Hex Calculator

What this calculator does

The Hex Calculator performs arithmetic on base-16 numbers and converts between hexadecimal and decimal. It supports addition, subtraction, multiplication, and integer division, and it shows the decimal equivalents of the inputs and the result.

Hexadecimal, usually shortened to hex, is a base-16 number system. It uses the digits 0–9 and the letters A–F, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15. Each position represents a power of 16. The hex value DAD therefore represents 13 × 256 + 10 × 16 + 13 = 3,501 in decimal.

How to use this calculator

1. Choose Hexadecimal arithmetic, Hexadecimal to decimal, or Decimal to hexadecimal.
2. Enter the value or values. For arithmetic, choose an operation.
3. Click Calculate.
4. Review the result and the decimal equivalents.

The default arithmetic example is 8AB + B78 = 1423, which is 2,219 + 2,936 = 5,155 in decimal. The conversion examples are DAD = 3,501 and 170 = AA.

Hex arithmetic

Hex arithmetic follows the same rules as decimal arithmetic, but carries and borrows happen at 16 instead of 10. When a digit reaches F, the next increment carries one to the next position. Letters are case-insensitive: 8ab and 8AB represent the same value.

A = 10    B = 11    C = 12
D = 13    E = 14    F = 15

The calculator converts each operand to an integer, performs the operation, and converts the result back to uppercase hex. Subtraction can produce a negative result, which is shown with a leading minus sign.

What the results mean

The result panel shows the answer in hex and in decimal. For arithmetic, both operands are also shown in both bases. Integer division discards the remainder, so the hex quotient is the whole-number part of the division.

Leading zeros do not change a hex value. The calculator removes unnecessary leading zeros, so 01423 is shown as 1423. Letter digits are always displayed in uppercase, regardless of how they were entered.

Assumptions and limitations

• Inputs are whole hex or decimal integers. Fractions and decimal points are not accepted.
• Hex values may contain only 0–9, A–F, and an optional leading minus sign.
• Division by zero is rejected.
• Division returns the integer quotient and discards the remainder.
• The calculator does not interpret bit patterns as signed two's-complement integers.
• Inputs are limited to 1,000 characters to keep the page responsive.

Frequently asked questions

Why does hex use letters?

Base 16 needs sixteen distinct symbols. The digits 0–9 provide ten, and the letters A–F provide the remaining six. Using letters avoids inventing new digit characters and is the convention used in programming and digital design.

How do I convert hex to decimal by hand?

Multiply each digit by its place value and add the results. For DAD, the place values are 256, 16, and 1. D is 13, A is 10, and D is 13, so the value is 13 × 256 + 10 × 16 + 13 = 3,501.

Is hex the same as binary?

No, but they are closely related. One hex digit represents exactly four binary bits, so hex is a compact way to write binary values. For example, the hex value F is 1111 in binary.

Does the calculator accept lowercase letters?

Yes. Both uppercase and lowercase letters are accepted. Results are always shown in uppercase for consistency.

Reference tables

Hex, binary, and decimal equivalents

Worked conversions

Hex multiplication examples

Reference tables

Full hex multiplication table

The row and column headings use hex notation: 10 means sixteen. For example, F × F = E1.

Source

Reference: Calculator.net — Hex Calculator.