We count in base-10 because we have ten fingers. But what if we had twelve? Or just two? Explore how numbers look, multiply, and divide across every base from 2 to 36.
Universal Base Converter
Decimal (Base 10) value
255
Multiplication Table
Divisibility by Base
Each base has different divisors. More divisors = more "clean" fractions. This is why base 12 and base 60 were historically popular.
Digit-by-Digit Explorer
See how each digit in a number contributes to its total value in any base.
How Many Digits?
Enter a number to see how many digits it needs in each base. Smaller bases need more digits.
Available Digits per Base
Why Bases Matter
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Base 10 (Decimal) — Our default because we have 10 fingers. Divisible by 2 and 5. Simple, but fractions like 1/3 and 1/6 are repeating decimals.
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Base 2 (Binary) — The language of computers. Every byte, image, and song is just 0s and 1s. Powers of 2 (2, 4, 8, 16, 32...) align perfectly with binary digits.
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Base 60 (Sexagesimal) — Inherited from the Babylonians. Still used today: 60 seconds in a minute, 60 minutes in an hour, 360 degrees in a circle. Highly divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20, 30.
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Base 12 (Duodecimal) — Divisible by 2, 3, 4, and 6. Proponents argue it's the best base for everyday math. We still use it: 12 hours, 12 months, 12 inches in a foot, a dozen eggs.
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Base 16 (Hexadecimal) — A compact way to write binary. Each hex digit = exactly 4 binary bits. Used for color codes (#FF5733), memory addresses, and cryptographic hashes.
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Base 64 / Base 36 — Base 36 uses digits 0–9 and letters A–Z. Perfect for compact identifiers. Base 64 (using A-Z, a-z, 0-9, +, /) encodes binary data in text — essential for URLs and email.
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Base 8 (Octal) — Used in early computing (before hex became standard). Each octal digit = 3 binary bits. Still appears in Unix file permissions (chmod 755) and escape sequences.
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Base 5 (Quinary) — Count on one hand! Used by the Aztecs and in some Chinese languages (wǔ = 5, shí = 10, wǔshí = 50). Clean multiples of 10 in base 5: it's just "20".
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Dozenal Movement — The Dozenal Society of America has been advocating for base-12 since 1944. They propose symbols: dek (10) and el (11). In dozenal, 1/3 = 0.4 exactly!
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Factorial Base — A special system where the place values are factorials: 1!, 2!, 3!, 4!... The number 3210 in factorial base = 3×6 + 2×2 + 1×1 + 0×1 = 23. Every number has a unique representation!