᠎᠎᠎          

Number's base changer

World's simplest number tool
Quickly change a number's base in your browser. To get your number in the new base, just enter it in the input field, set the input number's base and the output number's base, and this utility will convert the number to the new base. Created by developers from team Browserling.
A link to this tool, including input, options and all chained tools.
Import from file
Save as...
Copy to clipboard
Download
Export to Pastebin
Can't convert.
An error has occured.
Chain with...
Remove chain
Save as...
Copy to clipboard
Download
Export to Pastebin
Remove no tools?
This tool cannot be chained.
Old Base
Enter the input number base.
Allowed bases are from
-64 to 64, except -1 and 0.
New Base
Enter the output base.
Allowed bases are from
-64 to 64, except -1 and 0.
Output Format
Display the output numbers in the
new base as a power series sum.
Display the decimal value next to
each output number.
These two options don't work at
the same time. You must choose
one or the other.

What is a number's base changer?

learn more about this tool
This is an online browser-based utility for changing a number's base. Numbers are an abstract idea and to write them down, you need to select a base. The base can be anything and the most common base is 10 (decimal) and it's the default base in this tool. When you write a number 25 or 1044, it's assumed that it's in base 10 but it could be in any other base as there are infinitely many numeral systems. Other well-known numeral systems are binary (base 2), octal (base 8), and hexadecimal (base 16). Slightly less common are negative bases, such as negabinary (base -2), negaoctal (base -8), negadecimal (base -10), and negahexadecimal (base -16). Even less common and virtually unknown bases are rational (for example, base 2/3), irrational (for example, base e), fractional (for example, base π/2), imaginary and complex (for example, base i), and many more. At the moment we support only positive and negative integer bases. All bases use the same principle to represent a number with the only difference being the alphabet set of the digits and whether the sign symbol is used for negative numbers. For example, the binary base expresses each number using two characters "0" and "1", the decimal base uses ten digits "0123456789", and the hexadecimal base uses six more letters "0123456789abcdef". Given the alphabet and the base, we can express any number by the formula x = ∑anbn, where an is a digit from the alphabet and b is the given base. The sequence anan-1…a0 of indexes in this formula is the number x in the given base b. For example, in base 10, the number 25 can be written as a sum ∑an10n = a1*101 + a0*100 = 2*101 + 5*100. Here the indexes are a1 = 2 and a0 = 5 and a1a0 forms the number 25. In the base 2, the number 25 can be expressed as 1*24 + 1*23 + 0*22 + 0*21 + 1*20 and from this sum, we find that 11001 is the number 25 in base 2. With negative bases, it works the same way. For example, in base -8, the number 2510 is 1*(-8)2 + 5*(-8)1 + 1*(-8)0, which is 151-8. If the base is negative, then the minus sign is not used. For example, -2510 = 4*(-8)1 + 7*(-8)0 = 47-8. In positive bases, the minus sign needs to be used to express negative numbers. This tool accepts any number with the base from -64 to 64 as input (except bases 0 and -1, which don't exist) and outputs it in any other base from this range. It can convert multiple numbers at the same time if they are entered one per line. As it's not always easy to know what each number means, you can also print the decimal number after each converted number. Also, as sometimes you may need the full sum formula, you can select the "Use Sum Formula" option to print the sum terms. That's numberwang!

Number's base changer examples

Click to use
Decimal to Hexadecimal
This example converts five numbers from base 10 to base 16. It decomposes each number using the formula x = ∑anbn = ∑an16n and then prints the coefficients an, which represent the number in base 16. For example, the number 30 = a1*161 + a0*161 = 1*161 + 14*161 and therefore the coefficients are a1 = 1 and a0 = 14. The hex base uses letters a, b, c, d, e, and f for coefficients 10, 11, 12, 13, 14, 15, so we get that the coefficients actually are a1 = 1 and a0 = e, and we find that 3010 = 1e16.
