Hex Calculator
Convert between hexadecimal, decimal, and binary number systems.
Hex Calculator
What Is the Hex Calculator?
A hexadecimal calculator converts and computes in base sixteen, the compact shorthand programmers use for binary values. Each hex digit covers sixteen possibilities using 0 through 9 plus A through F, and one hex digit corresponds to exactly four binary bits, so a 32 bit value becomes just eight characters instead of thirty two digits. This tool adds, subtracts, multiplies, and divides hex numbers, converts among hex, decimal, and binary, and decodes color codes and memory addresses on sight. Web developers live in hex through CSS colors, embedded engineers through register dumps, and students through number system coursework.
Key Statistics
-
16 symbols
Hexadecimal uses digits 0 to 9 plus letters A to F
Source: Number system definition
-
4 bits
One hex digit encodes exactly four binary digits, called a nibble
Source: Computing convention
-
16.7 million
Colors expressible in six digit hex notation like web CSS uses
Source: 24 bit RGB color space
The Formula
Decimal to Hex: Repeatedly divide by 16 and read remainders (10=A, 11=B, etc.). Hex to Decimal: Sum of (digit value x 16^position).
Worked Examples
The web color deep sky blue has RGB values of 0, 191, and 255. In hex this becomes #00BFFF. The decimal number 255 (maximum for one byte) is FF in hex, and hex A0 equals decimal 160.
Hex to decimal conversion
- Take the hex value 1A3
- Place values are 256, 16, and 1
- Compute 1 times 256 plus 10 times 16 plus 3
Hex 1A3 equals decimal 419.
Decoding a web color
- Take the CSS color #FF6600
- Split into pairs: FF, 66, 00 for red, green, blue
- Convert each pair: FF is 255, 66 is 102, 00 is zero
The color is rgb(255, 102, 0), a vivid orange.
Real World Use Cases
Web development
Read, adjust, and blend CSS hex colors precisely rather than by eye.
Debugging and memory work
Interpret register values and addresses that debuggers print in hex.
Number system coursework
Master base conversion skills that computer science exams test directly.
Expert Tips
- ✓ Memorize A through F as 10 through 15; everything else follows from place value.
- ✓ Hex is binary in disguise: expand each digit to four bits to see the underlying pattern.
- ✓ 0x prefix marks hex literals in most programming languages, avoiding ambiguity with decimal.
- ✓ Lighten or darken hex colors by scaling each RGB pair proportionally rather than adding fixed amounts.
Frequently Asked Questions
How do I convert hexadecimal to decimal? ▼
Multiply each hex digit by 16 raised to its position from the right, using 10 for A up to 15 for F. Hex 2F is 2 times 16 plus 15, which equals 47 in decimal.
How do I convert decimal to hexadecimal? ▼
Divide the number by 16 repeatedly and record the remainders, then read them in reverse order, converting 10 to 15 into A to F. Decimal 47 becomes hex 2F.
Why is hexadecimal used in computing? ▼
Hex is a compact way to represent binary. Each hex digit maps to exactly four bits, so a long binary string becomes a short hex string. You see it in color codes, memory addresses, and error codes.
How do I convert hexadecimal to binary? ▼
Convert each hex digit to its four bit binary equivalent. Hex 0 is 0000, 5 is 0101, and F is 1111. So hex 5F becomes the binary 01011111.
What does FF mean in hexadecimal? ▼
FF is the largest two digit hex number, equal to 255 in decimal. In web colors, FF is the maximum value for a channel, which is why white is FFFFFF and black is 000000.
How do I add hexadecimal numbers? ▼
Add digit by digit from right to left in base 16, carrying when a column reaches 16. If a column sums to 20, you write 4 and carry 1, since 20 is 1 times 16 plus 4.
How do I convert hexadecimal to decimal? ▼
Multiply each digit by sixteen raised to its position power counting from zero at the right, then sum the products.
Why do programmers use hex instead of binary? ▼
It is far more compact while converting to and from binary instantly, four bits per character.
Common Mistakes to Avoid
- ⚠ Using letters beyond F in the hex field. Hexadecimal only goes up to F (value 15), so entering G, H, or any letter past F produces an invalid input and no conversion.
- ⚠ Mixing up hex color codes with decimal RGB values. The web color #FF5733 is a single hex number (16,777,215 + values), not three separate decimal numbers 255, 87, and 51. Entering the decimal RGB values as a combined hex string gives a different color.
- ⚠ Forgetting that hex values use A=10 through F=15 when converting mentally. Hex 2A equals 42 in decimal, but someone unfamiliar might read A as 1 instead of 10 and get 21, which is half the correct value.
- ⚠ Forgetting letter digits carry value. In hex, A is ten, so AF is not a mistake but one hundred seventy five.
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