Percentage Change Calculator
Compare a new value with an original value and report the relative change as a percent increase or decrease. The denominator is always the starting amount.
80 → 100 is a 25% increase
- Difference: 100 − 80 = 20.
- Divide by the original: 20 ÷ 80 = 0.25.
- Multiply by 100: 0.25 × 100 = 25.
- The signed change is positive, so this is a 25% increase.
All calculations run locally in your browser. Your entered values are not sent to an external service.
How to Use the Percentage Change Calculator
Type the starting amount and the later amount. Select Find Percent Change or press Enter. The page subtracts, divides by the original, multiplies by 100, and labels the result as an increase, a decrease, or no change.
- Enter the original value — the amount before the change.
- Enter the new value — the amount after the change.
- Read the percent, the raw difference, and the multiplier new ÷ original.
The work stays in your browser. Whole numbers, decimals, and negatives are allowed. An original of zero is rejected: there is no defined percent change from a starting amount of nothing. Finding “15% of 200” or “30 is what percent of 200” belongs on the Percentage Calculator. This page only compares two amounts.
What the multiplier means
The multiplier is new ÷ original. A 25% increase has multiplier 1.25, because the new value is 125% of the start. A 20% decrease has multiplier 0.80. No change has multiplier 1. You can recover the new value as original × multiplier.
How to Calculate Percentage Change
The three-step formula
First find the difference: new minus original. Then divide that difference by the original, not by the new value. Then multiply by 100 and write a percent sign. A positive result is an increase. A negative result is a decrease. Zero is no change.
Why the original is the denominator
Percent change answers “how large is this move compared with where we started?” The starting amount is the reference. Going from 80 to 100 adds 20 on a base of 80, which is one quarter of the start. Going from 100 to 80 subtracts 20 on a base of 100, which is one fifth of the start. Same dollar gap, different percents, because the bases differ.
Finding the new value from a known change
If a price of 80 rises 25%, the new price is 80 × 1.25 = 100. If 100 falls 20%, the new price is 100 × 0.80 = 80. That is why a 25% rise followed by a 20% fall returns to the start: 1.25 × 0.80 = 1. The percents do not cancel by subtraction.
Successive changes do not add
A 10% rise then another 10% rise is not 20%. After the first rise the base is larger, so the second 10% is 10% of a bigger number. The combined factor is 1.10 × 1.10 = 1.21, a 21% increase. Add percents only when they share the same original base.
Worked Percentage-Change Examples
A 25% increase: 80 to 100
Difference 100 − 80 = 20. 20 ÷ 80 = 0.25. 0.25 × 100 = 25. The signed change is +25%, a 25% increase. Multiplier 1.25.
A 20% decrease: 100 to 80
Difference 80 − 100 = −20. −20 ÷ 100 = −0.20. −0.20 × 100 = −20, a 20% decrease. Multiplier 0.80. This is the reverse trip of the first example, not a 25% drop.
No change: 50 to 50
Difference 0. 0 ÷ 50 = 0. The percent change is 0%. The multiplier is 1.
A later rise: 200 to 250
Difference 50. 50 ÷ 200 = 0.25. The change is again 25%. Different numbers can share the same percent when the ratio of difference to original matches.
A one-quarter drop: 40 to 30
Difference −10. −10 ÷ 40 = −0.25. That is a 25% decrease. One quarter of 40 is 10, so losing 10 is losing 25% of the start.
A half again: 10 to 15
Difference 5. 5 ÷ 10 = 0.50. A 50% increase. The new value is 1.5 times the original.
Decimals: 10.5 to 12.6
Difference 2.1. 2.1 ÷ 10.5 = 0.20. A 20% increase. The same formula accepts tenths and hundredths.
Two negatives: −20 to −10
Difference −10 − (−20) = 10. 10 ÷ −20 = −0.50. The algebraic change is −50%, a 50% decrease. The amount moved toward zero, so the signed percent is negative even though the number looks “larger” if you ignore the minus sign. Read the signed result, not the digits alone.
