{"id":216,"date":"2025-08-30T17:15:07","date_gmt":"2025-08-30T15:15:07","guid":{"rendered":"https:\/\/sandrock.co.za\/carl\/?p=216"},"modified":"2025-08-30T17:15:18","modified_gmt":"2025-08-30T15:15:18","slug":"relative-frequency-of-si-units-and-prefixes","status":"publish","type":"post","link":"https:\/\/sandrock.co.za\/carl\/2025\/08\/relative-frequency-of-si-units-and-prefixes\/","title":{"rendered":"Relative frequency of SI units and prefixes"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">I am huge a fan of the SI system, but I&#8217;ve often noticed that even my academic colleagues take a mix-and-match aproach to the <a href=\"https:\/\/www.bipm.org\/en\/publications\/si-brochure\">BIPM standards<\/a>. It is common for chemists to use \u00c5ngstrom over nanometre, and I don&#8217;t think I&#8217;ve ever seen anyone use megagram over tonne. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Perhaps people are so used to mg (miligram) that they instinctively feel that Mg (megagram) would be confusing, and I admit Gg looks a bit weird. Is that a trend? Do people avoid repeated letters in their unit names? Mm (megameter) does feel a bit odd, although mm (milimeter) feels much more familiar.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">These questions drove me to quantify the relative frequency of the SI units and prefixes.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Google search results<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">I used Google search results as a proxy for usage. I also tried the <a href=\"https:\/\/storage.googleapis.com\/books\/ngrams\/books\/20200217\/eng\/eng-1-ngrams_exports.html\">Google Ngram project<\/a>, but that turned out to be harder than I wanted it to be. After downloading all the data and parsing some of it, it didn&#8217;t contain all the terms I wanted.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here is the complete table showing log10(Google search results + 1) for every combination of the SI prefixes with the units mentioned in the SI brochure as base units or derived units. I&#8217;ve skipped degrees Celsius as the Google search API kept erroring on searches like &#8220;quettaCelsius&#8221;.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-794e3cfa wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"619\" src=\"https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/search_results_edited-3-1024x619.webp\" alt=\"\" class=\"wp-image-231\" srcset=\"https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/search_results_edited-3-1024x619.webp 1024w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/search_results_edited-3-300x181.webp 300w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/search_results_edited-3-768x464.webp 768w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/search_results_edited-3-1536x929.webp 1536w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/search_results_edited-3-2048x1238.webp 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">It&#8217;s always interesting when you get results like this &#8211; you can immediately start seeing some structure.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">These things jump out at me:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>quecto, ronto, ronna, and quetta were <a href=\"https:\/\/www.bipm.org\/en\/cgpm-2022\/resolution-3\">added in 2022<\/a> and you can clearly see they haven&#8217;t been as widely adopted as the other prefixes<\/li>\n\n\n\n<li>No-one uses prefixes with steradian<\/li>\n\n\n\n<li>The &#8220;-er&#8221; spellings of metre and litre are more popular than the &#8220;-re&#8221; spellings that the BIPM uses, but not by much (I&#8217;m not sure if this is an artefact of Google combining results for the two)<\/li>\n\n\n\n<li>For tonne, the negative power prefixes (milli) are much less popular than the positive ones (mega).<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Basic stats<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Here are the counts across all prefixes for the units. It&#8217;s obvious that the base unit counts are somewhat complicated by common words like &#8220;gray&#8221; or names like &#8220;Henry&#8221;. I&#8217;d imagine Pascal and Newton have the same problem.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/unit_frequency-683x1024.png\" alt=\"\" class=\"wp-image-243\" style=\"width:381px;height:auto\" srcset=\"https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/unit_frequency-683x1024.png 683w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/unit_frequency-200x300.png 200w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/unit_frequency-768x1152.png 768w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/unit_frequency-1024x1536.png 1024w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/unit_frequency.png 1200w\" sizes=\"auto, (max-width: 683px) 100vw, 683px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Then there are the prefixes, which I&#8217;ve kept in their power order.