Hexadecimal Calculator: Hex Arithmetic & Base-16 Conversion
Free hex calculator: add, subtract, multiply, divide hex. Hex to decimal converter, decimal to hex steps, base 16 conversion, nibble explanation. Hex calculator online for programmers and students.
What This Calculator Does & Who It's For
Calculator Purpose & Ideal Users
- What You'll Get:Hex arithmetic with result in hex and decimal; hex-to-decimal with positional expansion (digit ร 16^position); decimal-to-hex with division-by-16 steps; reference table 0โ63. All calculations client-side; no sign-up.
- Scope & Limits:Hex digits 0โ9 and AโF (case-insensitive). Arithmetic and conversions use JavaScript safe integer range. Reference table covers 0โ63.
This hex calculator (hexadecimal calculator) provides hex arithmetic (add, subtract, multiply, divide), hex to decimal and decimal to hex conversion with step-by-step breakdowns, and a quick reference table (0โ63) in hex, binary, and decimal.
What Is Hexadecimal? Base-16 Place Value
Hexadecimal (base-16) uses 16 symbols: 0โ9 for 0โ9 and AโF for 10โ15. Each position is a power of 16: rightmost = 16โฐ, next = 16ยน, then 16ยฒ, and so on. The decimal value of a base-16 number is the sum of (digit ร 16^position). For a short example: 1F = (1ร16ยน) + (15ร16โฐ) = 16 + 15 = 31. The next section shows the full hex to decimal expansion for a longer value; use the calculator's "Hexadecimal to decimal" section for any hex value.
Hexadecimal to Decimal: Positional Breakdown
To convert hex to decimal, expand each digit by its place value (digit ร 16^position), then add. The rightmost digit is position 0. Full example: 2AA = (2ร16ยฒ) + (Aร16ยน) + (Aร16โฐ) = (2ร256) + (10ร16) + (10ร1) = 512 + 160 + 10 = 682. Enter any hex value in the calculator's "Hexadecimal to decimal" field to see this expansion. For the formula in one line, see the FAQ "How do you convert hexadecimal to decimal?"
Decimal to Hexadecimal: Division by 16
To convert decimal to hex manually, repeatedly divide by 16 and record the remainder (0โ15). The hex digits are the remainders read from last to first; remainders 10โ15 are written AโF. For the full decimal to hex step by step procedure and a worked example (e.g. 682 โ 2AA), see the FAQ "How do you convert decimal to hexadecimal manually?" Use the calculator's "Decimal to hexadecimal" mode to see the division-by-16 steps for any integer.
Nibbles: Why One Hex Digit = 4 Bits
A nibble is 4 bits; there are 2โด = 16 values โ exactly one hex digit. So 1 hex digit = 4 bits, and two hex digits = 1 byte. Thatโs why hex to binary conversion is simple: each hex digit maps to one nibble (e.g. 2AA โ 0010 1010 1010). Programmers use hex because long binary strings are hard to read; hex shortens them and aligns with byte boundaries. Memory addresses, color codes (e.g. #2AA), and low-level data are often shown in hex. For "how many bits in a hex digit?" and "why do programmers use hex?", see the FAQ above.
Hexadecimal Calculator FAQ
What does A mean in hexadecimal?
In hexadecimal, the letter A represents the decimal value 10. Hexadecimal uses digits 0โ9 for 0โ9 and letters AโF for 10โ15: A=10, B=11, C=12, D=13, E=14, F=15. So "2A" in hexadecimal = 2ร16 + 10 = 42 in decimal.
How many bits are in a hexadecimal digit?
One hexadecimal digit represents exactly 4 bits (a "nibble"). There are 16 possible values (0โ15), which is 2โด, so each hexadecimal digit maps to one nibble. Two hexadecimal digits = 1 byte (8 bits).
Why do programmers use hexadecimal?
Programmers use hexadecimal because it compresses binary: every 4 bits become one hexadecimal digit. Long binary strings (e.g. 101010101010) are hard to read; the same value in hexadecimal (e.g. 2AA) is shorter and aligns with byte boundaries. Memory addresses, color codes, and low-level data are often shown in hexadecimal.
How do you convert decimal to hexadecimal manually?
Use successive division by 16: divide the number by 16, note the remainder (0โ15); repeat with the quotient until the quotient is 0. The hexadecimal digits are the remainders read from last to first. Example: 682 รท 16 = 42 R 10 (A), 42 รท 16 = 2 R 10 (A), 2 รท 16 = 0 R 2 โ hexadecimal = 2AA. The article below has the full procedure.
How do you convert hexadecimal to decimal?
Use positional notation: each digit is multiplied by 16 raised to its position (rightmost = 16โฐ). Example: 2AA = (2ร16ยฒ) + (Aร16ยน) + (Aร16โฐ) = (2ร256) + (10ร16) + (10ร1) = 512 + 160 + 10 = 682. The calculator shows this breakdown in "Hexadecimal to decimal"; the article below has the full method.