Percent Change vs Percentage Points
When the two values are already percents, say a poll moving from 40% to 50%, there are two honest descriptions. The gap is 10 percentage points. The relative change is (50 − 40) / 40 × 100 = 25%. “Up 10 points” and “up 25%” are both true and they are not interchangeable.
| Original | New | Difference | Percent change |
|---|---|---|---|
| 80 | 100 | 20 | 25% increase |
| 100 | 80 | −20 | 20% decrease |
| 40% | 50% | 10 points | 25% increase |
| 50% | 40% | −10 points | 20% decrease |
| 200 | 250 | 50 | 25% increase |
| 10 | 15 | 5 | 50% increase |
Interest rates, approval polls, and tax rates are often quoted both ways. State the unit. This calculator always reports the relative formula. If you only need 40% written as 0.40, use the Decimal to Percent Calculator.
Common Percentage-Change Mistakes
Dividing by the new value
The denominator is the original. From 80 to 100, divide 20 by 80, not by 100. Dividing by 100 would report 20% and hide the true 25% rise.
Treating the reverse trip as the same percent
80 → 100 is +25%. 100 → 80 is −20%. The dollar difference matches; the bases do not.
Adding two successive percents
10% then 10% is a 21% combined rise, not 20%. Multiply the factors: 1.10 × 1.10 = 1.21.
Confusing percentage points with percent change
40% to 50% is 10 points and a 25% relative increase. Name which one you mean.
Using a zero original
Starting at 0 and moving to 10 is not a 100% change or an infinite change you can report as a classroom percent. The ratio is undefined. This page rejects a zero start.
Calling any larger digit an increase
−20 to −10 looks “larger” if you drop the signs, but the signed formula is a 50% decrease. Keep the signs through the subtraction and the division.
Using this page for “X% of Y”
15% of 200 is a percent of a number, not a change between two amounts. Use the Percentage Calculator for that product.
How to Check a Percentage-Change Result
Multiply the original by (1 + change/100). You should recover the new value. For an 80 to 100 rise: 80 × 1.25 = 100. For a 100 to 80 drop: 100 × 0.80 = 80. If that product misses, the percent or the direction is wrong.
You can also compute the difference by hand and divide by the original on paper. The Percentage Calculator has a % change mode that should match this page for the same pair. If you need the change written as a fraction of the original, 20/80 reduces on the Simplify Fraction Calculator to 1/4, which is the 25% increase.
Related learning path
Convert a finished decimal such as 0.25 into 25% on the Decimal to Percent page. Browse the rest of the live tools on the Calculators hub or the Decimals & Percent cluster.
Percentage Change Calculator FAQs
How do you calculate percentage change?
Subtract the original from the new value, divide by the original, and multiply by 100. From 80 to 100: (20 / 80) × 100 = 25% increase.
How do you calculate a percent increase?
Use the same formula. A positive result is an increase. 10 to 15 is (5 / 10) × 100 = 50% increase.
How do you calculate a percent decrease?
A negative result is a decrease. 100 to 80 is (−20 / 100) × 100 = −20%, a 20% decrease.
Why is 80 to 100 not the same percent as 100 to 80?
The difference is 20 both ways, but the original bases are 80 and 100. 20/80 is 25% and 20/100 is 20%.
What is the difference between percent change and percentage points?
Percentage points are the raw gap between two percents. Percent change is that gap divided by the original percent. 40% to 50% is 10 points and a 25% relative increase.
Why can the original value not be zero?
Percent change divides by the original. Division by zero is undefined, so a start of zero has no percent change.
Are my numbers sent to a server?
No. The calculation runs locally in your browser.
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This page sits with the percent and fraction tools. The full live catalog is on the Calculators hub.
Browse All CalculatorsBrowse Percent ToolsReviewed by Prof. Dr. Khalil Mudassar (PhD) · Last updated: [mc_modified_date]
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Disclaimer
This calculator is intended for general educational and practical use. Review important results before relying on them in professional work.