Percentage change is the single most useful number for describing how two values compare over time. Whether you are tracking a salary raise, a product price hike, a stock's daily move, your monthly rent, or the change in your monthly credit-card balance, the question is always the same: by what percent did the number go up or down? This calculator takes your original (old) value and the new value and returns the absolute difference, the percentage change, the direction (increase or decrease), and the new-to-old ratio.
The formula itself is short, but the details trip people up: which number is the base, what happens when the old value is zero, and how to read a negative result. This page walks through all of it, with worked examples you can reproduce on your own numbers.
How to Use
- Enter the Original (Old) Value — the starting number before the change. This is the base, and it cannot be zero, because dividing by zero makes a percentage change undefined.
- Enter the New Value — the number you want to compare against the old one. It can be larger, smaller, or equal to the old value, and it may be negative (for example, a negative balance, a loss, or a temperature below zero).
- Optionally set Apply This Percent to Old Value. If you want to see what the old value becomes after a forward percent move (for example, a planned 10% raise or a 15% sale), enter that percent here and the calculator shows the projected result. Leave it at 0 if you only want the observed change.
- Optionally set Compounding Years. If the same percent change repeats every year (for example, an investment growing at the same rate annually), enter the number of years and the calculator projects the compounded future value.
- Read the result card. Absolute Change is the simple difference (new minus old). Percentage Change is that difference divided by the old value and multiplied by 100. A positive result is an increase; a negative result is a decrease.
- Use the New / Old Ratio to see the multiplier (for example, 1.30 means the new value is 130% of the old value, i.e. a 30% increase).
Tip: if you only want the percent increase on a price, leave the unit out of the boxes — the calculator works for dollars, euros, pesos, pounds, units sold, or any other quantity.
The Percentage Change Formula
The formula taught in every introductory algebra course and used by the U.S. Census Bureau, the IRS, and major financial data providers is:
Percentage Change = ((New − Old) / Old) × 100
Where:
- New is the value after the change.
- Old is the original, starting value.
- The result is a percentage; a positive number means an increase, a negative number means a decrease.
Worked example: an old value of 50 and a new value of 65. The absolute change is 65 − 50 = 15. Divide by the old value: 15 / 50 = 0.30. Multiply by 100: +30%. The new number is 30% larger than the old one.
Second example: an old value of 80 and a new value of 60. The absolute change is 60 − 80 = −20. Divide by the old value: −20 / 80 = −0.25. Multiply by 100: −25%. The new number is 25% smaller than the old one.
Why the Old Value Is the Base
A common mistake is to divide the difference by the new value instead of the old one. That gives the wrong answer. Percentage change is always relative to where you started, not where you ended up.
For example, if a price rises from $50 to $65, that is a 30% increase. But if it then falls from $65 back to $50, the drop is only 23.1% — not 30% — because the base has changed from $50 to $65. This asymmetry is exactly why a 50% loss requires a 100% gain to recover: a 50% drop on $100 leaves you with $50, and a 100% gain on $50 brings you back to $100. Keeping the old value as the base is what makes the math consistent.
Examples
Example 1 — A salary raise. You were earning $60,000 last year and $69,000 this year. The absolute change is +$9,000. Divide by the old salary: 9,000 / 60,000 = 0.15, so your raise is a 15.0% increase. The new-to-old ratio is 1.15.
Example 2 — A sale price. A jacket was priced at $80 and is marked down to $60. The absolute change is −$20. Divide by the old price: −20 / 80 = −0.25, so the discount is a 25.0% decrease. If the sale price is then raised back to $80, the increase is 20 / 60 = 33.3%, not 25%.
Example 3 — A stock dropping. A share traded at $200 at the open and $150 at the close. The absolute change is −$50. Divide by the open price: −50 / 200 = −0.25, a 25.0% decrease for the session. To break even the next day, the share must rise from $150 back to $200, a 33.3% gain.
Example 4 — A large company figure. A company's revenue grew from $1,000,000 last year to $1,450,000 this year. The absolute change is +$450,000. Divide by the old revenue: 450,000 / 1,000,000 = 0.45, a 45.0% increase. The ratio is 1.45.
Example 5 — A negative-to-positive swing. A balance moved from −$200 to +$800. The absolute change is +$1,000. Divide by the old (negative) value: 1,000 / (−200) = −5.0, or −500%. The sign flip here is a quirk of dividing by a negative base; intuitively the balance improved, but the textbook formula returns a negative percent. When the old value is negative, report the absolute dollar change alongside the percentage to avoid confusion.
FAQ
What is the difference between percent change and percent difference?
Percentage change compares two values where one is clearly the "before" and the other is the "after," and it always divides by the old value. Percentage difference is a symmetric comparison used when neither value is the base (for example, comparing two measured weights), and it divides by the average of the two values. Use this calculator for change; use a separate percent-difference tool for symmetric comparisons.
How do I calculate a percentage increase?
Subtract the old value from the new value, then divide that difference by the old value and multiply by 100. If the result is positive, it is a percentage increase. For example, old = 50 and new = 65 gives (65 − 50) / 50 × 100 = 30%.
How do I calculate a percentage decrease?
The formula is identical: subtract the old value from the new value, divide by the old value, multiply by 100. If the result is negative, it is a percentage decrease. For example, old = 80 and new = 60 gives (60 − 80) / 80 × 100 = −25%.
What if the old value is zero?
Percentage change is mathematically undefined when the old value is zero, because division by zero has no result. If a company had $0 in revenue last year and $1,000,000 this year, you cannot say revenue grew by "infinite percent" or by any meaningful percentage — the correct way to describe it is "from zero to $1,000,000," not a percent. This calculator flags that case as an error.
Why is a 20% decrease not undone by a 20% increase?
Because the base changes. If $100 drops by 20%, you land at $80. To get back to $100 from $80, you need a $20 increase, but $20 divided by $80 (the new base) is 25%, not 20%. This asymmetry is normal and is why recovery percentages always look larger than the loss that preceded them.
Can percentage change be more than 100%?
Yes. A value that doubles (old = 50, new = 100) is a 100% increase. A value that triples (old = 50, new = 150) is a 200% increase. Percentages above 100 are common when comparing small starting values to much larger ending values, especially in finance, population growth, and viral-metrics reporting.
Does this calculator work for negative numbers?
Yes, the old and new values may be negative (for example, a debt, a loss, or a temperature below zero). The formula still runs, but be aware that dividing by a negative old value flips the sign of the result. When the old value is negative, always report the absolute dollar change alongside the percentage so readers are not misled by the sign.
Disclaimer
This percentage change calculator is provided for informational purposes only and does not constitute financial, accounting, tax, or investment advice. Results are based on the standard percentage change formula ((new − old) / old × 100) and the exact values you enter; rounding, data entry, and negative-base conventions can affect how the result is interpreted. Always verify calculations against source documents and consult a qualified professional before making financial, tax, or business decisions based on these figures.