Exponent & Root Calculator

How to use the exponent & root calculator

1. Fill in the fields — they start with a worked example.
2. Read the answer, and the arithmetic shown beneath it.
3. Copy the results, or adjust the inputs to compare scenarios.

About this tool

Powers, roots and logarithms are three views of the same relationship: if 2⁵ is 32, then the fifth root of 32 is 2 and log₂ of 32 is 5. All three are shown together, since the one you need depends on which value is unknown.

Base 2 logarithms matter in computing — they count how many times a value can be halved, which is why they appear in algorithmic complexity.

Common uses

• Working out a compound growth factor.
• Taking a cube or nth root.
• Finding how many doublings separate two numbers.

Frequently asked questions

What is the difference between log and ln?

log usually means base 10, ln means base e (about 2.718). Both are shown, along with base 2.

Can I take a root of a negative number?

Only an odd root — the cube root of −8 is −2. Even roots of negatives have no real answer, and the tool says so.