{"id":45413,"date":"2021-08-16T10:00:00","date_gmt":"2021-08-16T14:00:00","guid":{"rendered":"https:\/\/www.shortform.com\/blog\/?p=45413"},"modified":"2021-08-16T11:58:03","modified_gmt":"2021-08-16T15:58:03","slug":"fermi-estimation","status":"publish","type":"post","link":"https:\/\/www.shortform.com\/blog\/fermi-estimation\/","title":{"rendered":"How to Solve a Fermi Estimation Problem"},"content":{"rendered":"\n

What’s a Fermi estimation problem? What kinds of information does the Fermi problem probe for? <\/p>\n\n\n\n

A Fermi problem is a problem that involves making a justified estimation about quantities, degrees, probabilities, or variances. Fermi problems are solved by breaking down seemingly impossible questions into smaller and smaller questions. The idea is that eventually, you\u2019ll be able to separate questions that are truly unknown from questions for which you can at least make an educated guess.<\/p>\n\n\n\n

Below is an example of a Fermi problem.<\/p>\n\n\n\n\n\n\n\n

Example Fermi Problem<\/strong><\/h2>\n\n\n\n

It\u2019s much easier to understand the Fermi estimation technique with an example, such as \u201cHow many oil changes are performed in one day in the U.S.A.?\u201d<\/strong> Unless you happen to work at Jiffy Lube, you probably have no idea how to even begin to answer this question. At best, you might take a wild guess. But Fermi\u2019s approach is more methodical.<\/p>\n\n\n\n

To answer this question, we need to determine what information we\u2019re missing. What would we need to know to figure this out? The number of oil changes probably depends on the number of cars in the country and how often those cars need an oil change. So, to figure out how many oil changes happen in a given day, we need to know:<\/p>\n\n\n\n

  1. The number of cars in the U.S.<\/li>
  2. How frequently cars need an oil change<\/li><\/ol>\n\n\n\n

    If we happened to know the answers to either of those questions, great! But if we don\u2019t, we can break them down even further into questions that we can<\/em> answer<\/a>. Let\u2019s do that now.<\/p>\n\n\n\n

    To figure out the number of cars in the U.S., we need to know:<\/p>\n\n\n\n

    1. The population of the U.S.<\/li>
    2. The percent of the population that owns a car<\/li><\/ol>\n\n\n\n

      To figure out how frequently cars need an oil change, we need to know:<\/p>\n\n\n\n

      1. How many miles cars can go between oil changes<\/li>
      2. How many miles the average car is driven in a year<\/li><\/ol>\n\n\n\n

        We may still need to wildly guess the answers to some <\/em>of these questions. However, because those wild guesses are only for smaller parts of the overall question, we\u2019re still likely to be more accurate than if we\u2019d just thrown out an answer to the original question.<\/p>\n\n\n\n

        Solving the Problem<\/h3>\n\n\n\n

        To solve this problem, we\u2019ll need to come up with some estimates for each of those questions. (Shortform note: Fermi questions are commonly used in job interviews. To get the most out of this exercise, assume you\u2019re in the middle of an interview and can\u2019t look up the real answers, so you\u2019ll need to rely on your best guess.)<\/p>\n\n\n\n

        1. First, we need to know the population of the U.S. You might have a rough idea of this answer\u2014it\u2019s about 320 million people<\/strong>. <\/li>
        2. Next, we need to know how many of those people own a car. This question isn\u2019t as clear cut, so we can break it down further. Let\u2019s assume that roughly 75% of the population can drive, which gives us 240 million drivers<\/strong>. 
          1. However, not everyone who can drive owns their own car. Let\u2019s assume there\u2019s an average of two drivers in a household, and one car per household. That\u2019s 120 million cars<\/strong>. <\/li><\/ol><\/li>
          2. If you have a car, you might remember that you\u2019re supposed to change the oil after about 3,000 miles of driving. However, people are busy, and oil changes might not always be a priority. Let\u2019s assume that the average car owner gets their oil changed after about 3,500 miles<\/strong> of driving. <\/li>
          3. Now, we need to know how many miles the average car is driven in a year. This is a tough one, so let\u2019s take a wild guess of 10,000 miles per car, per year<\/strong>. <\/li><\/ol>\n\n\n\n

            If each car owner gets an oil change after 3,500 miles of driving and drives 10,000 miles per year, they get about three oil changes per year. (Shortform note: In Fermi estimation, there\u2019s no need to stress over the exact math. Feel free to round numbers up or down to make the math easier since the end goal is a very rough guess, not an exact answer.) <\/p>\n\n\n\n

            Three oil changes per year for 120 million cars is 360 million oil changes per year, total.<\/strong> However, the question asked about the number of oil changes in one day<\/em>, not one year, so we need to divide this further. We know there are 365 days in a year, but most auto shops aren\u2019t open seven days a week, so let\u2019s bring that down to 320 days per year in which oil changes are being performed. To get our final answer, we divide 360 oil changes per year into 320 days, which equals about 1.1 million oil changes per day in the U.S.<\/strong><\/p>\n\n\n\n

            What\u2019s the real answer? Industry data shows that about 450 million oil changes happen per year in the United States<\/a>. If we keep our estimate of 320 working days per year for oil changes, that\u2019s 1.4 million oil changes per day, which is incredibly close to our rough estimate!<\/p>\n\n\n\n

            Tips for Improving Fermi Estimations<\/strong>

            Fermi problems are often used during job interviews to evaluate a candidate\u2019s critical thinking skills. For instance, Google often asks interviewees subject-specific Fermi questions<\/a>, such as \u201cHow many photos are taken on Android phones per day?\u201d If you want to practice this technique, here are some tips to improve your estimation skills:

            Memorize basic facts<\/strong><\/a>,<\/strong> such as the population of the world, the speed of light, or the average number of people per household. 
            Memorize basic unit conversions<\/strong>, like the number of feet in a mile (5,280) or pints in a gallon (eight). 
            When you finish a problem,             use common sense to double-check your answer<\/strong><\/a>. For example, if you go through all the steps of answering, \u201cHow many golf balls would it take to fill a football stadium?\u201d and your answer is \u201c350,\u201d you may need to go back and check some of your estimates. <\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"

            What’s a Fermi estimation problem? What kinds of information does the Fermi problem probe for? A Fermi problem is a problem that involves making a justified estimation about quantities, degrees, probabilities, or variances. Fermi problems are solved by breaking down seemingly impossible questions into smaller and smaller questions. The idea is that eventually, you\u2019ll be able to separate questions that are truly unknown from questions for which you can at least make an educated guess. Below is an example of a Fermi problem.<\/p>\n","protected":false},"author":7,"featured_media":45414,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[160,25],"tags":[203],"class_list":["post-45413","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-science","category-statistics","tag-superforecasting","","tg-column-two"],"yoast_head":"\nHow to Solve a Fermi Estimation Problem - Shortform Books<\/title>\n<meta name=\"description\" content=\"A Fermi problem is a problem that involves making a justified estimation about quantities, degrees, or variances. 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