Hex arithmetic
Select "Hexadecimal arithmetic" and enter two hex values plus an operator; result in hex and decimal.
Hexadecimal Calculator
Perform math operations on hexadecimal numbers.
Mode
Choose a tool: hexadecimal arithmetic, hex-to-decimal, or decimal-to-hex. Digits: 0–9, A–F (values 10–15).
Hexadecimal arithmetic
Enter two hexadecimal values and choose an operator.
Hexadecimal arithmetic
FF + 10
10F (271 in decimal)
📋
Quick reference (0–63)
Hexadecimal, binary, and decimal
Using the Hexadecimal Calculator
Use the calculator above: choose a mode (hex arithmetic, hex-to-decimal, or decimal-to-hex) and enter values; the 0–63 reference table is below. Base-16 definitions, conversion formulas, and nibble explanation are in the article below.
Workflow Tips
Hex to decimal
Select "Hexadecimal to decimal" and enter a hex value; see decimal and the power-of-16 breakdown.
Decimal to hex
Select "Decimal to hexadecimal" and enter an integer; see hex and the division-by-16 steps.
Quick reference
Use the 0–63 table for decimal, hex, and binary lookup.
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
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 (0–63) in hex, binary, and decimal.
- What You'll Get:Hex arithmetic with result in hex and decimal; hex-to-decimal with positional expansion (digit × 16^position); decimal-to-hex with division-by-16 steps; reference table 0–63. All calculations client-side; no sign-up.
- Scope & Limits:Hex digits 0–9 and A–F (case-insensitive). Arithmetic and conversions use JavaScript safe integer range. Reference table covers 0–63.
How the Math Works
Hexadecimal is a base-16 positional system. Converting hex to decimal means multiplying each digit by its positional power of 16 and summing the results:
where dk is the digit value (0–9 map directly; A–F map to 10–15) at position k, counted from the right starting at zero. For decimal-to-hex conversion, repeatedly divide by 16 and collect the remainders from last to first. Hex arithmetic (add, subtract, multiply, divide) follows the same carry-and-borrow rules as decimal but with a radix of 16.
- Hex → Decimal Example:2AA = (2 × 16²) + (10 × 16¹) + (10 × 16⁰) = 512 + 160 + 10 = 682.
- Decimal → Hex Example:682 ÷ 16 = 42 remainder 10 (A); 42 ÷ 16 = 2 remainder 10 (A); 2 ÷ 16 = 0 remainder 2 → result is 2AA.
- Nibble Relationship:Each hex digit encodes exactly 4 bits (one nibble). Two hex digits equal one byte. This direct mapping is why programmers prefer hex for memory addresses and color codes.
How to Use This Calculator
Choose one of three modes from the dropdown. In Hexadecimal arithmetic, enter two hex values and select an operator (+, −, ×, ÷) to see the result in both hex and decimal. In Hexadecimal to decimal, type a hex value to see the decimal equivalent with a positional-expansion breakdown showing each digit multiplied by its power of 16. In Decimal to hexadecimal, enter a base-10 integer to see the hex result with division-by-16 steps. All inputs accept digits 0–9 and letters A–F (case-insensitive).
- Input Format:Digits 0–9 and letters A–F, case-insensitive. No 0x prefix is needed.
- Reference Table:Scroll below the calculator for a 0–63 lookup table with decimal, hex, and binary columns for quick cross-referencing.
- Scope:Calculations use JavaScript’s safe integer range. For arbitrarily large values, see the Big Number Calculator.
What Is Hexadecimal? Base-16 Place Value
Hexadecimal (base-16) uses 16 symbols: 0–9 for 0–9 and A–F for 10–15. Each position is a power of 16: rightmost = 16⁰, next = 16¹, then 16², and so on. The decimal value of a base-16 number is the sum of (digit × 16^position). For a short example: 1F = (1×16¹) + (15×16⁰) = 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 × 16^position), then add. The rightmost digit is position 0. Full example: 2AA = (2×16²) + (A×16¹) + (A×16⁰) = (2×256) + (10×16) + (10×1) = 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 (0–15). The hex digits are the remainders read from last to first; remainders 10–15 are written A–F. For the full decimal to hex step by step procedure and a worked example (e.g. 682 → 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 2⁴ = 16 values, exactly one hex digit. So 1 hex digit = 4 bits, and two hex digits = 1 byte. That’s why hex to binary conversion is simple: each hex digit maps to one nibble (e.g. 2AA → 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 0–9 for 0–9 and letters A–F for 10–15: A=10, B=11, C=12, D=13, E=14, F=15. So "2A" in hexadecimal = 2×16 + 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 (0–15), which is 2⁴, 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 (0–15); repeat with the quotient until the quotient is 0. The hexadecimal digits are the remainders read from last to first. Example: 682 ÷ 16 = 42 R 10 (A), 42 ÷ 16 = 2 R 10 (A), 2 ÷ 16 = 0 R 2 → 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 = 16⁰). Example: 2AA = (2×16²) + (A×16¹) + (A×16⁰) = (2×256) + (10×16) + (10×1) = 512 + 160 + 10 = 682. The calculator shows this breakdown in "Hexadecimal to decimal"; the article below has the full method.
Mathematical Reference Note
Calculation Logic: This tool uses standard mathematical algorithms. While we strive for accuracy, errors in logic or user input can result in incorrect data.
Verification: Results should be cross-checked if used for important academic, professional, or personal calculations.
Standard Terms: This tool is provided free of charge and as-is. CalcRegistry provides no warranty regarding the accuracy or fitness of these results for your specific needs.
© 2026 CalcRegistry Reference Last System Check: May 2026Free Online Utility Tools