Repeated growth
Calculate the true total increase when a value grows by a percentage across multiple periods.
Compound Percentage Change Calculator
Calculate the true cumulative effect of multiple percentage increases and decreases applied one after another.
Total Compound Change
Final Value
Amount Changed
Combined Multiplier
Step-by-Step Calculation
Press Enter to calculate
Cumulative percentage change
Compound Percentage Change Calculator
A Compound Percentage Change Calculator helps you calculate the total effect of repeated percentage increases or decreases. It is useful when a value changes more than once and each new change is applied to the latest value, not only the original amount.
For example, if a price increases by 10% this year and then increases by another 10% next year, the total increase is not exactly 20%. The second increase is applied to the already increased price, so the final result is higher than simple addition.
This calculator is useful for investment returns, inflation, sales growth, salary increases, depreciation, repeated discounts, business forecasts, and financial planning. For a single old-to-new comparison, use the Percentage Change Calculator. For a one-step rise or fall, use the Percentage Increase Calculator or Percentage Decrease Calculator.
Ready to calculate compound percentage change?
Use the calculator at the top of this page to enter an initial value and multiple percentage changes in order.
Calculate Compound ChangeWhat Is a Compound Percentage Change Calculator?
A Compound Percentage Change Calculator finds the final value and total percentage change after multiple percentage changes are applied in sequence. A normal Percentage Change Calculator compares one starting value with one final value. A compound percentage change calculation handles repeated changes over time.
Use it when a value increases by 5% every year, a product price rises by 8% then falls by 3%, a business grows by several different rates, an asset loses value each month, or a salary increases for several years.
Repeated decline
Find the total decrease when each percentage loss is applied to the latest value.
Mixed changes
Combine increases and decreases, such as a price increase followed by a discount.
Simple example: start with 100, increase by 10%, then increase again by 10%. The final value is 121, so the total compound increase is 21%, not 20%.
Compound Percentage Change Formula
For multiple percentage changes, convert each change into a multiplier and multiply them in sequence.
Formula / Multiple Changes
Final Value = Initial Value × ∏(1 + r ÷ 100)
In this formula, Initial Value is the starting amount, r is each percentage change, a positive r means an increase, and a negative r means a decrease.
Formula / Total Compound Change
Compound Change = ((Final Value − Initial Value) ÷ Initial Value) × 100
If the same rate repeats for several periods, the formula is:
Formula / Same Rate Repeated
Final Value = Initial Value × (1 + r ÷ 100)n
This is why compound change is closely related to compounding in finance, but it can also be used for prices, traffic, salaries, revenue, population, and depreciation.
Need a quick answer?
Enter the initial value and each percentage change above to get the final value and net compound change.
Use the CalculatorHow to Calculate Compound Percentage Change Manually
Follow these steps to calculate compound percentage change by hand.
Write down the starting value
Example: 500
List each percentage change
Example: +12%, +8%, and −5%.
Convert each percentage into a multiplier
12% increase = 1.12, 8% increase = 1.08, and 5% decrease = 0.95.
Multiply the starting value by each multiplier
500 × 1.12 × 1.08 × 0.95 = 574.56
Compare the final value with the starting value
((574.56 − 500) ÷ 500) × 100 = 14.91%
The total compound percentage change is a 14.91% increase. This is different from simply adding the rates because every change is applied to the updated value.
Worked Examples
Growth
Example 1: Repeated Annual Growth
A business starts with revenue of $50,000. Revenue increases by 10% per year for 3 years.
50,000 × (1.10)3 = 66,550
Total compound change:
((66,550 − 50,000) ÷ 50,000) × 100 = 33.1%
The business revenue increased by 33.1% over 3 years. This is higher than a simple 30% because the growth compounds each year.
Mixed change
Example 2: Increase Followed by Decrease
A product price is $200. It increases by 25%, then decreases by 20%.
200 × 1.25 = 250
250 × 0.80 = 200
The final price is back to $200, so the total compound percentage change is 0%.
Inflation
Example 3: Inflation Over Several Years
A household expense starts at $1,000. It increases by 6%, 4%, and 7% over three years.
1000 × 1.06 × 1.04 × 1.07 = 1179.57
Total compound increase:
((1179.57 − 1000) ÷ 1000) × 100 = 17.96%
The expense increased by approximately 17.96% over three years.
Depreciation
Example 4: Monthly Decline
A machine has a value of $8,000. It loses 3% of its value each month for 6 months.
8000 × (0.97)6 = 6663.78
The machine value decreased by approximately 16.70% over 6 months. This is not a simple 18% decrease because each 3% loss is applied to a smaller value.
Sales
Example 5: Sales Growth With Different Rates
A store starts with 1,200 monthly orders. Orders grow by 15%, 10%, and 12%.
1200 × 1.15 × 1.10 × 1.12 = 1700.16
The total compound growth is 41.68%, so the store moved from 1,200 orders to about 1,700 orders.
How to Use This Compound Percentage Change Calculator
Enter the starting value and each percentage change in order. The calculator applies every increase or decrease step by step and shows the final result.
Initial Value
The original amount before any change, such as starting price, revenue, salary, investment, or population.
Percentage Changes
Enter positive values for increases and negative values for decreases. For example, use 10 for a 10% increase and -5 for a 5% decrease.
