Natural Logarithm Calculator

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On this page is a natural logarithm calculator. Enter a number to take the natural logarithm (log base e), and we'll return the result.

Want another tool? Try another logarithm calculator or the generic logarithm tool:

Natural Logarithm Calculator

What is the Natural Logarithm?

The natural logarithm is a logarithm which uses the base e. e is an irrational number known as Euler's number and approximately equal to:

e \approx 2.71828182845904523536028747135266249775724709

(and it keeps going from there).

The natural logarithm doesn't feel very natural. However, e is a special number. Basically, the rate of change – or slope – of the equation 𝑦=𝑒^𝑥 is equal to y.

Relatedly, the logarithm ln(x) has the derivative dx/dy = 1/x – making it easy to move back and forth in calculus when using the natural logarithm.

Natural Logarithm Formula

The formula for the common logarithm is:



  • e: the base of the equation, Euler's number (we raise e to the yth power to get x)
  • x: the argument; the number we need e^y to equal
  • y: the power or exponent we need to find

The natural logarithm is also written in a few other ways:

ln(x), log(x), Log(x)

But be careful - log(x) and Log(x) more commonly refer to the common logarithm, or log base 10. In all of these forms the base e is assumed.

Natural Logarithm Example

For example, let's say you wanted to find the log base e of 100. Here's how it'd look:

\log_{e}(100)\ or\ e^y=100\\y\approx4.60517019

In this case you need to raise e to the power to get 100.

Using the Natural Logarithm Calculator

Enter one number to get the natural logarithm: the argument x. Enter that to match a sentence form of "log base e of x" or "natural logarithm of x".

When finished, hit the button to Compute Natural Logarithm.

After this, try our other tools and calculators.



PK started DQYDJ in 2009 to research and discuss finance and investing and help answer financial questions. He's expanded DQYDJ to build visualizations, calculators, and interactive tools.

PK lives in New Hampshire with his wife, kids, and dog.

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