Base-N Calculator

What the base-N calculator does

This takes a single number and shows you what it looks like in every base from 2 to 36, all at once. You enter the number and the base it is currently in, and you get back the full spread of representations in one go.

It is the panoramic view of a number. Rather than asking for one particular base, you see the whole landscape and can pick out whichever form is useful, or just enjoy how differently the same quantity can be written.

How to use it

1. Enter your number. Type it using the digits valid for its base.
2. Choose the base it is in. Tell the tool which base your number is currently written in.
3. Press Calculate. The number appears written in every base from 2 to 36.

Press Reset to clear everything.

One number, many faces

A quantity does not change when you write it in a different base; only its costume does. The number of fingers on two hands is ten in base 10, 1010 in binary, and a in base 11, but it is the same amount throughout. Seeing all the bases side by side makes that vivid, and it is genuinely handy too. Some numbers that look awkward in base 10 turn out to be beautifully round in another base, and laying them all out lets you spot which base suits a number best.

How it works

The tool reads your number once, in the base you gave it, to find its plain value. Then it writes that value out in each base from 2 to 36 in turn, the same way you would convert to any single base, just repeated across the whole range. So the work is one reading followed by thirty-five writings, each using the place values of its own base.

A worked example with real numbers

Enter 255 as a base 10 number and a few rows leap out. In base 2 it is 11111111, eight 1s in a row. In base 16 it is ff, two of the highest hex digit. In base 8 it is 377. The reason 255 looks so tidy in binary and hexadecimal, yet unremarkable in base 10, is that 255 is one less than 256, which is a power of 2, so it fills every bit exactly. Spread across all the bases, that pattern is easy to see, where in base 10 alone it stays hidden.

How this differs from a base converter

It is worth being clear about the difference, since the two sound similar. A base converter asks you to choose one target base and gives you that single answer, which is what you want when you know exactly where the number is headed. This tool skips the choice and hands you every base at once, which is what you want when you are exploring, comparing, or not yet sure which base you need. Same underlying conversion, different serving: one targeted, this one panoramic.

Questions people ask

What does this tool show?

It writes your number in every base from 2 to 36 at once, starting from whatever base you entered it in. You get the full set of representations in a single result.

How is it different from a base converter?

A base converter gives one chosen target base. This shows them all at once, which suits comparing and exploring rather than a single targeted conversion.

Why do some numbers look neater in certain bases?

Because a number sits tidily in a base that matches its structure. A value like 255, one less than a power of 2, fills every bit, so it looks clean in binary and hex but ordinary in base 10.

Why do higher bases use letters?

Bases above 10 need more than ten digits, so letters stand in: a is 10 through to z for 35. Each is a single digit holding that value.

References

1. Weisstein, Eric W. "Radix." From MathWorld, A Wolfram Resource. https://mathworld.wolfram.com/Radix.html