30 260 -45 -100 2450
1e 104 -2d -64 992
Required options
These options will be used automatically if you select this example.
Enter the input number base.
Enter the output base.
Display the output numbers in the
new base as a power series sum.
Display the decimal value next to
each output number.
Create a Negabinary
In this example, we change a binary number's representation to negabinary, which is the base minus two (base -2). It's often used to encode negative binary numbers as it doesn't use the "-" sign. We have also activated the use decimal notation option so that we knew what the input numbers were without much thinking. The input number is first converted to decimal 1102 = 1*22 + 1*21 + 0*20 = 4 + 2 + 0 = 610 and then to negabinary 610 = 1*(-2)4 + 1*(-2)3 + 0*(-2)2 + 1*(-2)1 + 0*(-2)0 = 11010-2. Similarly, -11102 (-1410) is 110110-2 and as you can see, the minus sign disappears in this base.
110 -1110 10101
11010 (6) 110110 (-14) 10101 (21)
Required options
These options will be used automatically if you select this example.
Enter the input number base.
Enter the output base.
Display the output numbers in the
new base as a power series sum.
Display the decimal value next to
each output number.
Decode a Negadecimal
This example decodes negadecimal numbers. "Nega" means negative and "decimal" means ten, so it converts numbers from base -10 numbers to base 10. As the option "Print Sum" is enabled, it displays the new numbers as a decomposition sum. It seems that there are no signed numbers in the input as all numbers look positive but in fact, the third and fifth numbers are signed. After the conversion, you can see that these numbers are -45 and -505 as they use minus signs in the sum formula.
184 176 55 722 1515
2×(10)¹ + 4×(10)⁰ 3×(10)¹ + 6×(10)⁰ -4×(10)¹ - 5×(10)⁰ 6×(10)² + 8×(10)¹ + 2×(10)⁰ -5×(10)² - 0×(10)¹ - 5×(10)⁰
Required options
These options will be used automatically if you select this example.
Enter the input number base.
Enter the output base.
Display the output numbers in the
new base as a power series sum.
Display the decimal value next to
each output number.
Encode to Negaoctal
In this example, we convert three octal (radix 8) numbers to negaoctal (radix -8) numbers. We activate the "Use Sum Formula" option to get the numbers' power series from the formula ∑an(-8)n, where an is the octal base alphabet made from the digits 0 to 7. From the coefficients before the sum terms, we find that the number 558 is 135-8, the number -128 is 26-8, and the number 448 is 144-8.
55 -12 44
1×(-8)² + 3×(-8)¹ + 5×(-8)⁰ 2×(-8)¹ + 6×(-8)⁰ 1×(-8)² + 4×(-8)¹ + 4×(-8)⁰
Required options
These options will be used automatically if you select this example.
Enter the input number base.
Enter the output base.
Display the output numbers in the
new base as a power series sum.
Display the decimal value next to
each output number.
Unary Numeral System
This example loads two negahexadecimal numbers and expands them as repeated 1's in the unary numeral system. The unary number system, also known as base 1, uses only one symbol to represent each number. This symbol can be anything and we have hard-coded it to be "1". If a number in the decimal base is N, then in the unary base it has N ones. In our case, the number 1f2-16 is 18 in base 10, thus in base 1 it's equal to eighteen ones. The number 1c-16 is -4 in base 10 and in base 1 it's equal to minus four ones.
1f2 1c
111111111111111111 (18) -1111 (-4)
Required options
These options will be used automatically if you select this example.
Enter the input number base.
Enter the output base.
Display the output numbers in the
new base as a power series sum.
Display the decimal value next to
each output number.
Base -32 to Base -64
In this example, we convert from one negative base (-32) to another negative base (-64). To do it, this utility first finds decimal base 10 values of the input base -32 values and then converts them to base -64 values. As both bases are negative, the numbers don't use the "-" sign. These bases use an alphabet that not only contains numbers but also letters and even special characters ("$" and "_" in base -64). We also display the intermediate decimal value in brackets next to each base -64 output number.
g 1uk 1sm 1cr 4jh
g (16) 1_k (84) 1$m (150) 1Sr (667) 1aN (3505)
Required options
These options will be used automatically if you select this example.
