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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 for developers.
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Golden Ratio Digits 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.
Which φ value to output?
Calculate golden ratio digits by using formula (1+√5)/2.
Calculate golden ratio digits by using formula (1-√5)/2.
Golden Ratio Digits Separator
Separate φ digits with this symbol.
By default, digits are joined together. Enter the "\n" symbol to separate digits by the line break.
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
These options will be used automatically if you select this example.
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
These options will be used automatically if you select this example.
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
These options will be used automatically if you select this example.
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=
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