Hex to Decimal

About Hex to Decimal

Hex to Decimal turns hexadecimal numbers into ordinary decimal numbers. Paste one, or a whole list from a log, a crash dump or a spreadsheet. Each line is converted, exact to the last digit, and a line with a typo is marked at the bad character.

It reads hex as programmers write it: 0x80070005, #FF5733, 0FFh, upper or lower case, with spaces or underscores between digit groups. Set Signed to read error codes and register values as negative numbers.

The same tool, set up for other bases: Decimal to Hex, Binary to Decimal, Decimal to Binary, Hex to Binary, Binary to Hex, Number Base Converter.

How to use it

1. Paste hex numbers, one per line, or load a file. Commas, tabs and semicolons also split a line, so a column from a spreadsheet works.
2. Check From and To, next to Convert. On a phone they are under More.
3. Press Convert (Alt C). Results shows every number in the To base and in decimal, hex, binary and octal. Output shows only the answers, line for line, for Copy and Download.
4. Open Steps to see the math for one number, the way you would do it on paper.
5. Swap (Alt S) puts the answers in the editor and turns From and To around, so you can check the way back.
6. In Options: Signed for two's complement, Groups for 1111 0000 or 4,294,967,295, Prefix for 0x, 0b or 0o, and how many digits a fraction gets.

How to convert hex to decimal by hand

Hex is base 16. Each place counts 16 times more than the place to its right. Write the place values over the digits, multiply, and add:

Hex 7DE

Digit   Value   Place          Counts
  7       7     16² = 256      7 × 256 = 1792
  D      13     16¹ =  16     13 × 16  =  208
  E      14     16⁰ =   1     14 × 1   =   14
                                       ------
                                         2014

For a long number, work from the left: start at 0, then for each digit multiply what you have by 16 and add the digit. The result is the same, with smaller sums.

Hex digits and powers of 16

Hex  Decimal  Binary      Hex  Decimal  Binary
 0      0     0000         8      8     1000
 1      1     0001         9      9     1001
 2      2     0010         A     10     1010
 3      3     0011         B     11     1011
 4      4     0100         C     12     1100
 5      5     0101         D     13     1101
 6      6     0110         E     14     1110
 7      7     0111         F     15     1111

16⁰ = 1                    16⁴ = 65,536
16¹ = 16                   16⁵ = 1,048,576
16² = 256                  16⁶ = 16,777,216
16³ = 4,096                16⁷ = 268,435,456
FF = 255   FFFF = 65,535   FFFFFFFF = 4,294,967,295

Negative numbers and two's complement

Hex from a register or an error code is often two's complement, where the top bit makes the number negative. Set Signed to its width: FF is -1 at 8-bit, and 80000000 is -2147483648 at 32-bit.

How two's complement works, with a table and the method by hand.

Exact for big numbers

Hex IDs and hashes are often 64 or 128 bits. This tool uses BigInt, so FFFFFFFFFFFFFFFF gives 18446744073709551615, not the rounded 18446744073709552000.

Why other converters round past 2^53.

Common errors

A letter that is not hex

Hex uses 0 to 9 and A to F. A G or a Z often comes from a typo, or from a number in another base. The tool marks the letter and says which base would have it.

1A3G5
G is not a hex digit. Hex uses 0 to 9 and A to F. Remove the G,
or set From to base 17 or more.

1A3F5

Two of the most visited converters do not stop here. One cuts the number at the G and answers 419; the other drops the G and answers 6709. Both give a number with no word of warning.

The letter O for a zero

Typed by hand, a capital O and a zero look the same. The tool names the letter, so you know what to type.

12O4
The letter O is not a digit. Type the digit 0 (zero) in its place.

1204

Two numbers on one line

Spaces inside a number are digit groups: 1111 0000 is one number. When the groups are not the same size, the tool still reads one number but marks the line, because it may be a list.

FF 1A 7
Read as one number, FF1A7. If these are separate numbers, put each on
its own line or split them with commas.

FF, 1A, 7

Most converters glue two lines into one number with no warning: 1F on one line and 2A on the next become 1F2A, which is 7978.

A number too big for its bits

With Signed set to a width, every number must fit in it. 8 bits are two hex digits, so a third digit is too many.

1FF (Signed: 8-bit)
1FF does not fit in 8 bits. 8 bits hold up to FF in hex.
Pick a wider Signed setting, or set it to Off.

Hex to decimal in code and Excel

JavaScript  parseInt("ff", 16)                 // 255
            BigInt("0xffffffffffffffff")       // exact past 2^53
Python      int("ff", 16)                      # 255; "0xff" works too
C           strtol("ff", NULL, 16)             // 255, <stdlib.h>
Java        Long.parseLong("ff", 16)           // 255
            new BigInteger("ff", 16)           // any size
Excel       =HEX2DEC("FF")                     → 255

HEX2DEC takes up to 10 hex digits (40 bits), and a 10-digit number with a top bit of 1 is negative: =HEX2DEC("FFFFFFFFFF") is -1. JavaScript parseInt rounds past 2^53 and stops at the first bad character with no error.