Hexadecimal to Decimal Converter
developer · number system
Convert Hexadecimal to Decimal with a fixed input and output format, step-by-step formulas under the result, and reference tables. Parsing matches the main hub (0b, 0x, leading 0 for octal; one optional . for fractional digits on numeric bases; single character for character mode).
Calculator
From: Hexadecimal
To: Decimal
Formulas
About Hexadecimal
Hexadecimal (base 16) uses 0–9 and A–F. This tool accepts an optional 0x prefix. One radix point is allowed; fractional digits use 16⁻¹, 16⁻², …. Each hex digit covers four bits, so it is compact for memory addresses, colors, and byte dumps.
About Decimal
Decimal (base 10) uses digits 0–9; no prefix is required. A single . may separate the fractional part (10⁻¹, 10⁻², …). Values are parsed to a number and re-encoded into the target format; very long fractions are limited by floating-point precision.
How to convert hexadecimal to decimal
Three steps: symbols → the right math move for this pair → worked examples you can copy on paper. Numeric bases (binary, octal, decimal, hex) also support one radix point and digits after it; character mode stays a single code unit.
Step 1 — Identify the symbols
Input (Hexadecimal): Digits 0–9 plus letters A–F for values ten through fifteen.
Output (Decimal): Ordinary digits 0–9; each position is a power of ten.
Hex conversions use this letter-to-number map:
| Digit | Value | Digit | Value |
|---|---|---|---|
| 0 | 0 | 8 | 8 |
| 1 | 1 | 9 | 9 |
| 2 | 2 | A | 10 |
| 3 | 3 | B | 11 |
| 4 | 4 | C | 12 |
| 5 | 5 | D | 13 |
| 6 | 6 | E | 14 |
| 7 | 7 | F | 15 |
- 0x is a common prefix (e.g. 0xFF).
Step 2 — Hex Place Weights
A–F mapping: use 10–15 for letters when applying place weights.
Number positions from the right, starting at 0. At each position, multiply that digit by 16 raised to the position index, then add every term. The total is your decimal number.
Digits after the dot: use negative powers of 16 (16−1, 16−2, …). Each place is still (digit × weight); add the fractional side to the whole side.
A–F reminder: treat A as 10, B as 11, …, F as 15 when you multiply by powers of 16 (see Step 1 table).
Step 3 — Worked examples
Two practice values in Hexadecimal, converted to Decimal using the same rules as Step 2. Example 3 uses a fractional part (digits after the radix point); the hub and pair calculators accept a single . on binary, octal, decimal, and hex inputs.
Example 1
"1A" (Hexadecimal) → Decimal.
Toward decimal
Hexadecimal "1A"
= 1×16¹ + A×16⁰
= 16 + 10
= 26 (decimal)Verify: "1A" → 26
Example 2
"FF" (Hexadecimal) → Decimal.
Toward decimal
Hexadecimal "FF"
= F×16¹ + F×16⁰
= 240 + 15
= 255 (decimal)Verify: "FF" → 255
Example 3
"A.8" (Hexadecimal) → Decimal.
Toward decimal
Hexadecimal "A.8"
Left of . : A×16⁰ = 10
Right of .: 8×16^-1 = 0.5
= 10.5 (decimal)Verify: "A.8" → 10.5
Summary
To convert Hexadecimal to Decimal, the tool first parses your input strictly as hexadecimal, producing a decimal value. For binary, octal, decimal, and hex, you may include one radix point and fractional digits; character input remains a single code unit with no dot. That value is formatted as decimal using the same rules as the main Number System Converter (prefixes 0b, 0, 0x where applicable; character output uses symbolic names for common controls and requires a whole-number code point). Long fractional expansions are truncated to a fixed digit cap; ordinary floating-point rounding may appear in extreme cases.
Relationship context
Hexadecimal, Decimal, and the other numeric bases on this site all describe the same numeric value; only the radix changes (including optional fractional digits after one dot). Moving between them is equivalent to changing how the value is written, not to scaling or unit conversion. Binary, octal, and hex align with bit boundaries (powers of two), while decimal is optimized for human arithmetic.
Conversion tables
| Hexadecimal (input) | Decimal (output) |
|---|---|
| 0 | 0 |
| 0x1 | 1 |
| 0x2 | 2 |
| 0x3 | 3 |
| 0x4 | 4 |
| 0x5 | 5 |
| 0x6 | 6 |
| 0x7 | 7 |
| 0x8 | 8 |
| 0x9 | 9 |
| 0xa | 10 |
| 0xf | 15 |
| 0x10 | 16 |
| Hexadecimal (input) | Decimal (output) |
|---|---|
| 0xb | 11 |
| 0x20 | 32 |
| 0x40 | 64 |
| 0x80 | 128 |
| 0x100 | 256 |
| 0x200 | 512 |
| 0x400 | 1024 |
| 0x800 | 2048 |
| 0x1000 | 4096 |
| 0x2000 | 8192 |
| 0x4000 | 16384 |
| 0x8000 | 32768 |
| 0xffff | 65535 |
More number system pairs
Other fixed input/output converters use the same parsing rules as the hub. Open any pair for the same calculator layout and reference tables.
- bin to char (Binary to Character)Fixed input/output · same parsing as hub
- bin to dec (Binary to Decimal)Fixed input/output · same parsing as hub
- bin to hex (Binary to Hexadecimal)Fixed input/output · same parsing as hub
- bin to oct (Binary to Octal)Fixed input/output · same parsing as hub
- char to bin (Character to Binary)Fixed input/output · same parsing as hub
- char to dec (Character to Decimal)Fixed input/output · same parsing as hub
- char to hex (Character to Hexadecimal)Fixed input/output · same parsing as hub
- char to oct (Character to Octal)Fixed input/output · same parsing as hub
- dec to bin (Decimal to Binary)Fixed input/output · same parsing as hub
- dec to char (Decimal to Character)Fixed input/output · same parsing as hub
- dec to hex (Decimal to Hexadecimal)Fixed input/output · same parsing as hub
- dec to oct (Decimal to Octal)Fixed input/output · same parsing as hub