Natural Log Calculator
Compute the natural logarithm of a positive number.
Calculator
Use the Natural Log Calculator
Result
—
Formula
ln(x)
Step-by-step
- 1
Enter a positive number
ln is defined for x > 0.
- 2
Read the result
The exponent that gives x from e.
Worked example
Example input: n: 10
Result: 2.302585
Related tools
- Common Log
Logarithm base 10.
- Exponential Growth
e^x counterpart.
Frequently asked questions
What is the natural logarithm?
It is the logarithm with base e ≈ 2.71828. ln(x) answers the question: e raised to what power gives x? By definition ln(1) = 0 and ln(e) = 1.
Why is ln(10) about 2.302585?
Because e^2.302585 ≈ 10. The natural log is simply the power of e that produces the input, which is why it pairs with the exponential growth model e^x.
What about zero or negative inputs?
ln(x) is defined only for positive numbers, so 0 and negative values return no result. There is no real power of e that produces zero, and negative numbers are out of reach.
What exactly is the constant e?
e ≈ 2.718281828 is the base of natural growth and decay — it shows up in continuous interest, population models, and physics. Since ln is its inverse, ln(e) = 1 and ln(1) = 0; enter both above to check.