Tutorial
How to Convert Decimal to Hex by Hand
Divide by sixteen, collect the remainders, read them backwards.
The converters on this site will always be faster. The point of working through it manually is that afterwards you can read a hex value without a tool at all — which is what you need when you are looking at a stack trace or a datasheet rather than a browser tab.
The method
- Divide your number by 16. Write down the whole-number quotient and the remainder.
- Convert the remainder to a hex digit: 10 is A, 11 is B, 12 is C, 13 is D, 14 is E, 15 is F.
- Divide the quotient by 16 and record the next remainder.
- Repeat until the quotient reaches 0.
- Read the remainders from the last one back to the first. That is your answer.
Read the remainders upwards. The first remainder you calculate is the ones digit, so it belongs at the end of the answer. Reading them in the order you produced them gives you the digits reversed.
Worked example: 6699
6699 ÷ 16 = 418 remainder 11 → B
418 ÷ 16 = 26 remainder 2 → 2
26 ÷ 16 = 1 remainder 10 → A
1 ÷ 16 = 0 remainder 1 → 1
read upwards → 1A2B
check: 1×4096 + 10×256 + 2×16 + 11 = 6699 ✓
Worked example: 47
47 ÷ 16 = 2 remainder 15 → F
2 ÷ 16 = 0 remainder 2 → 2
read upwards → 2F
The shortcut for anything under 256
Values below 256 fit in one byte and need only one division. The quotient is the first digit, the remainder is the second.
200 → 200 ÷ 16 = 12 remainder 8 → C8 47 → 47 ÷ 16 = 2 remainder 15 → 2F 255 → 255 ÷ 16 = 15 remainder 15 → FF 128 → 128 ÷ 16 = 8 remainder 0 → 80
Both digits still need converting to letters where they exceed 9, and the remainder must be
written even when it is zero — 80, not 8.
An alternative: subtract the place values
Some people find this easier than dividing. Work out how many of each place value fit, largest first.
6699 using place values how many 4096s? 1 → digit 1, 6699 - 4096 = 2603 how many 256s? 10 → digit A, 2603 - 2560 = 43 how many 16s? 2 → digit 2, 43 - 32 = 11 how many 1s? 11 → digit B result → 1A2B
This produces the digits in reading order, which avoids the reversal mistake entirely. It needs the powers of sixteen to hand: 1, 16, 256, 4096, 65536.
Practice problems
- 31
- 160
- 255
- 256
- 683
- 4095
1. 31 → 31 ÷ 16 = 1 r 15 → 1F 2. 160 → 160 ÷ 16 = 10 r 0 → A0 3. 255 → 255 ÷ 16 = 15 r 15 → FF 4. 256 → 256 ÷ 16 = 16 r 0; 16 ÷ 16 = 1 r 0 → 100 5. 683 → 683 ÷ 16 = 42 r 11; 42 ÷ 16 = 2 r 10 → 2AB 6. 4095 → three divisions, all remainder 15 → FFF
Common mistakes
- Reading remainders downwards. The most common error by a wide margin.
- Leaving a remainder as a number above 9. Eleven is
B, not11. - Stopping too early. Keep dividing until the quotient is genuinely 0, not 1.
- Dropping a zero remainder. A remainder of 0 is a real digit and must be written.
Check your work
Convert your answer back with the hex to decimal method, or use the decimal to hex converter to confirm.
Frequently asked questions
How do I convert decimal to hex manually?
Divide by 16 repeatedly, writing down each remainder, until the quotient is zero. Then read the remainders from the last back to the first.
Why do I read the remainders backwards?
The first remainder is the ones digit, so it belongs at the end of the answer. Reading them in calculation order reverses the number.
What is the shortcut for numbers under 256?
One division. The quotient is the first hex digit and the remainder is the second. 200 gives 12 remainder 8, which is C8.
Is there a method that avoids reversing?
Yes. Subtract place values largest first: how many 4096s, then 256s, then 16s, then 1s. The digits come out in reading order.
What is 255 in hex?
FF. 255 divided by 16 is 15 remainder 15, and 15 is F.
When do I stop dividing?
When the quotient is zero, not when it is one. Stopping at one loses the leading digit.