Enter the input number base.
Enter the output base.
Display the output numbers in the
new base as a power series sum.
Display the decimal value next to
each output number.
Pro tips Master online number tools
You can pass input to this tool via ?input query argument and it will automatically compute output. Here's how to type it in your browser's address bar. Click to try!
https://onlinetools.com/number/change-number-base?input=30%0A260%0A-45%0A-100%0A2450&input-base=10&output-base=16&show-representation-sum=False&show-decimal=False
All number tools
Didn't find the tool you were looking for? Let us know what tool we are missing and we'll build it!
Generate an Arithmetic Progression
Quickly create a list of numbers in arithmetic series.
Generate a Geometric Progression
Quickly create a list of numbers in geometric series.
Draw Pascal's Triangle
Quickly calculate the coefficients of the binomial expansion.
Convert Numbers to a Picture
Quickly create a downloadable image from numbers.
Generate Random Numbers
Quickly create a list of random numbers.
Generate Random Prime Numbers
Quickly create a list of random primes from a specific interval.
Generate Random Matrices
Quickly create a matrix with random numbers as its elements.
Generate Random Vectors
Quickly create a random row or column vector.
Find the Transpose of a Matrix
Quickly exchange rows and columns of a matrix.
Find Matrix Inverse
Quickly find the inverse matrix of any square matrix.
Calculate Matrix Determinant
Quickly find the determinant of any square matrix.
Calculate Pi Digits
Quickly calculate any number of digits of number π.
Calculate e Digits
Quickly generate the specified number of Euler constant's digits.
Calculate Phi Digits
Quickly generate any number of golden ratio digits.
Generate Look and Say Numbers
Quickly generate numbers of say what you see sequence.
Calculate Fibonacci Numbers
Quickly calculate numbers of Fibonacci sequence.
Calculate Lucas Numbers
Quickly calculate numbers of Lucas series.
Calculate Fibonacci-like Series
Quickly generate Fibonacci-like series with custom start values.
Calculate Linear Recurrence Series
Quickly calculate members of a linear recurrence series.
Calculate Prime Numbers
Quickly create a sequence of prime numbers.
Number Primality Test
Quickly check if the given number is a prime.
Calculate Prime Factors
Quickly compute all prime factors of a number.
Calculate All Factors of a Number
Quickly compute all divisors of a number.
Find Greatest Common Divisor
Quickly calculate the GCD of two or more numbers.
Find Least Common Multiple
Quickly calculate the LCM of two or more numbers.
Generate an Integer Sequence
Quickly create a list of increasing or decreasing integers.
Generate Even Numbers
Quickly create a sequence of even numbers.
Generate Odd Numbers
Quickly create a sequence of odd numbers.
Generate a Sequence of Squares
Quickly create a list of squares.
Generate a Sequence of Cubes
Quickly create a list of cubes.
Generate Powers of Two
Quickly generate a series of numbers in the form 2^n.
Generate Powers of Ten
Quickly generate a series of numbers in the form 10^n.
Pick a Number
Quickly choose one or more numbers from a list of numbers.
Round a Number
Quickly round one or more numbers to the given accuracy.
Sort a List of Numbers
Quickly sort numbers in ascending or descending order.
Sort Digits in a Number
Quickly sort number's digits in ascending or descending order.
Shuffle Digits in a Number
Quickly randomize the order of digits in a number.
Filter a List of Numbers
Quickly filter numbers according to certain criteria.
Calculate Number Sum
Quickly add up all the numbers in the given list and find their sum.
Calculate Number Product
Quickly multiply all the numbers together and find their product.
Calculate Digit Sum
Quickly add up all the digits of the given numbers.
