# φ digit calculator

## World's simplest number tool

Quickly calculate golden ratio digits in your browser. To get your φ digits, just specify how many of them you need in the options below, and this utility will generate a sequence of that many digits. Created by developers from team Browserling.

a new physics project!
announcement

Love physics as much as we do? Then you'll also love our new project – PHYSURLS – a super neat physics news aggregator. Check it out!

*fullscreen*

*fullscreen_exit*

A link to this tool, including input, options and all chained tools.

Can't convert.

φ digit calculator tool
What is a φ digit calculator?

This is an online browser-based utility for generating a list of digits of the golden ratio. It's said that two objects are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two objects. Roughly speaking, this proportion can be expressed as 62% to 38%. The golden ratio is denoted by the Greek letter phi (Φ or φ) and often appears in science and nature. Many other names are used for the phi constant, in particular, golden mean, golden number, golden section, and lesser-known – extreme and mean ratio. The golden section can be calculated by solving the quadratic equation φ² - φ - 1 = 0. It has two solutions: φ = (1+√5)/2 (positive constant) and φ = (1-√5)/2 (negative constant). In this tool, you can calculate both the positive and negative golden proportion and get any number of φ digits, up to one million values. You can also get only digits of the ratio, without the whole number part (either "1." for positive phi or "-0." for negative), and optionally set a separator between φ digits. That's numberwang!

φ digit calculator examples
Click to use

1000 Golden Ratio Digits

In this example, we find the first one thousand digits of the positive golden number, that is, of the constant φ = (1+√5)/2.

1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374847540880753868917521266338622235369317931800607667263544333890865959395829056383226613199282902678806752087668925017116962070322210432162695486262963136144381497587012203408058879544547492461856953648644492410443207713449470495658467885098743394422125448770664780915884607499887124007652170575179788341662562494075890697040002812104276217711177780531531714101170466659914669798731761356006708748071013179523689427521948435305678300228785699782977834784587822891109762500302696156170025046433824377648610283831268330372429267526311653392473167111211588186385133162038400522216579128667529465490681131715993432359734949850904094762132229810172610705961164562990981629055520852479035240602017279974717534277759277862561943208275051312181562855122248093947123414517022373580577278616008688382952304592647878017889921990270776903895321968198615143780314997411069260886742962267575605231727775203536139362

**Required options**

Calculate this amount of φ digits.

Write prefix "1." in front of the
positive φ digits and prefix "-0."
in front of the negative φ digits.

Calculate golden ratio digits
by using formula (1+√5)/2.

Separate φ digits with this symbol.

200 Negative φ Digits

In this example, we calculate 200 digits of the second golden mean root. This root is negative and is calculated using the formula φ = (1-√5)/2.

-0.61803398874989484820458683436563811772030917980576286213544862270526046281890244970720720418939113748475408807538689175212663386222353693179318006076672635443338908659593958290563832266131992829026788

**Required options**

Calculate this amount of φ digits.

Write prefix "1." in front of the
positive φ digits and prefix "-0."
in front of the negative φ digits.

Calculate golden ratio digits
by using formula (1-√5)/2.

Separate φ digits with this symbol.

Dash-separated Phi Digits

In this example, we exclude the whole part from the golden section (that is, we don't print the "1." at the start), and generate 100 digits, separating them with the dash symbol.

6-1-8-0-3-3-9-8-8-7-4-9-8-9-4-8-4-8-2-0-4-5-8-6-8-3-4-3-6-5-6-3-8-1-1-7-7-2-0-3-0-9-1-7-9-8-0-5-7-6-2-8-6-2-1-3-5-4-4-8-6-2-2-7-0-5-2-6-0-4-6-2-8-1-8-9-0-2-4-4-9-7-0-7-2-0-7-2-0-4-1-8-9-3-9-1-1-3-7-4

**Required options**

Calculate this amount of φ digits.

Write prefix "1." in front of the
positive φ digits and prefix "-0."
in front of the negative φ digits.

Calculate golden ratio digits
by using formula (1+√5)/2.

Separate φ digits with this symbol.

