Percentage changes over time do **not** add up linearly. A common mistake is assuming that if a value changes by 1% per day, it must change by roughly 30% in a month (1% × 30 days). But percentage change compounds — each day’s change applies to a new value, not the original one. This is the same geometric effect used in a percentage change calculation repeated over time.

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Why daily percentages don’t simply add up

Example
A stock starts at $100 and increases by exactly 1% every day for 30 days. If you naïvely add 1% × 30 = 30%, you’d expect a final price of $130. But the real result is:

100 × (1.01)³⁰ = 134.78

The actual increase is **34.78%**, not 30%. Each day’s 1% is applied to the previous day’s already‑higher value — not to the original $100.

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Converting a monthly rate to a daily rate

If you know the monthly percentage change and want the equivalent constant daily rate (assuming a 30‑day month), use:

daily rate = (1 + monthly rate)^1/30 − 1

Example
A value grows by 10% over a month. What constant daily rate produces the same result?

(1.10)^1/30 − 1 = 1.00319 − 1 = 0.00319

That’s a daily rate of **about 0.32%**.

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Converting a daily rate to a monthly rate

To find the monthly change from a known constant daily rate:

monthly rate = (1 + daily rate)³⁰ − 1

Example
A value changes by 0.5% every day. Over a 30‑day month:

(1.005)³⁰ − 1 = 1.1614 − 1 = 0.1614

That’s a monthly change of **about 16.14%**, not the 15% you’d get by simply multiplying 0.5% × 30.

This same compounding logic is why a CAGR figure cannot be found by averaging yearly percentages — it requires the same geometric approach shown above.

Want to calculate the change between two specific values instead? Use the percentage change calculator.