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"819\" height=\"1024\" src=\"https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/prefix_frequency-819x1024.png\" alt=\"\" class=\"wp-image-244\" style=\"width:377px;height:auto\" srcset=\"https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/prefix_frequency-819x1024.png 819w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/prefix_frequency-240x300.png 240w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/prefix_frequency-768x960.png 768w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/prefix_frequency.png 1200w\" sizes=\"auto, (max-width: 819px) 100vw, 819px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">I was a bit surprised at how unpopular deca\/deci are. I think there is just a strong preference for powers of three in the &#8220;engineering units&#8221;.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Tonne<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s dig in to more detail for the mass units (gram and tonne). I&#8217;ve plotted equal masses on the same vertical height to compare. I was surprised that only tonne meaningfully shadows megagram. On this view it&#8217;s also quite clear how infrequently people use tonne with negative power prefixes.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"714\" src=\"https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/tonne_gram-1-1024x714.png\" alt=\"\" class=\"wp-image-240\" srcset=\"https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/tonne_gram-1-1024x714.png 1024w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/tonne_gram-1-300x209.png 300w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/tonne_gram-1-768x536.png 768w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/tonne_gram-1-1536x1072.png 1536w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/tonne_gram-1.png 1783w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Spelling<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The &#8220;-er&#8221; spelling is consistently higher than the &#8220;-re&#8221; spelling for meter\/metre and liter\/litre. The following chart shows the ratio of the spellings for different prefixes.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/spelling-683x1024.png\" alt=\"\" class=\"wp-image-242\" style=\"width:417px;height:auto\" srcset=\"https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/spelling-683x1024.png 683w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/spelling-200x300.png 200w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/spelling-768x1152.png 768w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/spelling-1024x1536.png 1024w, https:\/\/sandrock.co.za\/carl\/wp-content\/uploads\/sites\/2\/2025\/08\/spelling.png 1200w\" sizes=\"auto, (max-width: 683px) 100vw, 683px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Coding information<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The basics of the search code are pretty simple:<\/p>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro\" data-code-block-pro-font-family=\"Code-Pro-Fira-Code\" style=\"font-size:.875rem;font-family:Code-Pro-Fira-Code,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;line-height:1.25rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span role=\"button\" tabindex=\"0\" style=\"color:#839496;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><pre class=\"code-block-pro-copy-button-pre\" aria-hidden=\"true\"><textarea class=\"code-block-pro-copy-button-textarea\" tabindex=\"-1\" aria-hidden=\"true\" readonly>def search(term):\n    response = requests.get(URL, params=BASE_PARAMS | {\"q\": term, \"exactTerms\": term, \"num\": 0})\n    time.sleep(0.5)\n\n    try:\n        return int(response.json()&#91;\"queries\"&#93;&#91;\"request\"&#93;&#91;0&#93;&#91;\"totalResults\"&#93;)\n    except Exception:\n        print(response.json())<\/textarea><\/pre><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki solarized-dark\" style=\"background-color: #002B36\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #93A1A1; font-weight: bold\">def<\/span><span style=\"color: #839496\"> <\/span><span style=\"color: #268BD2\">search<\/span><span style=\"color: #839496\">(term):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #839496\">    response <\/span><span style=\"color: #859900\">=<\/span><span style=\"color: #839496\"> requests.get(<\/span><span style=\"color: #CB4B16\">URL<\/span><span style=\"color: #839496\">, params<\/span><span style=\"color: #859900\">=<\/span><span style=\"color: #CB4B16\">BASE_PARAMS<\/span><span style=\"color: #839496\"> <\/span><span style=\"color: #859900\">|<\/span><span style=\"color: #839496\"> {<\/span><span style=\"color: #2AA198\">&quot;q&quot;<\/span><span style=\"color: #839496\">: term, <\/span><span style=\"color: #2AA198\">&quot;exactTerms&quot;<\/span><span style=\"color: #839496\">: term, <\/span><span style=\"color: #2AA198\">&quot;num&quot;<\/span><span style=\"color: #839496\">: <\/span><span style=\"color: #D33682\">0<\/span><span style=\"color: #839496\">})<\/span><\/span>\n<span class=\"line\"><span style=\"color: #839496\">    time.sleep(<\/span><span style=\"color: #D33682\">0.5<\/span><span style=\"color: #839496\">)<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #839496\">    <\/span><span style=\"color: #859900\">try<\/span><span