Example 1
- x = 1
0
What is ln(1)? 0, because e⁰ = 1.
Natural logarithm
Type an x greater than zero. The natural logarithm, ln(x), asks what power of e returns x. e is about 2.71828. ln(e) = 1. ln(1) = 0. ln(20) ≈ 2.99573.
The base is e, not 10. Common log and an arbitrary base live on the neighbouring cards. x ≤ 0 leaves a blank result.
Results
Enter data and click Calculate.
How it works
The natural logarithm undoes a power of e. You want y such that e^y = x. For x = e you get 1. For x = 1 you get 0, because e⁰ = 1. For x = 20 the calculator computes ln and shows 2.995732.
e is the base that shows up in continuous growth and in the integral of 1/x. You do not type it. It is baked into ln. If you want 10, open the common logarithm. If you want another base, open the logarithm card.
The field is x. Zero and a minus have no real ln. The calculator stays blank. A comma and a dot are the same decimal. Type 20, or about 2.71828 to see a one.
ln(e²) = 2. ln(e³) = 3. That is clean when x is a pure power of e. For 10 the result is ln(10) ≈ 2.302585, the bridge from log₁₀ to ln: ln(x) = log₁₀(x) · ln(10).
The header units switch does not multiply anything here. 20 stays 2.99573 whatever the label says. This is an exponent, not a centimetre.
ln(1) = 0. ln(e) = 1. ln(20) ≈ 2.99573. ln(0.5) ≈ −0.69315. A fraction smaller than 1 gives a minus. x itself stays positive.
Formula
ln(x) = Math.log(x), for x > 0
How to use
- Type x, for example 20.
- Click Calculate. ln(20) ≈ 2.99573.
- 1 gives 0. e, about 2.71828, gives 1.
- Zero and a minus leave a blank field.
- Base 10 lives on the common logarithm. Another base lives on the logarithm card.
ln(e) = 1
Natural logarithm ln(x) has base e ≈ 2.718. ln(1) = 0. ln(e) = 1. ln(20) ≈ 2.99573. x must be positive.
- ln
- Natural logarithm, ln. ln(1) = 0. ln(e) = 1. ln(20) ≈ 2.99573.
- e
- The base, about 2.71828. You do not type it in a second field. 10 lives on the common logarithm.
- x
- A positive argument. 20 gives ≈ 2.99573. 0.5 gives a minus. Blank when x ≤ 0.
Examples
Example 2
- x = 20
2.995732
What is ln(20)? About 2.99573.
Example 3
- x = 2.718281828459045
1
Is ln(e) one? Yes. Type e ≈ 2.71828.
Related calculators
Common questions
What are ln(1) and ln(e)?
ln(1) = 0. ln(e) = 1. You type e as about 2.71828. The calculator has no separate “e” button.
What does natural logarithm mean?
Logarithm base e. ln(x) asks what power of e returns x.
What is ln(20)?
About 2.99573. 20 is not a clean power of e, so the result is not a whole number.
Do 0 and negative numbers pass?
No. Real ln needs x > 0. The result is a blank.
How is ln different from log₁₀?
Another base. ln(10) ≈ 2.302585 joins the two scales: ln(x) = log₁₀(x) · ln(10).
What is ln(0.5)?
About −0.69315. x is positive, the result is negative, because 0.5 is smaller than 1.
Where do I type the base?
You do not. e is in the formula. Another base goes on the logarithm card.
Is ln the same as log₁₀?
Natural log is ln. Common log is log₁₀. This calculator computes ln.
Why e in growth?
Continuous growth stacks into a power of e. Here you invert it: from x you return to the exponent.
Does a comma in 2.718 work?
Yes. 2.718 and 2,718 are the same approximation of e and the result is close to 1, not exact 1.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.