Percentage Change Calculator
Percentage change is the single most-used percentage calculation: it turns any two numbers into one comparable figure. A price that moves from $80 to $100 rose 25%; a price that moves from $100 to $80 fell 20%. Same $20 move, different percentages — because the base changed. The percentage change calculator above computes the change in either direction, tells you whether it is an increase or a decrease, and shows the working.
The formula is ((new − old) ÷ old) × 100. A positive answer is an increase, a negative answer is a decrease. The calculator also answers the follow-up question people always ask: how much would it take to undo the change? Reversing a 25% increase takes a 20% decrease, because the second move is measured from the new, larger base.
The Percentage Change Formula
Percentage change has one formula, and the sign of the answer tells you the direction:
Percentage change = ((new value − old value) ÷ old value) × 100
If the new value is bigger, the answer is positive — an increase. If it is smaller, the answer is negative — a decrease. If the two values are equal, the change is 0%. The old value is always the base, because the change is measured against where you started. The calculator above has a dedicated “change” mode, and it also shows the reverse move: the percentage needed to get back from the new value to the old one.
Step by Step: 80 to 100, and Back Again
- Find the change. 100 − 80 = +20.
- Divide by the old value. 20 ÷ 80 = 0.25.
- Multiply by 100. 0.25 × 100 = +25% — an increase of 25%.
- Reverse it. From 100 back to 80: (80 − 100) ÷ 100 = −0.20, or a 20% decrease.
The asymmetry is the key lesson: a 25% rise needs only a 20% fall to undo it, because the fall is measured from the larger number. A 50% rise needs a 33.33% fall; a 100% rise (a doubling) needs a 50% fall. The bigger the rise, the smaller the fall that undoes it.
Worked Examples: Increases and Decreases
The table below covers both directions, so you can see the pattern: the same dollar move gives different percentages depending on the direction, because the base is different each way.
| Change | Calculation | Percentage change |
|---|---|---|
| $80 → $100 | (100 − 80) ÷ 80 × 100 | +25% (increase) |
| $100 → $80 | (80 − 100) ÷ 100 × 100 | −20% (decrease) |
| $50 → $75 | (75 − 50) ÷ 50 × 100 | +50% (increase) |
| $75 → $50 | (50 − 75) ÷ 75 × 100 | −33.33% (decrease) |
| 200 → 150 | (150 − 200) ÷ 200 × 100 | −25% (decrease) |
| 150 → 200 | (200 − 150) ÷ 150 × 100 | +33.33% (increase) |
| $120 → $90 | (90 − 120) ÷ 120 × 100 | −25% (decrease) |
| $90 → $120 | (120 − 90) ÷ 90 × 100 | +33.33% (increase) |
Notice the pairs: 200 to 150 is a 25% decrease, but 150 to 200 is a 33.33% increase. The calculator shows both the change and the reverse move for any pair you enter, which is the fastest way to internalise the asymmetry. The discount calculator applies the same maths to sale prices, where the decrease is the discount and the original price is the base.
Percentage Change vs Percentage Difference
Two similar-sounding calculations answer different questions, and mixing them up is a common error. Percentage change picks one value as the base — the old one — and measures the move from it. Percentage difference treats neither value as the base: it divides the difference by the average of the two values. For 90 and 110, the percentage change from 90 to 110 is +22.22% (20 ÷ 90), but the percentage difference is 20% (|90 − 110| ÷ 100, where 100 is the average). The calculator has a separate mode for percentage difference, for comparing two measurements where neither is “before” and neither is “after.”
| Values | Percentage change (90 → 110) | Percentage change (110 → 90) | Percentage difference |
|---|---|---|---|
| 90 and 110 | +22.22% | −18.18% | 20% |
| 40 and 60 | +50% | −33.33% | 40% |
| 100 and 150 | +50% | −33.33% | 40% |
| 80 and 120 | +50% | −33.33% | 40% |
Use percentage change when there is a before and an after — a price yesterday and today, a salary last year and this year. Use percentage difference when you are comparing two things side by side with no time order — two products, two measurements, two estimates. The numbers differ, and using the wrong one gives a wrong answer to the question you actually asked.
Finding the Original Value After a Change
The reverse question is just as common: a price is $115 after a 15% increase — what was it before? Divide the final value by (1 + the rate): $115 ÷ 1.15 = $100. After a 25% decrease, a value of $90 came from $90 ÷ 0.75 = $120. The calculator’s “reverse” mode does this directly: enter the final value and the percentage, and it returns the original, with a check that multiplies it back. The table below gives the common cases.
| Final value | Change that produced it | Original value | Check |
|---|---|---|---|
| $115 | After a 15% increase | $100 | $100 × 1.15 = $115 |
| $88 | After a 10% increase | $80 | $80 × 1.10 = $88 |
| $90 | After a 25% decrease | $120 | $120 × 0.75 = $90 |
| $120 | After a 20% decrease | $150 | $150 × 0.80 = $120 |
| $230 | After a 15% increase | $200 | $200 × 1.15 = $230 |
| $56 | After a 30% decrease | $80 | $80 × 0.70 = $56 |
The trap here is subtracting the percentage from the final value instead of dividing: $115 minus 15% of $115 is $97.75, not $100, because the 15% was applied to the original $100, not to the final $115. Always divide by (1 + rate) for an increase or (1 − rate) for a decrease. The Khan Academy — Percentages explains the same reverse calculation with free practice problems.