style=\"color: #839496\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #839496\">        <\/span><span style=\"color: #859900\">return<\/span><span style=\"color: #839496\"> <\/span><span style=\"color: #859900\">int<\/span><span style=\"color: #839496\">(response.json()&#91;<\/span><span style=\"color: #2AA198\">&quot;queries&quot;<\/span><span style=\"color: #839496\">&#93;&#91;<\/span><span style=\"color: #2AA198\">&quot;request&quot;<\/span><span style=\"color: #839496\">&#93;&#91;<\/span><span style=\"color: #D33682\">0<\/span><span style=\"color: #839496\">&#93;&#91;<\/span><span style=\"color: #2AA198\">&quot;totalResults&quot;<\/span><span style=\"color: #839496\">&#93;)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #839496\">    <\/span><span style=\"color: #859900\">except<\/span><span style=\"color: #839496\"> <\/span><span style=\"color: #CB4B16\">Exception<\/span><span style=\"color: #839496\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #839496\">        <\/span><span style=\"color: #268BD2\">print<\/span><span style=\"color: #839496\">(response.json())<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Then a loop like<\/p>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro\" data-code-block-pro-font-family=\"Code-Pro-Fira-Code\" style=\"font-size:.875rem;font-family:Code-Pro-Fira-Code,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;line-height:1.25rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span role=\"button\" tabindex=\"0\" style=\"color:#839496;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><pre class=\"code-block-pro-copy-button-pre\" aria-hidden=\"true\"><textarea class=\"code-block-pro-copy-button-textarea\" tabindex=\"-1\" aria-hidden=\"true\" readonly>for prefix, unit in product(prefixes, units):\n    searchterm = f\"{prefix}{unit}\"\n    \n    if searchterm not in db:\n        db&#91;searchterm&#93; = search(searchterm)<\/textarea><\/pre><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki solarized-dark\" style=\"background-color: #002B36\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #859900\">for<\/span><span style=\"color: #839496\"> prefix, unit <\/span><span style=\"color: #859900\">in<\/span><span style=\"color: #839496\"> product(prefixes, units):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #839496\">    searchterm <\/span><span style=\"color: #859900\">=<\/span><span style=\"color: #839496\"> <\/span><span style=\"color: #93A1A1; font-weight: bold\">f<\/span><span style=\"color: #2AA198\">&quot;<\/span><span style=\"color: #CB4B16\">{<\/span><span style=\"color: #839496\">prefix<\/span><span style=\"color: #CB4B16\">}{<\/span><span style=\"color: #839496\">unit<\/span><span style=\"color: #CB4B16\">}<\/span><span style=\"color: #2AA198\">&quot;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #839496\">    <\/span><\/span>\n<span class=\"line\"><span style=\"color: #839496\">    <\/span><span style=\"color: #859900\">if<\/span><span style=\"color: #839496\"> searchterm <\/span><span style=\"color: #859900\">not<\/span><span style=\"color: #839496\"> <\/span><span style=\"color: #859900\">in<\/span><span style=\"color: #839496\"> db:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #839496\">        db&#91;searchterm&#93; <\/span><span style=\"color: #859900\">=<\/span><span style=\"color: #839496\"> search(searchterm)<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Some details have been omitted from this code for brevity: <code>db<\/code> is a <a href=\"https:\/\/docs.python.org\/3\/library\/shelve.html\">shelve<\/a> database. I&#8217;m  using <a href=\"http:\/\/requests.readthedocs.io\">requests<\/a> for the API access and <code>BASE_PARAMS<\/code> contains the details for my <a href=\"https:\/\/developers.google.com\/custom-search\/v1\/overview\">Google Custom Search API<\/a> engine, which means that I had to pay $2 of my own money to get the answers I was craving.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I am huge a fan of the SI system, but I&#8217;ve often noticed that even my academic colleagues take a mix-and-match aproach to the BIPM standards. It is common for chemists to use \u00c5ngstrom over nanometre, and I don&#8217;t think I&#8217;ve ever seen anyone use megagram over tonne. Perhaps people are so used to mg [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_hide_featured_image":false,"_jetpack_featured_image_duplicate_dismissed":0,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[1],"tags":[],"class_list":["post-216","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/posts\/216","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/comments?post=216"}],"version-history":[{"count":5,"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/posts\/216\/revisions"}],"predecessor-version":[{"id":245,"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/posts\/216\/revisions\/245"}],"wp:attachment":[{"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/media?parent=216"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/categories?post=216"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/tags?post=216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}