Irish Calculators
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Log Return Calculator from a Price Series

Paste prices in chronological order to calculate each logarithmic return and reconcile the cumulative change. Adjust for dividends and splits beforehand if they belong in your return measure.

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Your numbers

Comma-separated positive adjusted prices. Same currency and adjustment basis; no headings.
Your figures stay on this device.

How the calculation works

Logarithmic returns express successive price changes as natural logarithms of price ratios. Their useful property is additivity across adjacent observations, which lets the cumulative log change reconcile directly with the first and last price.

Log return at t = ln(price[t] ÷ price[t−1]). Sum(log returns) = ln(last price ÷ first price).

  1. Form adjacent price ratios

    Divide each price by the immediately previous price. Ratios above one represent increases and ratios below one represent decreases between those observations.

  2. Take natural logarithms

    Apply the natural logarithm to each ratio. Unlike simple percentage changes, the resulting log changes can be added across consecutive observations.

  3. Reconcile the cumulative change

    Sum the log returns and convert back with the exponential minus one. That equivalent simple return matches the total change between the first and last supplied prices.

Worked example: Check Equivalent simple total return

Sample inputs demonstrate the method. They are not a forecast or product offer.

The first example contains prices 100, 110 and 121. Both adjacent ratios are 1.10; their log returns add to the logarithm of 1.21, which converts back to a 21% simple total return.

Prices in chronological order
100,110,121

Expected result

Equivalent simple total return
21%
Worked example: Check Cumulative log return

Sample inputs demonstrate the method. They are not a forecast or product offer.

Prices in chronological order
100,50,25

Expected result

Cumulative log return
-1.38629436

Understanding your result

A log return is not numerically identical to the corresponding simple percentage return. Small changes may look similar, but the difference becomes more pronounced for large changes.

The series has no date input. Its entries could be daily, weekly or irregular, so the calculator does not label the resulting return as annual or infer annual volatility.

Questions you might have

What does the result include?

Calculate successive logarithmic returns from a consistent positive price series and reconcile the cumulative change.

Which limits should I check?

Use adjusted prices if the intended return includes splits or dividends; no data is fetched.

Choosing the right inputs

Prices in chronological order
Enter strictly positive prices in chronological order, without headings. Use the same currency and adjustment basis throughout; dividends and splits must be reflected consistently before pasting.

Common mistakes to avoid

  • Zero or negative prices cannot be used because their logarithmic ratios are undefined.
  • Do not add simple percentage returns and expect the same cumulative result as compounding their factors.

Assumptions to check

  • Use adjusted prices if the intended return includes splits or dividends; no data is fetched.
  • All calculations run on your device. Figures are scenarios based on your inputs, not investment recommendations.

Sources and method

Read our calculation and testing approach.