Add More
Add additional percentage changes when the value changes across more periods or steps.
Final Result
The result shows the total compound change, final value, and whether the overall result is a gain or loss.
Input tip: Do not enter a decrease as a positive number. A 5% decrease should be entered as -5, not 5.
Compound Percentage Change vs Simple Percentage Change
Compound percentage change and simple percentage change are not the same. A simple Percentage Change Calculator compares one initial value with one final value. Compound percentage change calculates the effect of several percentage changes applied one after another.
| Simple Percentage Change | Compound Percentage Change |
|---|---|
| Measures one old-to-new change | Measures several changes in sequence |
| Uses original and final values | Uses initial value and one or more rates |
| Best for one-time comparison | Best for repeated growth or decline |
| Example: 100 to 120 = 20% | Example: 100 +10% +10% = 121, or 21% |
If you know the final value and only need one comparison, use the Percentage Change Calculator. If you already know the result is only an increase, use the Percentage Increase Calculator. If it is only a decrease, use the Percentage Decrease Calculator.
Applications of Compound Percentage Change
Finance and investing
Estimate portfolio growth, long-term returns, repeated losses, and investment performance. For one investment result, use the ROI Calculator.
Business revenue
Measure sales growth, revenue increases, customer growth, and changing costs across several periods.
Inflation and costs
Understand how repeated annual price increases compound over time.
Salary growth
Calculate the real effect of repeated raises because each raise applies to the updated salary.
Discounts and pricing
Evaluate multiple discounts or price changes. For one simple markdown, use the Discount Calculator or Sale Price Calculator.
Marketing growth
Track traffic, leads, subscribers, conversions, and campaign performance over several periods. For conversion share, use the Conversion Rate Calculator.
Tips for Accurate Compound Percentage Calculations
Convert rates into multipliers
Use 1 + rate for increases
Use 1 − rate for decreases
Do not add rates directly
Use the correct number of periods
Match rate and time period
Keep decimal precision
Round at the end
Compound calculations are most accurate when each rate is applied to the latest value and not repeatedly applied to the original amount. This matters for business growth, inflation, depreciation, repeated discounts, and investment returns.
Common Mistakes When Calculating Compound Percentage Change
Adding percentages directly
Two increases of 10% do not equal a 20% compound increase. 100 × 1.10 × 1.10 = 121, so the total increase is 21%.
Treating a decrease like an increase
A 15% decrease should be converted to 0.85, not 1.15.
Using the original value every time
In compound change, each new percentage is applied to the latest value, not the starting value.
Confusing a decrease and recovery
If a value drops by 10%, it must increase by more than 10% to return to the original value.
Mixing time periods
Do not apply a monthly rate as if it were an annual rate unless you adjust the number of periods correctly.
Rounding each step too early
Rounding after every period can make the final answer slightly inaccurate. Keep full precision and round the final result.
Frequently Asked Questions
What is a Compound Percentage Change Calculator
A Compound Percentage Change Calculator finds the total effect of multiple percentage increases or decreases applied one after another.
How do you calculate compound percentage change?
Convert each percentage change into a multiplier, multiply all the multipliers by the starting value, then compare the final value with the original value.
What is the compound percentage change formula?
For repeated equal rates, use [(1 + r/100)n − 1] × 100. For different rates, multiply each percentage change factor together and compare the final value with the original value.
How do you calculate repeated percentage increases?
Use Final Value = Initial Value × (1 + r/100)n. For example, a 10% increase for 3 periods uses (1.10)3.
Are two 10% increases equal to 20%?
No. Two 10% increases create a 21% compound increase because 100 × 1.10 × 1.10 = 121.
Is a 50% increase followed by a 50% decrease equal to no change?
No. Starting from 100, a 50% increase gives 150. A 50% decrease from 150 gives 75, which is 25% below the original value.
Can compound percentage change be negative?
Yes. If the final value is lower than the starting value, the compound percentage change is negative.
Is compound percentage change used for investments?
Yes. It is commonly used for investment growth, annual returns, portfolio performance, and long-term financial growth. For a single investment return calculation, the ROI Calculator is also useful.
How do I calculate compound change with both increases and decreases?
Convert increases into multipliers above 1 and decreases into multipliers below 1, then multiply them in sequence. For example, +20% is 1.20 and −10% is 0.90, so the combined multiplier is 1.08.
Related Calculators
Use these related tools for one-step percentage comparisons, business metrics, sales, tax, and performance calculations.
Percentage Change Calculator
Compare an original value with a new value.
Percentage Increase Calculator
Calculate growth from a starting amount.
Percentage Decrease Calculator
Find how much a value dropped.
Percentage Difference Calculator
Compare two independent values.
ROI Calculator
Measure return on investment.
Profit Margin Calculator
Calculate profit as a percentage.
Discount Calculator
Find savings and final price.
Sales Tax Calculator
Calculate tax and total price.
Conversion Rate Calculator
Calculate conversions as a percentage.
Final Note
A Compound Percentage Change Calculator gives the true result when a value changes repeatedly over time. Whether you are calculating investment growth, inflation, price changes, salary raises, business performance, depreciation, or repeated discounts, compound percentage change shows the real final effect instead of a simple estimate.
Calculate the true net change now.
Enter your starting value and each percentage change to get the final compound result.
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