Natural Logarithm Calculator

Work out natural logarithm instantly with clear inputs, formula shown and shareable results.

About Natural Logarithm Calculator

The natural logarithm answers the question 'e to what power gives x?'. It is the inverse of the exponential function, so ln(eˣ) = x, and its derivative 1/x makes it the backbone of calculus with growth and decay.

Formulas

Natural logarithm

ln x = y ⇔ eʸ = x

Conversion

log₁₀ x = ln x / ln 10

Worked example

With the default values below, Natural Logarithm Calculator returns ln x of 2.99573227. Change any input above and every figure here is recalculated in your browser.

Inputs used

Value xminimum 0: 20
Multiply x by: 1

Results

ln x: 2.99573227
log₁₀ x: 1.30103000
log₂ x: 4.32192809
eˣ: 485,165,195.409790

Step by step

1Values used
2Natural logarithm
3Conversion
4ln x= 2.99573227
5log₁₀ x= 1.30103000
6log₂ x= 4.32192809
7eˣ= 485,165,195.409790

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is ln 20?

About 2.9957323, since e² ≈ 7.389 and e³ ≈ 20.086.

Why is the logarithm undefined at zero and below?

No real power of e produces zero or a negative number, so the function has no real value there.