Percentage Change Calculator
Calculate the percentage increase or decrease between two values quickly and accurately.
What Is the Percentage Change Calculator?
This percentage change calculator handles four related problems: computing the percentage change between two values, finding a new value after a given percentage change, finding the original value before a change, and computing compound annual growth rate (CAGR) over multiple years.
- ›% Change: Signed result with increase/decrease badge and absolute change.
- ›Find New Value: Apply a percentage increase or decrease to a starting value.
- ›Find Original: Reverse a percentage change to recover the pre-change value.
- ›CAGR: Average annual growth rate for a value growing from start to end over n years.
Formula
| Mode | Formula | Use case |
|---|---|---|
| % Change | ((New − Old) / |Old|) × 100 | Price, stock, revenue change |
| Find New Value | Old × (1 + % / 100) | Forecast after known % growth |
| Find Original | New / (1 + % / 100) | Pre-increase/pre-tax value |
| CAGR | ((End/Start)^(1/n) − 1) × 100 | Annual growth rate over n years |
How to Use
- 1Select a mode: % Change, Find New Value, Find Original, or CAGR.
- 2Enter the required values. For CAGR, enter starting value, ending value, and number of years.
- 3Press Enter or click Calculate.
- 4Read the percentage result with direction badge (increase/decrease).
- 5Click Clear to reset.
Example Calculation
CAGR example: investment growth
CAGR vs simple average growth rate
Understanding Percentage Change
Percentage Change Formula
Percentage change measures change relative to the starting value: % change = ((New − Old) / |Old|) × 100. Using the absolute value |Old| ensures that when the original is negative, a larger (less negative) new value is correctly flagged as an increase. This is the standard formula used in finance, economics, and data analysis.
When Percentage Changes Compound
Percentage changes do not add, they multiply. A 20% increase followed by a 20% decrease gives: 1.20 × 0.80 = 0.96, a net −4% change, not zero. Three 10% raises give: 1.10³ = 1.331, a 33.1% total increase, not 30%.
- ›+10% then +10% = +21%, not +20%
- ›+50% then −50% = −25%, not 0%
- ›n% increase followed by n% decrease: (1+n/100)(1−n/100) = 1 − n²/10000 < 1
CAGR vs Other Growth Measures
Compound Annual Growth Rate (CAGR) answers: "If this value grew at a constant rate every year for n years, what would that rate be?" It is the geometric mean of annual growth rates, not the arithmetic mean. CAGR is the standard measure for investment returns, revenue growth, and population growth.
| Measure | Formula | Best for |
|---|---|---|
| Simple % change | ((End/Start) − 1) × 100 | Single-period comparison |
| CAGR | ((End/Start)^(1/n) − 1) × 100 | Multi-year growth rate |
| Arithmetic mean | Sum of annual rates / n | Quick estimate (misleading for volatile series) |
Frequently Asked Questions
What is the formula for percentage change?
% Change = ((New − Old) / |Old|) × 100
The absolute value of Old handles negative base values correctly.
How do I find the new value after a percentage increase?
Use Find New Value mode. Formula: New = Old × (1 + %/100).
How do I find the original value before a percentage change?
Use Find Original mode. Formula: Original = Final / (1 + %/100).
A common mistake is subtracting the percentage from the final value: 120 − 20% of 120 = 96 ≠ 100. Always divide by (1 + p/100).
What is CAGR and how is it calculated?
CAGR (Compound Annual Growth Rate) = ((End / Start)^(1/n) − 1) × 100, where n is the number of years. It is the constant annual rate that, if applied every year, would produce the same total growth.
Why is a percentage increase not symmetric with its reverse decrease?
The base changes between the two steps. A +25% increase goes from 100 to 125. To undo it, you need to decrease 125 by 20% (not 25%): 125 × 0.80 = 100. The required reversal percentage is: reversal = p/(100+p) × 100 where p is the original increase.
When should I use CAGR instead of total percentage change?
Use CAGR when comparing growth across different time periods, it normalises to a per-year basis. Use total % change when you want to communicate the full magnitude of growth in a single period.
- ›Fund A: +100% over 10 years → CAGR = 7.18%/year
- ›Fund B: +50% over 4 years → CAGR = 10.67%/year
- ›Total % change says A doubled; CAGR says B grew faster per year
Can percentage change be calculated for negative numbers?
Yes, using |Old| (absolute value) in the denominator. However, when the original value is negative and becomes less negative (improving), the sign can be counterintuitive:
When both values have opposite signs (e.g., −10 to +10), percentage change is technically infinite or undefined because the direction of change is ambiguous. Use absolute change instead.