Base 36 to Ternary (Base 3) Converter
Convert base 36 numbers to ternary.
73 (base 36) = 100110 (base 3)
Digits in base 36: 0 to 9 and A to Z. Digits in base 3: 0 to 2.
How to convert Base 36 to Ternary
Every positional number system works the same way: a digit is worth its own value times the base raised to the power of its position. In base 36 the place values, from the right, are 360 = 1, 361 = 36, 362 = 1296 and so on.
Most pairs have no direct trick, so go through decimal, the base we all calculate in. First turn the base 36 number into decimal, then divide by 3 and read the remainders from the bottom up. Two short steps, and you can check the number in the middle.
The method
decimal value = each digit × its place value, all added upplace values in base 36: 1, 36, 1296, 46656, 1679616, and so ondivide by 3, keep the remainder, repeat until the quotient is 0the answer is the remainders read from last to firstdigits in base 36: 0 to 9 and A to Zdigits in base 3: 0 to 2
Worked example 1: 19 from base 36 to ternary
Step 1: base 36 to decimal19 (base 36) = 1 × 361 + 9 × 360= 36 + 9= 45Step 2: decimal to base 345 ÷ 3 = 15 remainder 015 ÷ 3 = 5 remainder 05 ÷ 3 = 1 remainder 21 ÷ 3 = 0 remainder 1Read the remainders from the bottom up: 120019 (base 36) = 1200 (base 3)
Letters stand for values from 10 up: A = 10, B = 11, C = 12 and so on. Remainders come out last digit first, which is why you read them from the bottom up. Digits that are 0 add nothing to the sum, so they are left out of the expansion.
Worked example 2: 73 from base 36 to ternary
Step 1: base 36 to decimal73 (base 36) = 7 × 361 + 3 × 360= 252 + 3= 255Step 2: decimal to base 3255 ÷ 3 = 85 remainder 085 ÷ 3 = 28 remainder 128 ÷ 3 = 9 remainder 19 ÷ 3 = 3 remainder 03 ÷ 3 = 1 remainder 01 ÷ 3 = 0 remainder 1Read the remainders from the bottom up: 10011073 (base 36) = 100110 (base 3)
Worked example 3: RS from base 36 to ternary
Step 1: base 36 to decimalRS (base 36) = 27 × 361 + 28 × 360= 972 + 28= 1,000Step 2: decimal to base 31,000 ÷ 3 = 333 remainder 1333 ÷ 3 = 111 remainder 0111 ÷ 3 = 37 remainder 037 ÷ 3 = 12 remainder 112 ÷ 3 = 4 remainder 04 ÷ 3 = 1 remainder 11 ÷ 3 = 0 remainder 1Read the remainders from the bottom up: 1101001RS (base 36) = 1101001 (base 3)
Need the other direction? Open the Ternary to Base 36 converter.
Base 36 to Ternary examples
The decimal number 255 is written 73 in base 36 and 100110 in ternary.
| Base 36 | Ternary | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 7 | 21 | 7 |
| 8 | 22 | 8 |
| A | 101 | 10 |
| F | 120 | 15 |
| G | 121 | 16 |
| W | 1012 | 32 |
| 1S | 2101 | 64 |
| 2S | 10201 | 100 |
| 73 | 100110 | 255 |
| RS | 1101001 | 1000 |
Where Base 36 to Ternary comes up
Base 36 uses 0 to 9 and A to Z, the largest base you can write with digits and letters alone. Short IDs and URL slugs often use it, and JavaScript number.toString(36) and parseInt(text, 36) work in base 36.
Ternary uses the digits 0, 1 and 2, and each ternary digit (a trit) carries about 1.58 bits of information. Ternary is rare in real hardware, though the Soviet Setun computer of 1958 used a balanced ternary design. Today it shows up mostly in computer science courses and puzzles.
Going to a smaller base spreads the same value over more digits, so the result is longer. The number 255 needs 2 digits in base 36 and 6 in ternary.
Base 36 to Ternary FAQ
How do I convert base 36 to ternary?
Convert to decimal first by adding up each digit times its place value, then divide that decimal number by 3 repeatedly and read the remainders from last to first.
Which digits does base 36 use?
Base 36 uses the digits 0 to 9 and A to Z. Letters are not case sensitive on this converter, and results are shown in capitals.
Will the ternary number be longer or shorter?
Longer. Going to a smaller base spreads the same value over more digits, so the result is longer. Roughly 3.26 ternary digits for every base 36 digit. The number 255 needs 2 digits in base 36 and 6 in ternary.
What is 73 in ternary?
73 in base 36 is 100110 in ternary. Both are the decimal number 255.
Can I convert negative numbers or fractions?
The converter handles whole numbers, and a leading minus sign works for negatives. Fractions use a different method, where you repeatedly multiply the fractional part by the new base, and they are not supported here.