Log calculator
Logarithms in base 10, base e, base 2 or any base.
About this calculator
This log calculator works out logarithms in base 10, the natural log in base e, base 2 or any base you choose.
It shows all three common logs at once, with a check that raises the base back to the answer.
How it works
log_b(x) is the power you raise b to in order to get x. Any base can be worked out from natural logs: log_b(x) = ln(x) ÷ ln(b).
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Worked example
- Number (x): 1,000
- Base: 10
log_10(1,000): 3
Common questions
What is a logarithm?
The power a base must be raised to in order to give a number. log₁₀(1000) = 3, because 10³ = 1000.
What is ln?
The natural logarithm, in base e (about 2.71828). It appears throughout science, finance and growth calculations.
Can you take the log of a negative number?
Not with real numbers. Logarithms are only defined for numbers above 0.
The story behind it
Where the idea came from: John Napier published the first tables of logarithms in 1614, turning long multiplications into simple additions.
Astronomers and navigators seized on Napier's tables, which saved them days of work. Slide rules, built on logarithms, were the engineer's calculator until the 1970s. Today logs measure everything from earthquakes to sound levels.
Why you can trust this calculator
- It runs in your browser. Nothing you type into it is sent anywhere.
- The method is explained on this page, so you can check it yourself.
- Free to use, with no sign-up.
- Results are estimates, so please double-check anything important.
- Spotted a mistake? Tell us and we'll look into it.
After 15 years as a mathematics educator, I built CalculStore to give students, teachers, professionals and anyone working with numbers simple, reliable tools.
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