Percentage Change Calculator
Free percentage change calculator: find percentage increase or decrease instantly. Includes formula, worked examples, and real-world use cases.
The percentage change calculator finds exactly how much a value has grown or shrunk between two points — expressed as a percentage. Enter any two numbers and this percentage change calculator returns the result instantly, along with the formula and a worked breakdown.
Percentage Change Formula
The standard percentage change formula is:
Percentage Change = ((New Value − Old Value) ÷ |Old Value|) × 100
The vertical bars around Old Value mean you use its absolute value (ignore the negative sign if it is negative). A positive result means an increase; a negative result means a decrease.
How to Calculate Percentage Change — Step by Step
Follow these three steps every time:
- Step 1 — Subtract: New Value minus Old Value. Keep the sign.
- Step 2 — Divide: Divide the result by the absolute value of the Old Value.
- Step 3 — Multiply: Multiply by 100 to convert the decimal to a percentage.
Example: A product price rises from $40 to $52.
- Step 1: 52 − 40 = 12
- Step 2: 12 ÷ 40 = 0.30
- Step 3: 0.30 × 100 = 30% increase
Percentage Increase Formula
When the new value is larger than the old value, the result is a percentage increase. The percentage increase formula is identical to the general formula above. The positive sign tells you it is an increase. Use the percentage increase calculator above to verify any increase instantly.
To understand how to calculate percentage increase, treat the original (old) value as your 100% baseline. Then measure how far above it the new value sits.
Example — Salary raise: Maria's monthly salary moves from $3,500 to $3,850.
- (3,850 − 3,500) ÷ 3,500 × 100 = 10% increase
This is how employers and employees verify that a stated raise percentage matches the actual dollar change.
Percentage Decrease Formula
When the new value is smaller, the result is negative — that is your percentage decrease. Drop the minus sign when reporting the decrease as a plain number. The percentage decrease calculator above shows the result as a positive number labeled "decrease" automatically.
Example — Retail discount: A jacket was $120; it is now on sale for $90.
- (90 − 120) ÷ 120 × 100 = −25%
- Report as: 25% decrease (or 25% off)
How to Calculate Percentage Change Between Two Numbers
To calculate percentage change between two numbers, you need to know which came first (the old value) and which came second (the new value). Order matters — reversing the two values gives a different answer.
| Old Value | New Value | Percentage Change |
|---|---|---|
| 50 | 75 | +50% |
| 75 | 50 | −33.3% |
| 200 | 150 | −25% |
| 150 | 200 | +33.3% |
| 1,000 | 1,250 | +25% |
| 1,000 | 800 | −20% |
Calculate Percent Growth — Investment Example
Investors use percentage change daily to calculate percent growth on a portfolio or individual asset.
Example: James buys shares at $4,200. They are worth $5,460 one year later.
- (5,460 − 4,200) ÷ 4,200 × 100 = 30% growth
The same formula works for calculate percent improvement in any metric — website traffic, test scores, production output. Old value is always the baseline. To calculate percentage increase online, simply enter both values above and the result appears instantly.
Calculate Raise Percentage
To calculate a raise percentage, use your current salary as the old value and your new salary as the new value.
Example: Hassan earns $52,000/year. After his annual review he is offered $56,160.
- (56,160 − 52,000) ÷ 52,000 × 100 = 8% raise
This lets you confirm exactly what percentage your employer is offering before you sign. If you already know the percentage and want to find the new salary, multiply: 52,000 × 1.08 = $56,160. The rate of change calculator above handles this automatically.
Calculate Percentage Increase in Price
To calculate percentage increase in price, apply the same formula with the old price as the base.
Example: A grocery basket that cost $85 last month now costs $94.35.
- (94.35 − 85) ÷ 85 × 100 = 11% price increase
Tracking price changes this way helps consumers spot inflation patterns and businesses monitor supplier cost changes accurately. The same method is used by the U.S. Bureau of Labor Statistics to calculate the Consumer Price Index (CPI), which measures price changes across thousands of goods and services.