Calculate Digit Product
Quickly multiply all the digits of the given numbers.
Add Fractions
Quickly sum up all the fractions in the given list and find their total.
Find the Maximum Number
Quickly find the largest number in a number sequence.
Find the Minimum Number
Quickly find the smallest number in a number sequence.
Generate a Unit Matrix
Quickly create a diagonal matrix with ones on the main diagonal.
Convert Numbers to Words
Quickly spell cardinal and ordinal numbers using English words.
Convert Words to Numbers
Quickly convert spelled numbers to regular numbers.
Convert a Number to the Power of Two
Quickly convert a number to the form 2^x.
Convert a Number to the Power of Ten
Quickly express a number in the form 10^x.
Convert a Number to the Negadecimal Base
Quickly convert base 10 numbers to base -10.
Change a Number's Base
Quickly convert a number from one base to any other base.
Create Unicode Fractions
Quickly convert simple fractions to pretty Unicode fractions.
Create a Palindrome from a Number
Quickly add digits to a number so that it becomes a palindrome.
Check if a Number is a Palindrome
Quickly test if the given numbers are palindromes.
Coming soon These number tools are on the way
Generate Numberwang Numbers
Create a list of numberwang numbers.
Generate Magic Numbers
Create a list of neat looking numbers.
Draw a Magic Square
Create a matrix of numbers with rows and cols having same sum.
Rewrite Numbers
Given numbers and a grammar, recursively rewrite them.
Create a Floating Point Number
Create a number from the mantissa, base, and exponent.
Visualize a Floating Point Number
Show how a fp number is represented in a computer.
Convert a Number to the Scientific Notation
Convert a number to the a×10<sup>b</sup> form.
Convert Scientific Notation to a Number
Convert a number in scientific notation to a regular number.
Generate Unary Numbering
Create a list of unary numbers (1, 11, 111, 1111, …).
Generate Symbolic Numbering
Create a list of alphabetic numbers (a, b, c, …, z, aa, ab, …).
Generate Roman Numbering
Create a list of Roman numbers (i, ii, iii, iv, v…).
Generate Braille Numbering
Create a list of Braille numbers (⠂, ⠆, ⠒, ⠲, ⠢, …).
Generate Random Binary Numbers
Create a list of random binary numbers.
Generate Random Octal Numbers
Create a list of random octal numbers.
Generate Random Decimal Numbers
Create a list of random decimal numbers.
Generate Random Hex Numbers
Create a list of random hexadecimal numbers.
Calculate a Running Sum
Calculate a cumulative sum of a list of numbers.
Calculate a Running Difference
Calculate a cumulative difference of a list of numbers.
Calculate a Running Product
Calculate a cumulative product of a list of numbers.
Calculate Number Quotient
Divide two numbers and find their quotient.
Calculate Digit Quotient
Divide the digits of the given number.
Calculate the Factorial
Find the factorial of a number.
Create Number Anagrams
Create one or more anagrams of a number.
Generate Number Bigrams
Create a list of digit bigrams from a number.
Generate Number Trigrams
Create a list of digit trigrams from a number.
Generate Number N-grams
Create a list of digit ngrams from a number.
Generate a Polynomial Sequence
Create a list of polynomial progression numbers.
Generate SI Prefixes
Create a list of metric prefixes.
Analyze a Number
Report how many digits appear how many times.
Convert a Number to an Ordinal
Convert a cardinal number to an ordinal number.
Convert an Ordinal to a Number
Convert an ordinal number to a cardinal number.
Convert a Number to Roman Number
Convert Arabic numerals to Roman numerals.
Convert a Roman Number to Regular Number
Convert Roman Numerals to Arabic numerals.
Generate Negafibonacci Numbers
Calculate a series of extended Fibonacci numbers.
Generate Fibonacci Primes
Find numbers that are both Fibonacci numbers and primes.
Fibonacci Number Test
Check if a number is a Fibonacci number.
