<span class="mw-page-title-main">0</span>

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<p><b>0</b> (<b>zero</b>) is a <a href="/en/Number" title="Number" class="wl">number</a> representing an empty <a href="/en/Quantity" title="Quantity" class="wl">quantity</a>. In <a href="/en/Place-value_notation" title="Place-value notation" class="mw-redirect wl">place-value notation</a> such as the <a href="/en/Hindu–Arabic_numeral_system" title="Hindu–Arabic numeral system" class="wl">Hindu–Arabic numeral system</a>, 0 also serves as a placeholder <a href="/en/Numerical_digit" title="Numerical digit" class="wl">numerical digit</a>, which works by <a href="/en/Multiplication" title="Multiplication" class="wl">multiplying</a> digits to the left of 0 by the <a href="/en/Radix" title="Radix" class="wl">radix</a>, usually by <a href="/en/10" title="10" class="wl">10</a>. As a number, 0 fulfills a central role in <a href="/en/Mathematics" title="Mathematics" class="wl">mathematics</a> as the <a href="/en/Additive_identity" title="Additive identity" class="wl">additive identity</a> of the <a href="/en/Integer" title="Integer" class="wl">integers</a>, <a href="/en/Real_number" title="Real number" class="wl">real numbers</a>, and other <a href="/en/Algebraic_structure" title="Algebraic structure" class="wl">algebraic structures</a>.</p>

