Hex Calculator: Arithmetic & Conversion

Dec	Hexadecimal	Binary
0	0	000000
1	1	000001
2	2	000010
3	3	000011
4	4	000100
5	5	000101
6	6	000110
7	7	000111
8	8	001000
9	9	001001
10	A	001010
11	B	001011
12	C	001100
13	D	001101
14	E	001110
15	F	001111
16	10	010000
17	11	010001
18	12	010010
19	13	010011
20	14	010100
21	15	010101
22	16	010110
23	17	010111
24	18	011000
25	19	011001
26	1A	011010
27	1B	011011
28	1C	011100
29	1D	011101
30	1E	011110
31	1F	011111
32	20	100000
33	21	100001
34	22	100010
35	23	100011
36	24	100100
37	25	100101
38	26	100110
39	27	100111
40	28	101000
41	29	101001
42	2A	101010
43	2B	101011
44	2C	101100
45	2D	101101
46	2E	101110
47	2F	101111
48	30	110000
49	31	110001
50	32	110010
51	33	110011
52	34	110100
53	35	110101
54	36	110110
55	37	110111
56	38	111000
57	39	111001
58	3A	111010
59	3B	111011
60	3C	111100
61	3D	111101
62	3E	111110
63	3F	111111

Hexadecimal Calculator: Hex Arithmetic & Base-16 Conversion

This calculator performs hex arithmetic and base-16 conversion with step-by-step work panels. All computation runs locally in your browser within JavaScript safe integer limits.

What this calculator does

The widget supports three modes: hexadecimal arithmetic (+, −, ×, ÷ on two hex values), hexadecimal to decimal with a positional expansion panel, and decimal to hexadecimal with divide-by-16 steps. Results show in hex and decimal where both apply. A scrollable Quick reference (0–63) table lists decimal, hex, and binary columns. Inputs use digits 0–9 and A–F without a 0x prefix. Calculations stay within JavaScript safe integer range; the widget does not offer arbitrary-precision hex or bitwise operations.

Hex to decimal:

$D = \sum_{k=0}^{n-1} d_k \times 16^{k}$
Decimal to hex:

Repeatedly divide by 16; map remainders 10–15 to A–F; read digits last to first.

How the math works

Hexadecimal (base 16) uses sixteen symbols: digits 0–9 for zero through nine and letters A–F for ten through fifteen. Each column is a power of 16, with the rightmost digit at 16⁰. The canonical example on this page is 2AA in hex, which equals 682 in decimal.

To convert 2AA to decimal in Hexadecimal to decimal mode, multiply each digit by its place value: (2 × 16²) + (10 × 16¹) + (10 × 16⁰) = 512 + 160 + 10 = 682. The positional breakdown panel shows each term. To convert back, divide 682 by 16 repeatedly: remainder 10 (A), then 10 (A), then 2, read right to left as 2AA.

In Hexadecimal arithmetic mode, the widget converts both operands to decimal, applies the operator, and converts the answer back to hex when it is non-negative. With defaults FF (255) plus 10 (16), the sum is 271, which displays as hex 10F. Carries and borrows follow base-16 rules the same way base-10 arithmetic carries at ten.

One hex digit equals four binary bits (a nibble); two hex digits equal one byte (eight bits). That is why the quick reference table includes a binary column and why hex shortens long binary strings. For example, 2AA corresponds to the bit pattern 0010 1010 1010.

Limits of the model

This page uses JavaScript number arithmetic, not arbitrary precision. Integers beyond the safe range may round incorrectly. The widget rejects invalid characters, does not parse 0x prefixes, and shows decimal only (not hex) for negative arithmetic results. It does not perform bitwise AND, OR, XOR, or shift operations.

Hexadecimal Calculator FAQ

What does A mean in hexadecimal?

In hexadecimal (base 16), the letter A stands for decimal 10. Digits 0–9 keep their usual values; letters A–F represent 10 through 15. So hex 2AA equals (2 × 16²) + (10 × 16) + 10, which is 682 in decimal. The widget accepts A–F in any mode that takes hex input.

How many bits are in a hexadecimal digit?

One hex digit is exactly 4 bits (one nibble). Sixteen possible values (0–15) need 2⁴ bits, so two hex digits make one byte (8 bits). The Quick reference (0–63) table at the bottom of the widget shows decimal, hex, and binary side by side for quick lookup.

How do you convert decimal to hexadecimal in this calculator?

Choose Decimal to hexadecimal in the Choose mode dropdown. Enter a non-negative integer (default 682). The dark results panel shows the hex answer, and the white Decimal to hexadecimal steps box lists each divide-by-16 step with remainders read right to left. Default output: 2AA.

How do you convert hexadecimal to decimal here?

Choose Hexadecimal to decimal mode and enter hex digits (default 2AA). The results panel shows 682 in decimal. The Positional breakdown panel expands each digit times 16 raised to its place (rightmost digit uses 16⁰).

How does hex arithmetic work on this page?

Choose Hexadecimal arithmetic mode. Defaults: first number FF, operator +, second number 10. The widget converts both values to decimal, applies the operator, and displays the hex result 10F with decimal 271 in parentheses. Division uses integer floor when the quotient is not whole.

Do I need a 0x prefix for hex input?

No. Type digits 0–9 and letters A–F only (case-insensitive). The widget parses base 16 directly; a 0x prefix is not required and should not be typed.

What is the quick reference table for?

The scrollable Quick reference (0–63) table below the inputs lists decimal, hexadecimal, and binary for values 0 through 63. Use it to check a nibble or byte without switching modes, for example confirming that decimal 42 is hex 2A.

What are this calculator’s limits?

All math runs in JavaScript’s safe integer range; very large integers may lose precision. The widget does not accept a 0x prefix, fractional decimals in hex, or arbitrary-precision hex. Negative hex results in arithmetic mode show decimal only. It does not perform bitwise AND, OR, or shift operations.

Hexadecimal Calculator: Arithmetic & Conversion

Mode

Hexadecimal arithmetic

Quick reference (0–63)

Reading your hex result

Example: Hex arithmetic (default) → FF + 10 = 10F

Example: Hex to decimal → 2AA = 682

Example: Decimal to hex → 682 = 2AA

Nibbles in the reference table