Common Mistakes
Most wrong percentage answers come from the same short list of errors. Check yours against it before trusting the result.
- Using the wrong base. A 25% rise followed by a 25% fall does not return to the start — the second move is measured from a bigger number.
- Forgetting to divide by 100. 25% means 25 ÷ 100 = 0.25; multiplying by 25 instead of 0.25 gives a number 100 times too big.
- Confusing percentage points with percent. A rate rising from 10% to 15% is a 5-percentage-point rise but a 50% increase.
- Calculating change from zero. Percentage change from zero is undefined — there is no base to compare against.
- Adding percentages directly. Two 10% increases in a row are a 21% increase, not 20%, because the second applies to the new total.
- Rounding too early. Round only at the end — rounding the percentage first can shift the final answer.
Related Tools
Related tools on this site: the main percentage change calculator for any percentage question, the discount calculator for sale prices and stacked discounts, the ratio calculator for the ratio behind a percentage, and the fraction calculator for the fraction behind it.
Key Takeaways
If you remember nothing else from this page, remember these five points.
- 25% of 200 is 50: divide the percent by 100, then multiply.
- 45 is 25% of 180: divide the part by the whole, then multiply by 100.
- 80 to 100 is a 25% increase; 100 to 80 is a 20% decrease — the base changes the answer.
- Two 10% increases in a row give 21%, not 20%, because the second applies to the new total.
- A rate rising from 10% to 15% is a 5-percentage-point rise but a 50% increase.
Try It Yourself
- Pick the mode that matches your question in the calculator above.
- Enter the two numbers and read the answer with the working.
- Check the result by reversing it — 25% of 200 is 50, and 50 is 25% of 200.
- For sale prices with stacked discounts, use the discount calculator.
Quick Reminders
- The old value is always the base for percentage change.
- Percentage change from zero is undefined — there is no base.
- Round only at the end; rounding the percentage first shifts the answer.
- 10% of any number is the number with the decimal point moved one place left.
| Percentage | Of 250 | Of 200 | Of 80 |
|---|---|---|---|
| 10% | 25 | 20 | 8 |
| 15% | 37.50 | 30 | 12 |
| 20% | 50 | 40 | 16 |
| 25% | 62.50 | 50 | 20 |
| 50% | 125 | 100 | 40 |
Keep the three core formulas handy — percent of a number, what percent X is of Y, and percentage change — and almost every percentage question answers itself.
Frequently Asked Questions
How do I calculate percentage change?
Subtract the old value from the new value, divide by the old value, and multiply by 100. The formula is ((new − old) ÷ old) × 100. A positive answer is an increase; a negative answer is a decrease.
What is the percentage change from 80 to 100?
An increase of 25%. The change is 20, and 20 ÷ 80 = 0.25. Going the other way, from 100 to 80, is a decrease of 20% — the percentages differ because the base is different.
What is the percentage change from 100 to 80?
A decrease of 20%. The change is −20, and −20 ÷ 100 = −0.20. The same $20 move is 25% in one direction and 20% in the other, because percentage change is always measured against the starting value.
How do I undo a 25% increase?
With a 20% decrease. After a 25% increase, the value is 1.25 times the original, so dividing by 1.25 — a 20% fall — returns to the start. In general, undoing an increase of r% takes a decrease of r ÷ (100 + r) × 100%.
What is the difference between percentage change and percentage difference?
Percentage change uses the old value as the base and measures a move from before to after. Percentage difference divides by the average of the two values and treats neither as the base — it is for comparing two things side by side. For 90 and 110, the change from 90 is +22.22% but the difference is 20%.
Can percentage change be more than 100%?
Yes. If a value doubles, the change is +100%; if it triples, +200%. There is no upper limit on an increase. A decrease, though, cannot pass −100% — a 100% decrease takes the value to zero, and it cannot go below that.
What is the percentage change from 50 to 60?
An increase of 20%. The change is 10, and 10 ÷ 50 = 0.20. Going the other way, from 60 to 50, is a decrease of 16.67%.
What is a 100% decrease?
A fall to zero. A 100% decrease takes any value to 0, and a value cannot decrease by more than 100% — there is nothing left below zero.
Disclaimer: This calculator is for general information only. Percentages are exact arithmetic, but the numbers you enter — prices, rates, measurements — should be checked against the original source.