<div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none" about="#mwt1">Number</div>
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<p></p>
<style data-mw-deduplicate="TemplateStyles:r1097763485" typeof="mw:Extension/templatestyles mw:Transclusion">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}html.client-js body.skin-minerva .mw-parser-output .mbox-text-span{margin-left:23px!important}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}</style>
<p class="mw-empty-elt"></p>
<div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none" about="#mwt21">Natural number</div><style data-mw-deduplicate="TemplateStyles:r1066479718" typeof="mw:Extension/templatestyles">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}body.skin-minerva .mw-parser-output .infobox-header,body.skin-minerva .mw-parser-output .infobox-subheader,body.skin-minerva .mw-parser-output .infobox-above,body.skin-minerva .mw-parser-output .infobox-title,body.skin-minerva .mw-parser-output .infobox-image,body.skin-minerva .mw-parser-output .infobox-full-data,body.skin-minerva .mw-parser-output .infobox-below{text-align:center}</style><div class='mobile-collapse'><header class="mobile-collapse-header mobile-collapse-btn"><b>Quick facts: 
← −1 
0
 1 →
, Cardinal, Ordinal, Binary, Te...</b> <span class='arrow'>▼</span></header> <table class="infobox mobile-collapse-element" style="line-height: 1.5em"><tbody><tr><th colspan="2" class="infobox-above" style="font-size: 150%"><table style="width:100%; margin:0"><tbody><tr>
<td style="width:15%; text-align:left; white-space: nowrap; font-size:smaller"><a href="/en/−1_(number)" title="−1 (number)" class="mw-redirect wl"><span>←</span> −1 </a></td>
<td style="width:70%; padding-left:1em; padding-right:1em; text-align: center;">0</td>
<td style="width:15%; text-align:right; white-space: nowrap; font-size:smaller"><a href="/en/1_(number)" title="1 (number)" class="mw-redirect wl"> 1 <span>→</span></a></td>
</tr></tbody></table></th></tr><tr><td colspan="2" class="infobox-subheader" style="font-size:100%;"><div style="text-align:center;">  <a href="/en/−1" title="−1" class="wl">−1</a> <a href="/en/0" title="0" class="wl">0</a> <a href="/en/1" title="1" class="wl">1</a> <a href="/en/2" title="2" class="wl">2</a> <a href="/en/3" title="3" class="wl">3</a> <a href="/en/4" title="4" class="wl">4</a> <a href="/en/5" title="5" class="wl">5</a> <a href="/en/6" title="6" class="wl">6</a> <a href="/en/7" title="7" class="wl">7</a> <a href="/en/8" title="8" class="wl">8</a> <a href="/en/9" title="9" class="wl">9</a> <a href="/en/10_(number)" title="10 (number)" class="mw-redirect wl">→</a></div><div style="text-align:center;"> <style data-mw-deduplicate="TemplateStyles:r1129693374" typeof="mw:Extension/templatestyles">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><div class="hlist"><ul><li><a href="/en/List_of_numbers" title="List of numbers" class="wl">List of numbers</a></li><li><a href="/en/Integer" title="Integer" class="wl">Integers</a></li></ul></div></div><div style="text-align:center;"><a href="/en/Negative_number" title="Negative number" class="wl">←</a> <a href="/en/0" title="0" class="wl">0</a> <a href="/en/10" title="10" class="wl">10</a> <a href="/en/20_(number)" title="20 (number)" class="wl">20</a> <a href="/en/30_(number)" title="30 (number)" class="wl">30</a> <a href="/en/40_(number)" title="40 (number)" class="wl">40</a> <a href="/en/50_(number)" title="50 (number)" class="wl">50</a> <a href="/en/60_(number)" title="60 (number)" class="wl">60</a> <a href="/en/70_(number)" title="70 (number)" class="wl">70</a> <a href="/en/80_(number)" title="80 (number)" class="wl">80</a> <a href="/en/90_(number)" title="90 (number)" class="wl">90</a> <a href="/en/100_(number)" title="100 (number)" class="mw-redirect wl">→</a></div></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/en/Cardinal_numeral" title="Cardinal numeral" class="wl">Cardinal</a></th><td class="infobox-data">0, zero, <span class="nowrap">"oh" (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt"><a href="/en/Help:IPA/English" title="Help:IPA/English" class="wl">/<span style="border-bottom:1px dotted"><span>oʊ</span></span>/</a></span></span>)</span>, nought, naught, nil</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/en/Ordinal_numeral" title="Ordinal numeral" class="wl">Ordinal</a></th><td class="infobox-data">Zeroth, noughth, 0th</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/en/Binary_number" title="Binary number" class="wl">Binary</a></th><td class="infobox-data">0<sub>2</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/en/Ternary_numeral_system" title="Ternary numeral system" class="wl">Ternary</a></th><td class="infobox-data">0<sub>3</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/en/Senary" title="Senary" class="wl">Senary</a></th><td class="infobox-data">0<sub>6</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/en/Octal" title="Octal" class="wl">Octal</a></th><td class="infobox-data">0<sub>8</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/en/Duodecimal" title="Duodecimal" class="wl">Duodecimal</a></th><td class="infobox-data">0<sub>12</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/en/Hexadecimal" title="Hexadecimal" class="wl">Hexadecimal</a></th><td class="infobox-data">0<sub>16</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/en/Eastern_Arabic_numerals" title="Eastern Arabic numerals" class="wl">Arabic</a>, <a href="/en/Central_Kurdish" title="Central Kurdish" class="mw-redirect wl">Kurdish</a>, <a href="/en/Persian_language" title="Persian language" class="wl">Persian</a>, <a href="/en/Sindhi_language" title="Sindhi language" class="wl">Sindhi</a>, <a href="/en/Urdu_numerals" title="Urdu numerals" class="mw-redirect wl">Urdu</a></th><td class="infobox-data"><span style="font-size:150%;">٠</span></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/en/Indian_numerals" title="Indian numerals" class="mw-redirect wl">Hindu Numerals</a></th><td class="infobox-data"><span style="font-size:150%;">०</span></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/en/Chinese_numerals" title="Chinese numerals" class="wl">Chinese</a></th><td class="infobox-data">零, 〇</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/en/Burmese_numerals" title="Burmese numerals" class="wl">Burmese</a></th><td class="infobox-data">၀</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/en/Khmer_numerals" title="Khmer numerals" class="wl">Khmer</a></th><td class="infobox-data">០</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/en/Thai_numerals" title="Thai numerals" class="wl">Thai</a></th><td class="infobox-data">๐</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/en/Bengali_numerals" title="Bengali numerals" class="wl">Bangla</a></th><td class="infobox-data">০</td></tr></tbody></table> <footer class='mobile-collapse-footer mobile-collapse-btn'><b>Close</b> <span class='arrow'>▲</span></footer></div>
<p>Common <a href="/en/Names_for_the_number_0_in_English" title="Names for the number 0 in English" class="wl">names for the number 0 in English</a> are <i>zero</i>, <i>nought</i>, <i>naught</i> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt"><a href="/en/Help:IPA/English" title="Help:IPA/English" class="wl">/<span style="border-bottom:1px dotted"><span>n</span><span>ɔː</span><span>t</span></span>/</a></span></span>), <i>nil</i>. In contexts where at least one adjacent digit distinguishes it from the <a href="/en/O" title="O" class="wl">letter O</a>, the number is sometimes pronounced as <i>oh</i> or <i>o</i> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt"><a href="/en/Help:IPA/English" title="Help:IPA/English" class="wl">/<span style="border-bottom:1px dotted"><span>oʊ</span></span>/</a></span></span>). Informal or <a href="/en/Slang" title="Slang" class="wl">slang</a> terms for 0 include <i>zilch</i> and <i>zip</i>. Historically, <i>ought</i>, <i>aught</i> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt"><a href="/en/Help:IPA/English" title="Help:IPA/English" class="wl">/<span style="border-bottom:1px dotted"><span>ɔː</span><span>t</span></span>/</a></span></span>), and <i>cipher</i> have also been used.</p>



0 is a number representing an empty quantity. In place-value notation such as the Hindu–Arabic numeral system, 0 also serves as a placeholder numerical digit, which works by multiplying digits to the left of 0 by the radix, usually by 10. As a number, 0 fulfills a central role in mathematics as the additive identity of the integers, real numbers, and other algebraic structures. Common names for the number 0 in English are zero, nought, naught , nil. In contexts where at least one adjacent digit distinguishes it from the letter O, the number is sometimes pronounced as oh or o . Informal or slang terms for 0 include zilch and zip. Historically, ought, aught , and cipher have also been used. 