📐 Math
Percentage Change Calculator
Find the percentage increase or decrease between two values.
📝 Your Assumptions
Calculate the percentage change between any two values. Enter the original value and the new value to see the percentage increase or decrease, plus the absolute difference. Useful for tracking price changes, salary adjustments, investment returns, or any measurement that changes over time.
How to Use This Calculator
Follow these steps to find the percentage change between two numbers.
1
Enter the original value
Type the starting number in the "Original value" field. For example, if a stock was $80 last month, enter 80.
2
Enter the new value
Type the ending number in the "New value" field. If that same stock is now $92, enter 92.
3
Read the percentage change
The primary result shows the percentage change: in this example, (92 − 80) / 80 × 100 = 15%. A positive number means an increase, a negative means a decrease.
4
Check the absolute difference
The second output shows the raw difference in the same units as your inputs. For the stock example, the difference is $12.
5
Test different scenarios
Change the new value to see how the percentage changes. Going from 80 to 60 gives −25%, and going from 80 to 100 gives +25%.
What Your Results Mean
Understanding the output helps you interpret the change correctly.
Percentage Change
The relative change from the original value, expressed as a percent. It uses the original value as the denominator — this is the standard for "percentage change" in finance and statistics.
Absolute Difference
The raw numeric difference between the two values (new − original). Same units as your inputs, not a percentage.
Positive vs. Negative
A positive result means the value increased. A negative result means it decreased. Zero means no change at all.
Comparing Non-Sequential Values
If neither value is clearly "before" or "after," use our percentage difference calculator instead — it uses the average of both values as the base.
Compounding
Repeated percentage changes compound. A 10% increase followed by another 10% increase is 21% total, not 20%.
Common Uses
Price changes, salary raises, investment returns, population growth, sales performance, and any measurement tracked over time.
Key Terms
Percentage Change
The difference between two values divided by the original value, expressed as a percentage. Formula: (new − original) / original × 100.
Original Value
The starting or baseline number in a comparison. It serves as the denominator in the percentage change formula.
New Value
The ending number in a comparison. It is compared against the original value to determine the change.
Percentage Increase
A positive percentage change. Example: going from 100 to 120 is a 20% increase.
Percentage Decrease
A negative percentage change. Example: going from 120 to 100 is a 16.67% decrease.
❓ Frequently Asked Questions
The formula is: (New Value − Original Value) ÷ Original Value × 100. For example, if your rent went from $1,200 to $1,350: (1350 − 1200) ÷ 1200 × 100 = 12.5%. So your rent increased by 12.5%. If the result is negative, the value decreased. This calculator does the math automatically — just enter the original value and the new value. Remember, the original value is always the denominator, not the new value. Using the wrong denominator is the most common mistake.
Percentage change uses the original value as the base and is directional: from 100 to 120 is +20%, but from 120 to 100 is −16.67%. Percentage difference uses the average of both values as the base and is non-directional: the difference between 100 and 120 is 18.18% regardless of order. Use percentage change when there is a clear "before" and "after" — prices, salaries, returns. Use percentage difference when comparing two values that don't have a natural starting point — like two products, two cities, or two measurements.
Yes. A 150% increase on $40 gives $100 (40 × 2.5). A 200% increase on $50 gives $150 (50 × 3). There is no upper limit. When a value doubles, that is a 100% increase. When it triples, that is a 200% increase. Just be careful interpreting: a 100% increase means adding the full original value on top of itself, not multiplying by 100. For example, "a 100% increase from $50" means $100, not $5,000.
Divide the new value by (1 + percentage/100). For example, if a price after a 20% increase is $120, the original was $120 ÷ 1.20 = $100. For a 25% decrease ending at $75, the original was $75 ÷ 0.75 = $100. This reverse calculation is useful when you know the final amount and the percentage change but need the starting point. Be careful not to just subtract the percentage — that gives the wrong answer because the percentage was calculated from the original value, not the new one.
Going from 100 to 120 is a +20% change, but going from 120 to 100 is only a −16.67% change. This asymmetry happens because the denominators are different (100 in the first case, 120 in the second). This is why financial losses hurt more than equivalent gains help — losing 50% requires a 100% gain to recover. The asymmetry is a feature of percentage math, not a bug. It means you must be precise about which value is the "original" when comparing changes.
Percentage change cannot be calculated when the original value is zero — dividing by zero is undefined. If the original value is 0 and the new value is 100, there is no meaningful percentage change because the base was zero. Our calculator will return 0 in this case rather than an error. In practice, when the baseline is zero you should use absolute difference rather than percentage change, since percentages are only meaningful relative to a non-zero base.
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