reference | Symmetric? |
|---|---|---|---|
| Percent change | You have an original baseline | Old value | No |
| Percent difference | Neither value is the baseline | Average of both | Yes |
Multipliers: The Fast Way to Apply Percentages
A powerful shortcut is the multiplier. If a value changes by p%, then:
Examples:
- +25% → multiplier = 1.25 (multiply the original by 1.25)
- −15% → multiplier = 0.85 (multiply the original by 0.85)
Multipliers are especially useful in pricing, taxes, discounts, markups, and growth projections, because they let you chain changes: you can apply multiple percent changes by multiplying multiple multipliers.
Important: Increases and Decreases Don’t Cancel
A common misconception is that “up 20% then down 20% returns to the original.” It does not. If a value increases from 100 to 120 (+20%), and then decreases by 20% of the new value, it becomes 96.
This is why the reverse percent change tab exists: when you know the final value and the percent change, you can compute the original correctly.
Reverse Percentage Change
Reverse percent change answers questions like: “If the final price is 120 after a 20% increase, what was the original price?” Start with the forward relationship:
Solve for Original:
If the change is a decrease (for example, −20%), then the multiplier is 0.80, and you divide by 0.80 to recover the original. The calculator also checks for invalid cases like a multiplier of 0 (which happens at −100%).
Handling Negative Values Carefully
Percent change still works with negative numbers, but interpretation can be tricky because the denominator (Old) determines the sign. For example, moving from −50 to −25 is an increase in numeric value (less negative), yet the formula yields:
The negative sign here is a mathematical result of using a negative baseline. In these cases, it’s often better to explain the context (e.g., “loss reduced by 50 units”) or use percent difference for a symmetric comparison. This calculator’s step-by-step section helps you see exactly where the sign comes from.
When to Use Each Mode
- Percent Change: sales from last month to this month, price before vs after, old score vs new score.
- Percent Difference: comparing two measurements, two estimates, experimental vs control values.
- Reverse Percent Change: recover original price after a discount/markup, undo an applied percent.
- Apply Percent: calculate percent-of, add tax/markup, subtract discount.
Common Mistakes This Calculator Helps Prevent
- Dividing by the new value instead of the old value for percent change.
- Forgetting the sign and mislabeling a decrease as an increase.
- Assuming +x% and −x% cancel out (they don’t).
- Using percent change when percent difference is needed for symmetric comparisons.
- Ignoring old = 0 and producing impossible results.
Quick Examples You Can Copy
| Scenario | Old | New | Result | Meaning |
|---|---|---|---|---|
| Price increases | 100 | 125 | +25% | Increase by one quarter |
| Traffic drops | 10,000 | 8,000 | −20% | Decrease by one fifth |
| Reverse a discount | ? | 80 | Original = 80 ÷ 0.8 = 100 | 80 after −20% came from 100 |
| Percent difference | 80 | 100 | ≈ 22.22% | Relative gap using average baseline |
FAQ
Percentage Change Calculator – FAQs
Answers to the most common percent increase/decrease and reverse percent change questions.
Percentage change measures how much a value increased or decreased relative to the original value. It is calculated as (New − Old) ÷ Old × 100%.
Percent increase is (New − Old) ÷ Old × 100% when the new value is greater than the old value.
Percent decrease is (Old − New) ÷ Old × 100% when the new value is less than the old value. It can also be shown as a negative percent change using (New − Old) ÷ Old × 100%.
Percent change is undefined when the old value is 0 because you cannot divide by 0. In that case, use an absolute change instead, or choose a different reference point.
Percent change compares a new value to an original value. Percent difference compares two values without treating either one as “original,” using the average of the two values in the denominator.
If Final = Original × (1 + p/100), then Original = Final ÷ (1 + p/100). For a −20% change, divide by 0.8.
Yes. A negative percentage change indicates a decrease from the old value to the new value.
The formula still works, but interpretation changes. If Old is negative, the sign of the percentage can flip in ways that feel counterintuitive. Use the step-by-step view to verify meaning.
Multiplier = 1 + (p/100). For +25% the multiplier is 1.25. For −15% the multiplier is 0.85.
For money and pricing, 2 decimals is common. For scientific or analytics work, 3–6 decimals may be helpful. This calculator lets you control precision.