Number System & Angle Converter
Convert between number bases (binary, hex, Roman, base 36) and angle units (degrees, radians, gradians). Instant results for integers and angles.
How It Works
Converts numbers across different numeral systems (Decimal, Binary, Octal, Hexadecimal) by applying division-by-base algorithms for integers, and multiplication-by-base for fractions.
Formula
Decimal to Base-N: Repeatedly divide by N. The remainders (read bottom to top) form the converted number.
To convert 13 to binary (Base 2): 13/2 = 6 (R1), 6/2 = 3 (R0), 3/2 = 1 (R1), 1/2 = 0 (R1). Read remainders backwards: 1101.
Worked Example
Converting Decimal 255 to Hexadecimal (Base 16)
- Decimal Number: 255
- Divide 255 by 16: Quotient = 15, Remainder = 15
- Divide 15 by 16: Quotient = 0, Remainder = 15
- Convert remainders to Hex: 15 corresponds to 'F'
- Read backwards: FF
- Result: 0xFF
Common Mistakes
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Misinterpreting letters in Hexadecimal
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Hex uses A-F to represent numbers 10-15. Ensure you treat 'A' as 10, 'B' as 11, etc.
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Losing leading zeros in Binary
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Binary numbers are often padded to 8 bits (a byte). 101 is mathematically the same as 00000101, but padding is required in computing.
Frequently Asked Questions
Related Guide & Instructions
2026-07-15
Number System Conversions: Binary, Hexadecimal, and Roman Numerals Explained
Learn how computers read base-2 binary and base-16 hex, convert between numbering bases, and understand angles in radians.
Read full guide →