Why daily percentages don't just add up
Example
A stock price starts at $100 and increases by exactly 1% every day for 30 days. Naively adding 1% × 30 = 30% suggests a final price of $130. But the real result is:
100 × (1.01)^30 = 134.78
The actual increase is 34.78%, not 30% — because each day's 1% is calculated on the previous day's already-higher value, not on the original $100.
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%.
Converting a daily rate to a monthly rate
Going the other way, 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 can't be found by averaging yearly percentages either — it needs the same geometric approach shown above.
Want to calculate the change between two specific values instead? Use the percentage change calculator.