Logarithm calculator
Enter a number and choose the base: 10 (log), e (ln), 2 or your own. You get the logarithm and how it is calculated.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
What is a logarithm?
The logarithm answers the question "to what power do I raise the base to get this number?". log₁₀(1000) = 3 because 10³ = 1000, and log₂(8) = 3 because 2³ = 8. The natural logarithm ln uses the number e ≈ 2.71828.
Any base
With the change of base rule, logₐ(x) = ln(x) ÷ ln(a), you can use any base greater than 0 except 1. The number itself must be greater than 0; there is no logarithm of 0 or of a negative number.
Where you use it
The Richter scale, decibels and pH are logarithmic scales. Logarithms also tell you how long exponential growth takes, as in the doubling time of the exponential growth calculator.
Frequently asked questions
Is the logarithm calculator free?
Yes. The logarithm calculator is completely free, with no account, sign-up or usage limit.
How accurate is the result?
The tool calculates with your browser's number precision. For important calculations, always double-check what you entered.
Does it work on my phone?
Yes. The tool works in any modern browser on a phone, tablet or computer.