Instant Base Conversion Tool
Convert whole numbers between any bases from 2 to 36 (binary, octal, decimal, hexadecimal, and more).
Tip: Use digits 0-9 and letters A-Z for bases above 10. Underscores and spaces are ignored.
What Is a Base-to-Base Calculator?
A base-to-base calculator converts a number written in one numeral system into another numeral system. The numeral system base tells you how many unique symbols are used before place values roll over. For example, base 10 uses digits 0 through 9, base 2 uses 0 and 1, and base 16 uses 0-9 plus A-F.
This tool is especially useful for programming, networking, computer architecture, cybersecurity, and math classes. Instead of converting by hand each time, you can quickly switch between binary, octal, decimal, hexadecimal, or any base up to 36.
How to Use This Calculator
- Enter your number in the Number to Convert field.
- Set the number's current base in From Base.
- Choose the destination base in To Base.
- Click Convert to see the result instantly.
You can also click Swap Bases to reverse conversion direction and Clear to reset all fields.
Common Base Systems
Binary (Base 2)
Used in digital electronics and low-level computing. Only digits 0 and 1 are allowed.
Octal (Base 8)
Historically used in computing because it maps neatly to binary in groups of three bits.
Decimal (Base 10)
The everyday number system used in finance, measurements, and general arithmetic.
Hexadecimal (Base 16)
Extremely common in software development, memory addressing, color codes, and debugging.
Quick Examples
- Binary to Decimal: 101101 (base 2) = 45 (base 10)
- Decimal to Hex: 255 (base 10) = FF (base 16)
- Hex to Binary: 7F (base 16) = 1111111 (base 2)
- Base 3 to Base 9: 12021 (base 3) = 136 (base 9)
How Conversion Works (Conceptually)
Any number can be converted to decimal by expanding place values, then converted from decimal to the target base via repeated division. For example, in base 16, the number 3A means:
3A16 = (3 × 161) + (10 × 160) = 48 + 10 = 5810
The calculator automates this process using exact integer math, so it handles very large whole numbers reliably.
Frequently Asked Questions
What bases are supported?
Any base from 2 through 36.
Can I use lowercase letters?
Yes. Input is normalized internally, so both lowercase and uppercase letters are accepted.
Can I convert negative numbers?
Yes. Prefix the number with a minus sign, such as -1010 in base 2.
Does this tool handle fractions?
This version focuses on whole-number conversion. Fractional base conversion requires additional handling of radix points and precision rules.