Hex to Decimal Converter

How to convert from hex to decimal

A regular decimal number is the sum of the digits multiplied with a power of 10.

137 in base 10 is equal to each digit multiplied with its corresponding power of 10:

137₁₀ = 1×10²+3×10¹+7×10⁰ = 100+30+7

Hex numbers are read the same way, but each digit counts the power of 16 instead of the power of 10.

For hex numbers with n digits:

d_n-1 … d₃ d₂ d₁ d₀

Multiply each digit of the hex number with its corresponding power of 16 and sum:

decimal = d_n-1×16^n-1 + … + d₃×16³ + d₂×16² + d₁×16¹+d₀×16⁰

How to Calculate Hexadecimal to Decimal

Hex is a base 16 number, and decimal is a base 10 number. Therefore, we need to know the decimal equivalent of every hex number digit. 

Here are the steps to transform hex to decimal:

• Get the decimal equivalent of hex from the table.
• Multiply every digit with 16 power of digit location.
• (zero-based, 7DE: E location is 0, D location is 1, and the 7 location is 2)
• Sum all the multipliers.

Here is an example:

7DE is a hex number
7DE = (7 * 162) + (13 * 161) + (14 * 160) 
7DE = (7 * 256) + (13 * 16) + (14 * 1) 
7DE = 1792 + 208 + 14 
7DE = 2014 (in decimal number)

Example #1

3B in base 16 is equal to each digit multiplied with its corresponding 16ⁿ:

3B₁₆ = 3×16¹+11×16⁰ = 48+11 = 59₁₀

Example #2

E7A9 in base 16 is equal to each digit multiplied with its corresponding 16ⁿ:

E7A9₁₆ = 14×16³+7×16²+10×16¹+9×16⁰ = 57344+1792+160+9 = 59305₁₀

Example #3

0.8 in base 16:

0.8₁₆ = 0×16⁰+8×16^-1 = 0+0.5 = 0.5₁₀

Hex to the decimal conversion table

Hex base 16	Decimal base 10	Calculation
0	0	–
1	1	–
2	2	–
3	3	–
4	4	–
5	5	–
6	6	–
7	7	–
8	8	–
9	9	–
A	10	–
B	11	–
C	12	–
D	13	–
E	14	–
F	15	–
10	16	1×161+0×160 = 16
11	17	1×161+1×160 = 17
12	18	1×161+2×160 = 18
13	19	1×161+3×160 = 19
14	20	1×161+4×160 = 20
15	21	1×161+5×160 = 21
16	22	1×161+6×160 = 22
17	23	1×161+7×160 = 23
18	24	1×161+8×160 = 24
19	25	1×161+9×160 = 25
1A	26	1×161+10×160 = 26
1B	27	1×161+11×160 = 27
1C	28	1×161+12×160 = 28
1D	29	1×161+13×160 = 29
1E	30	1×161+14×160 = 30
1F	31	1×161+15×160 = 31
20	32	2×161+0×160 = 32
30	48	3×161+0×160 = 48
40	64	4×161+0×160 = 64
50	80	5×161+0×160 = 80
60	96	6×161+0×160 = 96
70	112	7×161+0×160 = 112
80	128	8×161+0×160 = 128
90	144	9×161+0×160 = 144
A0	160	10×161+0×160 = 160
B0	176	11×161+0×160 = 176
C0	192	12×161+0×160 = 192
D0	208	13×161+0×160 = 208
E0	224	14×161+0×160 = 224
F0	240	15×161+0×160 = 240
100	256	1×162+0×161+0×160 = 256
200	512	2×162+0×161+0×160 = 512
300	768	3×162+0×161+0×160 = 768
400	1024	4×162+0×161+0×160 = 1024

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