Fibonacci Prime Test
Check if a number is both a Fibonacci number and a prime.
Construct Fibonacci Words
Create a sequence of Fibonacci words.
Construct Tribonacci Words
Create a sequence of Tribonacci words.
Construct Tetranacci Words
Create a sequence of Tetranacci words.
Construct Pentanacci Words
Create a sequence of Pentanacci words.
Generate Negalucas Numbers
Calculate a series of extended Lucas numbers.
Generate Lucas Primes
Calculate a series of extended Lucas numbers.
Lucas Prime Test
Check if a number is both a Lucas number and a prime.
Generate Moser de Bruijn Numbers
Calculate a sequence of Moser-Bruijn numbers.
Generate Kolakoski Numbers
Calculate a sequence of Oldenburger-Kolakoski numbers.
Generate Stanley Numbers
Calculate a sequence of Stanley numbers.
Generate Gijswijt Numbers
Calculate a sequence of self-describing Gijswijt numbers.
Generate Rudin-Shapiro Numbers
Calculate a sequence of Rusin-Shapiro numbers.
Generate Baum-Sweet Numbers
Calculate a sequence of Baum-Sweet numbers.
Generate Thue-Morse Sequence
Calculate members of Thue-Morse number series.
Generate Perfect Numbers
Create a list of perfect numbers.
Generate Almost Perfect Numbers
Create a list of almost perfect numbers.
Generate Excessive Number Sequence
Calculate a sequence of abundant numbers.
Generate Deficient Number Sequence
Calculate a sequence of deficient numbers.
Calculate Dragon Curve Numbers
Generate a list of paperfolding sequence numbers.
Generate Composite Numbers
Create a list of numbers that are not prime.
Draw a Number on an LCD
Generate an LCD display that shows the given number.
Draw a Numbers Table
Generate a table of numbers.
Test if a Number is Perfect
Check if the given number is a perfect number.
Test if a Number is Abundant
Check if the given number is an abundant number.
Test if a Number is Deficient
Check if the given number is a deficient number.
Calculate the Modulo
Find the modulus of a number.
Group Number Digits
Group together digits of a number.
Split a Number into Digits
Create a list of digits from a number.
Printf Numbers
Apply sprintf or printf function to numbers.
Create Zalgo Numbers
Let Zalgo destroy your numbers.
Repeat a Number
Repeat a number multiple times.
Mirror a Number
Create a mirror copy of a number.
Zero-pad a Number
Add zeros to a number.
Custom-pad a Number
Add a padding of custom symbols to a number.
Reverse a Number
Reverse the order of digits of a number.
Rotate a Number
Cyclically rotate digits of a number to the left or right.
Increase a Number
Add one to the given number.
Increase All Digits in a Number
Add one to every digit in a number.
Decrease a Number
Subtract one from the given number.
Decrease All Digits in a Number
Subtract one from every digit in a number.
Find Patterns in Numbers
Discover patterns in sequences of numbers.
Count Number Occurrences
Find how often numeric values occur.
Calculate Percentages
Find x% of a number.
Generate Custom Numbers
Create numbers of arbitrary length and properties.
Print Googol
Print the Googol/Google number, which is 10<sup>100</sup>.
Generate Big Numbers
Create a list of big numbers.
Generate Small Numbers
Create a list of small numbers.
Generate Natural Numbers
Create a list of natural numbers.
Generate Rational Numbers
Create a list of rational numbers.
Generate Constant Sequence
Create a series of numbers where all terms are the same.
Generate Real Numbers
Create a sequence of real numbers.
Generate Complex Numbers
Create a list of complex numbers.
Generate Binary Numbers
Create a sequence of binary numbers.
Generate Pairs of Numbers
Create a sequence of number pairs.
Generate Triples of Numbers
Create a sequence of number triples.
Generate Tuples of Numbers
Create a sequence of number n-tuples.
Generate a Short Number
Create a number with not that many digits.