Percentage Change with Negative Numbers
The formula still works when one or both values are negative. The key rule: divide by the absolute value of the old number.
Example: A company's profit moves from −$8,000 (loss) to −$3,000 (smaller loss).
- (−3,000 − (−8,000)) ÷ |−8,000| × 100
- = 5,000 ÷ 8,000 × 100 = +62.5% (improvement)
Note: if the old value is zero, percentage variation is mathematically undefined — you cannot divide by zero. Use absolute change (the raw difference) in that case.
Percentage Change vs Percentage Points
These two terms measure different things and are often confused. Understanding the difference between percentage change and percentage points is essential for reading financial news accurately.
| Term | What it measures | Example |
|---|---|---|
| Percentage change | Relative change from a base value | Rate rises from 4% to 6%: that is a 50% change |
| Percentage points | Arithmetic difference between two percentages | Rate rises from 4% to 6%: that is 2 percentage points |
When an interest rate rises from 4% to 6%, both statements are correct: "it rose 50%" (percentage change) and "it rose 2 points" (percentage points). They describe different aspects of the same change. News headlines almost always mean percentage points when they say a rate "rose 2%."
Percentage Difference vs Percentage Change
These are related but not the same concept. Use the percentage difference calculator approach when neither value is clearly the starting point:
- Relative change (percentage change) — directional; uses the original value as the base. Used for changes over time (before vs after).
- Percentage difference — symmetric; uses the average of both values as the base. Used when comparing two independent measurements.
Use percentage change when one value clearly came before the other. Use percentage difference when comparing two independent measurements (e.g., two different products' prices). This is why the percent change formula always specifies an old and new value, never just two values.
How to Calculate Percentage Difference
To calculate percentage difference, use the average of both values as the denominator:
Percentage Difference = |Value A − Value B| ÷ ((Value A + Value B) ÷ 2) × 100
This gives a symmetric result — the order of the two values does not matter. This is useful when comparing two products, two groups, or two measurements taken at the same time.
Calculate Percentage Change Between Two Numbers — Quick Reference
When you need to calculate percentage increase between two numbers or find the decrease, the order is what matters. Always put the earlier or baseline figure as the old value. The percentage between two numbers is always relative to where you started.
Quick rule: if the result is positive, it is an increase. If it is negative, it is a decrease. The size of the number tells you by how much, relative to the starting point.
Reverse Percentage Change — Finding the Original Value
If you know the final value and the percentage change, you can work backwards to find the original value:
Original Value = New Value ÷ (1 + (% Change ÷ 100))
Example: A laptop now costs $792 after a 10% price increase. What was the original price?
- 792 ÷ (1 + 0.10) = 792 ÷ 1.10 = $720
Common Mistakes When Calculating Percentage Change
| Mistake | What goes wrong | Correct approach |
|---|---|---|
| Dividing by the new value instead of the old | Wrong base gives wrong result | Always divide by the original (old) value |
| Swapping old and new values | Turns an increase into a decrease | Confirm which value came first |
| Forgetting the absolute value for negative old values | Sign error changes the direction | Use |old value| in the denominator |
| Confusing percentage change with percentage points | Overstates or understates the change | Use percentage points only for difference between two percentages |
| Adding percentage changes together | +50% then −50% is not 0% (it is −25%) | Always recalculate from the current base each time |
Limitations of Percentage Change
- Zero base: If the old value is 0, the formula is undefined. Use absolute change instead.
- Sign changes: If the value crosses zero (e.g., profit turns from negative to positive), the result can be misleading. Provide context alongside the percentage.
- Non-additive: Percentage changes cannot be added across periods. A 20% increase followed by a 20% decrease leaves you 4% below where you started.
- Context required: A 100% increase on a base of $1 is still only $2. Raw numbers alongside percentages give a complete picture.
- Growth rate interpretation: Percentage change measures a single-period growth rate. For multi-period growth, use compound annual growth rate (CAGR) instead.
For related calculations, try DigiCalc's average calculator or mean calculator to analyze your dataset before computing how it changed over time. If you work with financial figures, the salary calculator can pair with this tool to model take-home pay after a raise.