Pro tips
Master online number tools

You can pass options to this tool using their codes as query arguments and it will automatically compute output. To get the code of an option, just hover over its icon. Here's how to type it in your browser's address bar. Click to try!

https://onlinenumbertools.com/calculate-phi-digits?&count=1000&include-base=true&positive-phi=true&separator=

All number tools

Quickly create a list of numbers in arithmetic series.

Quickly create a list of numbers in geometric series.

Quickly calculate the coefficients of the binomial expansion.

Quickly create a downloadable image from numbers.

Quickly create a list of random numbers.

Quickly create a list of random primes from a specific interval.

Quickly create a matrix with random numbers as its elements.

Quickly create a random row or column vector.

Quickly exchange rows and columns of a matrix.

Quickly find the inverse matrix of any square matrix.

Quickly find the determinant of any square matrix.

Quickly calculate any number of digits of number π.

Quickly generate the specified number of Euler constant's digits.

Quickly generate any number of golden ratio digits.

Quickly generate numbers of say what you see sequence.

Quickly calculate numbers of Fibonacci sequence.

Quickly calculate numbers of Lucas series.

Quickly generate Fibonacci-like series with custom start values.

Quickly calculate members of a linear recurrence series.

Quickly create a sequence of prime numbers.

Quickly check if the given number is a prime.

Quickly compute all prime factors of a number.

Quickly compute all divisors of a number.

Quickly calculate the GCD of two or more numbers.

Quickly calculate the LCM of two or more numbers.

Quickly create a list of increasing or decreasing integers.

Quickly create a sequence of even numbers.

Quickly create a sequence of odd numbers.

Quickly create a list of squares.

Quickly create a list of cubes.

Quickly generate a series of numbers in the form 2^n.

Quickly generate a series of numbers in the form 10^n.

Quickly choose one or more numbers from a list of numbers.

Quickly round one or more numbers to the given accuracy.

Quickly sort numbers in ascending or descending order.

Quickly sort number's digits in ascending or descending order.

Quickly randomize the order of digits in a number.

Quickly filter numbers according to certain criteria.

Quickly add up all the numbers in the given list and find their sum.

Quickly multiply all the numbers together and find their product.

Quickly add up all the digits of the given numbers.

Quickly multiply all the digits of the given numbers.

Quickly sum up all the fractions in the given list and find their total.

Quickly find the largest number in a number sequence.

Quickly find the smallest number in a number sequence.

Quickly create a diagonal matrix with ones on the main diagonal.

Quickly spell cardinal and ordinal numbers using English words.

Quickly convert spelled numbers to regular numbers.

Quickly convert a number to the form 2^x.

Quickly express a number in the form 10^x.

Quickly convert base 10 numbers to base -10.

Quickly convert a number from one base to any other base.

Quickly convert simple fractions to pretty Unicode fractions.

Quickly add digits to a number so that it becomes 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.

Rewrite Numbers

Given numbers and a grammar, recursively rewrite them.

Create a Floating Point Number

Create a number from the mantissa, base and exponent.

Convert a Number to the Scientific Notation

Convert a number to the a*10^b form.

Convert Scientific Notation to a Number

Convert a number in scientific notation to a regular number.

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 Product

Calculate a cumulative product of a list of numbers.

Calculate the Factorial

Find the factorial 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.

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.

Calculate the Trace of a Matrix

Find the sum of main diagonal elements of a matrix.

Calculate the Eigenvalues of a Matrix

Find the eigenvalues of a matrix.

Multiply Matrices

Compute the product of two matrices.

Add Matrices

Compute the sum of two matrices.

Subtract Matrices

Compute the difference of two matrices.

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 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.

Mirror a Number

Create a mirror copy of a number.

Zero-pad a Number

Add zeros 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 All Digits in a Number

Add one to every digit in a number.

Decrease All Digits in a Number

Subtract one from every digit in a number.

Count Number Occurrences

Find how often numeric values occur.

Calculate Percentages

Find x% of a number.

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.

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.

Numberwang Number Test

Test if the given number is numberwang.

Subscribe!
Never miss an update

Cool!

Notifications
We'll let you know when we add this tool

Cool!