# Natural Log Calculator

URL: https://speedycalculator.com/calculators/math/natural-log/
Last updated: 2026-10-30

> The natural log calculator finds ln x, the logarithm to base e ≈ 2.71828, of any positive number – and the number from its natural log.

## Inputs

- Number x

## Results

- ln x
- log₁₀ x
- log₂ x

## Formula

```
ln x = log_e x,  e^(ln x) = x,  e ≈ 2.718281828
```

## Explanation

The natural logarithm is the logarithm calculus loves: its derivative is 1/x. It appears in continuous growth and decay, half-lives, compound interest, entropy and the time constant of circuits.

### How to use the Natural Log Calculator

- **Number x**
- Every result field is editable: type into **ln x** and **Number x** plus every other field update to match.

Results update as you type, and everything is calculated in your browser.

### How it works

Enter x, or type a value into the ln x field to get x = e^(value).

### What each result means

- **ln x** = ln([Number x])
- **log₁₀ x** = ln([Number x])÷ln(10)
- **log₂ x** = ln([Number x])÷ln(2)

### Example values

How the main result changes when **Number x** changes and everything else stays at the example values above:

Number xln x51.60947.52.0149102.302612.52.5257152.7081202.9957

## Worked example

Inputs — Number x: 10.

Results — **ln x = 2.302585092994**; log₁₀ x = 1; log₂ x = 3.321928094887.

## Key terms

- **e**: Euler's number, ≈ 2.718281828.

## FAQ

**What is ln e?**
1.

**What is ln 0?**
Undefined – ln x goes to −∞ as x approaches 0.

**How do I convert ln to log?**
log₁₀ x = ln x / ln 10 ≈ ln x / 2.302585.

**Why is it called "natural"?**
It arises naturally from continuous growth and from the integral of 1/x.


## Sources

- [OpenStax – College Algebra 2e](https://openstax.org/details/books/college-algebra-2e)
- [OpenStax – Precalculus 2e](https://openstax.org/details/books/precalculus-2e)
- [Wolfram MathWorld – Natural logarithm](https://mathworld.wolfram.com/NaturalLogarithm.html)