Natural Log Calculator
Use our natural log calculator to calculate natural log (ln) instantly. Includes how natural logs work, natural log properties, key values like natural log of 1, e, and 0, plus tips for how to put natural log in calculator and natural log in Excel.
What is Natural Log?
The natural log (written ln) is a logarithm with base e, where e ≈ 2.718281828. It’s one of the most important functions in math, science, finance, and statistics.
If you’re wondering what does natural log mean, it answers the question: “What power do I raise e to, to get this number?” In other words, ln(x) is the exponent y such that e^y = x.
Natural logs show up in growth and decay models, continuous compounding, probability, and calculus. That’s also where natural log comes from historically—ln is tied to the exponential function and the constant e.
Natural Log Formula
Natural log is the logarithm base e. It’s defined as the inverse of e^x.
Real ln(x) is defined only for x > 0.
Because e^0 = 1.
Because e^1 = e.
How to Use the Natural Log Calculator
- 1
Enter the number you want the natural log of (x).
- 2
The calculator computes ln(x).
- 3
Review the result (ln value).
- 4
If you’re using a calculator, look for the LN button to put natural log in calculator form.
Frequently Asked Questions
Use ln(x), which is the log base e. A natural log calculator computes ln(x) directly.
They reverse exponentiation with base e: ln(x) is the exponent y such that e^y = x.
For special values, you can use known identities (ln(1)=0, ln(e)=1) and logarithm properties. For general numbers, exact values often require approximation methods.
Yes. ln(x) is negative when 0 < x < 1 (for example ln(0.5) is negative).
ln(1) = 0.
ln(0) is undefined (in real numbers) and tends toward negative infinity as x approaches 0 from the positive side.
As x grows without bound, ln(x) also increases without bound (it tends to infinity, but grows slowly).
Use the LN key on a scientific calculator. If you only have LOG (base 10), you can convert using ln(x) = log10(x) ÷ log10(e).
Excel uses LN(number). Example: =LN(10).
People use this phrase to ask what happens as x becomes extremely large. ln(x) increases without bound, but slowly compared to x.
The natural log function y=ln(x) is only defined for x>0, passes through (1,0), increases slowly, and has a vertical asymptote at x=0.
It comes from the exponential function base e and appears naturally in calculus, continuous growth, and area under the curve of 1/x.
Key properties include: ln(ab)=ln(a)+ln(b), ln(a/b)=ln(a)-ln(b), and ln(a^k)=k·ln(a).
The natural log function is y = ln(x), the inverse of y = e^x.