Repeated Percentage Increase Calculator
Increase a starting amount by a percentage, then increase the new total by the same percentage again — as many times as you need. This is also called compound growth or a compound percentage increase. You get the final amount, the total percentage change, and every step in a table.
Just need a single percentage change, or the percentage between two numbers? Use the Percentage Increase Calculator.
Background
When a percentage is applied again and again, each step uses the latest total — not the starting amount. That is why raising 100 by 10% five times gives 161.05, not 150. Each repeat multiplies the amount by (1 + percent/100), so after n repeats the amount is start × (1 + percent/100)ⁿ.
How to use this calculator
- Enter the starting amount.
- Enter the percentage to apply each time (for example 10 or 7.5%). Use a negative number for a decrease.
- Enter how many times to repeat it (1 to 1,000).
- Click Calculate (or press Enter in a box) to see the final amount, the total percentage change, every step, and a chart.
- Tick Round each step if you want every step rounded to 2 decimal places before the next one, as you would with money.
- Optional: enter a target amount to see which repeat first reaches it, and whether it is reached within the repeats you chose.
- Optional: choose what to call each repeat (step, year, month, week or day) so the results read naturally, for example “after 10 years”.
How this calculator works
- One step: new amount = amount × (1 + percent/100)
- Repeating it n times: final = start × (1 + percent/100)ⁿ
- Total percentage change: ((1 + percent/100)ⁿ − 1) × 100%
- Each row of the table starts from the previous row’s result.
- Time to double (or halve): ln 2 ÷ ln(1 + percent/100) repeats.
- Repeats needed to reach a target: ln(target ÷ start) ÷ ln(1 + percent/100), rounded up to a whole repeat.
Formula & Equations Used
Multiplier per step: m = 1 + percent/100
Final amount: final = start × mⁿ
Total change: final − start
Total percent change: (final ÷ start − 1) × 100%
Repeats to reach a target: ln(target ÷ start) ÷ ln m
Time to double: ln 2 ÷ ln m (halve: ln 0.5 ÷ ln m)
Example Problems & Step-by-Step Solutions
Example 1 — 100, increased by 10% five times
Step 1: 100 × 1.10 = 110. Step 2: 110 × 1.10 = 121. Step 3: 121 × 1.10 = 133.1. Step 4: 133.1 × 1.10 = 146.41. Step 5: 146.41 × 1.10 = 161.051. The total increase is 61.051%, not 5 × 10% = 50%.
Example 2 — 1,000, increased by 5% ten times
final = 1,000 × 1.05¹⁰ = 1,000 × 1.628895 ≈ 1,628.89. The total increase is about 62.89%.
Example 3 — 500, decreased by 10% four times
Use −10%. final = 500 × 0.90⁴ = 500 × 0.6561 = 328.05. The total decrease is 34.39%, not 4 × 10% = 40%.
Example 4 — How long to double 1,000 at 5% a year?
Doubling means reaching 2,000. Repeats needed = ln(2,000 ÷ 1,000) ÷ ln(1.05) = 0.693147 ÷ 0.048790 ≈ 14.21. A year can’t be part-done, so it takes 15 years: after 14 years the amount is 1,979.93, and after 15 years it is 2,078.93.
Frequently Asked Questions
Q: Why isn’t 10% repeated 5 times the same as 50%?
Because each step uses the latest total. The second 10% is taken from 110, not from 100, so it adds 11 instead of 10, and so on. The calculator shows the difference.
Q: Is this the same as compound interest?
Yes, the maths is identical. For interest, the percentage is the rate for one period (a year, a month) and the number of times is the number of periods.
Q: Can I use it for a decrease?
Yes. Enter a negative percentage, such as −10, and the amount shrinks by 10% of the latest total each time.
Q: What does “Round each step” do?
It rounds the amount to 2 decimal places after every step before the next percentage is applied, which is what happens when you repeat the calculation with money. Without it, the calculator keeps full precision and only rounds what it shows.
Q: How many times can I repeat it?
Up to 1,000. For long runs the table shows the first 20 and last 20 steps, and the chart still covers every step.
Q: How do I find how many times it takes to reach a target?
Type the amount you are aiming for in Target amount. The calculator shows the first repeat that gets there, highlights that row in the table, and tells you if your chosen number of repeats is not enough (and how many would be).
Q: What does “Time to double” mean?
It is how many repeats it takes for the amount to become twice as big (or, for a decrease, half as big): ln 2 ÷ ln(1 + percent/100). At 5% a repeat it is about 14.2 repeats.
Q: Can I call each repeat a year, month, week or day?
Yes. Use “Call each repeat a” in the options, and the results, table and chart will say years, months, weeks or days instead of steps.
Q: How do I work out one percentage increase between two numbers?
Use the Percentage Increase Calculator. Enter the original and new values and it gives the percentage increase or decrease, or enter any two of original, new and percent to find the third.
Q: How do I find the single percentage that equals all the repeats?
Use the total percent change shown in the results: ((1 + percent/100)ⁿ − 1) × 100%.
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