Generate a Long Number
Create a number with many digits.
Interweave Numbers
Interweave two or more number digit-by-digit.
Find the Decimal Expansion of a Number
Rewrite a number in the decimal representation.
Convert a Fraction to a Decimal
Convert a fraction to a decimal number.
Convert a Decimal to a Fraction
Convert a decimal number to a fraction.
Convert a Binary Number to Octal Number
Convert a base two number to base eight number.
Convert a Binary Number to Decimal Number
Convert a base two number to base ten number.
Convert a Binary Number to Hex Number
Convert a base two number to base sixteen number.
Convert a Octal Number to Binary Number
Convert a base eight number to base two number.
Convert a Octal Number to Decimal Number
Convert a base eight number to base ten number.
Convert a Octal Number to Hex Number
Convert a base eight number to base sixteen number.
Convert a Decimal Number to Binary Number
Convert a base ten number to base two number.
Convert a Decimal Number to Octal Number
Convert a base ten number to base eight number.
Convert a Decimal Number to Hex Number
Convert a base ten number to base sixteen number.
Convert a Hex Number to Binary Number
Convert a base sixteen number to base two number.
Convert a Hex Number to Octal Number
Convert a base sixteen number to base eight number.
Convert a Hex Number to Decimal Number
Convert a base sixteen number to base ten number.
Convert Any Number to Any Base
Convert any number in any base to any other base.
Change Number's Mantissa
Change the significand of a number.
Change Number's Exponent
Change the power of a number.
Replace Digits with Letters
Replace digits in a number with alphabet letters.
Create a Number Spiral
Form a spiral from the digits of a number.
Create a Number Circle
Form a circle from the digits of a number.
Create a Number Tree
Form a tree from the given numbers.
Create a Number Digit Tree
Form a tree from the digits of a number.
Remove Decimal Point
Remove the decimal separator from a decimal number.
Add Errors to Numbers
Modify numbers so they are almost the same but have errors.
Create Number Typos
Generate various number typos.
Change Number Font
Write numbers in a different font.
Generate Bold Numbers
Write numbers in a bold font.
Generate Underline Numbers
Write numbers with an underline below them.
Generate Strikethrough Numbers
Write numbers with a strikethrough on them.
Generate Superscript Numbers
Write numbers in a superscript font.
Generate Subscript Numbers
Write numbers in a subscript font.
Create Fake Numbers
Change digits in a number to Unicode look-alikes.
Perturb Numbers
Change the given numbers a little bit.
Perturb Number Digits
Change the digits of the given numbers a little bit.
Find Entropy of a Number
Calculate the complexity (entropy) of a number.
Numberwang Number Test
Test if the given number is numberwang.
Created with love by
51K
@browserling
We're Browserling — a friendly and fun cross-browser testing company powered by alien technology. At Browserling we love to make peoples' lives easier, so we created this collection of number crunching tools. Our tools have the simplest user interface that doesn't require advanced computer skills and they are used by millions of people every month. Our number tools are actually powered by our web developer tools that we created over the last couple of years. Check them out!
Secret message
If you love our tools, then we love you, too! Use coupon code NUMBERLING to get a discount for our premium plans.
Privacy Policy we don't log data!
All conversions and calculations are done in your browser using JavaScript. We don't send a single bit about your input data to our servers. There is no server-side processing at all. We use Google Analytics and StatCounter for site usage analytics. Your IP address is saved on our web server for additional analytics. The free plan doesn't use cookies and don't store session information in cookies. The premium and team plans use cookies to store session information so that you are always logged in. We use your browser's local storage to save tools' input. It stays on your computer.
Terms of Service the legal stuff
By using Online Tools you agree to our Terms of Service. All tools are free for personal use but to use them for commercial purposes, you need to get a premium plan. You can't do illegal or shady things with our tools. We may block your access to tools, if we find out you're doing something bad. We're not liable for your actions and we offer no warranty. We may revise our terms at any time.