<?xml version="1.0" encoding="UTF-8"?><rss xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:atom="http://www.w3.org/2005/Atom" version="2.0" xmlns:itunes="http://www.itunes.com/dtds/podcast-1.0.dtd" xmlns:googleplay="http://www.google.com/schemas/play-podcasts/1.0"><channel><title><![CDATA[Plot Arithmetic]]></title><description><![CDATA[Welcome to my publication]]></description><link>https://plotarithmetic.substack.com</link><image><url>https://substackcdn.com/image/fetch/$s_!Wwws!,w_256,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fplotarithmetic.substack.com%2Fimg%2Fsubstack.png</url><title>Plot Arithmetic</title><link>https://plotarithmetic.substack.com</link></image><generator>Substack</generator><lastBuildDate>Tue, 18 Aug 2026 18:42:01 GMT</lastBuildDate><atom:link href="https://plotarithmetic.substack.com/feed" rel="self" type="application/rss+xml"/><copyright><![CDATA[Plot Arithmetic]]></copyright><language><![CDATA[en]]></language><webMaster><![CDATA[plotarithmetic@substack.com]]></webMaster><itunes:owner><itunes:email><![CDATA[plotarithmetic@substack.com]]></itunes:email><itunes:name><![CDATA[Plot Arithmetic]]></itunes:name></itunes:owner><itunes:author><![CDATA[Plot Arithmetic]]></itunes:author><googleplay:owner><![CDATA[plotarithmetic@substack.com]]></googleplay:owner><googleplay:email><![CDATA[plotarithmetic@substack.com]]></googleplay:email><googleplay:author><![CDATA[Plot Arithmetic]]></googleplay:author><itunes:block><![CDATA[Yes]]></itunes:block><item><title><![CDATA[Can a 500 m² backyard grow a year's worth of calories for one person?]]></title><description><![CDATA[A calorie-and-land model using extension yield data, with the assumptions left open to inspection.]]></description><link>https://plotarithmetic.substack.com/p/can-a-500-m-backyard-grow-a-years</link><guid isPermaLink="false">https://plotarithmetic.substack.com/p/can-a-500-m-backyard-grow-a-years</guid><dc:creator><![CDATA[Plot Arithmetic]]></dc:creator><pubDate>Tue, 18 Aug 2026 04:08:17 GMT</pubDate><content:encoded><![CDATA[<p>500 square metres sounds like a lot of garden.</p><p>So I wanted to reduce the question to something measurable: not whether that much land can grow &#8220;a lot of food,&#8221; but whether it can grow enough <strong>calories</strong> for one person for one year.</p><p>Using 2,000 kcal/day as a reference gives:</p><p><strong>730,000 kcal/year.</strong></p><p>That isn&#8217;t a dietary recommendation. It&#8217;s just a convenient number to test against.</p><p>And to make the test relatively easy for the garden, I didn&#8217;t model a normal backyard full of lettuce, tomatoes and herbs.</p><p>I gave most of the growing area to two calorie-dense staples:</p><ul><li><p><strong>70% potatoes</strong></p></li><li><p><strong>30% dry beans</strong></p></li></ul><p>This is not supposed to be a sensible diet. It is deliberately biased toward making the smallest possible amount of land look good.</p><p>If that version struggles, adding lower-calorie vegetables isn&#8217;t going to rescue the calorie arithmetic.</p><h2>Start with the yields</h2><p><a href="https://extension.usu.edu/smallfarms/research/expected-vegetable-yields-in-utah">Utah State University</a> Extension gives an average potato yield of about <strong>20,000 lb/acre</strong>.</p><p>For dry beans, its <a href="https://extension.usu.edu/yardandgarden/research/beans-in-the-garden">home-garden guidance</a> gives roughly <strong>20&#8211;25 lb of dry seed per 100 ft of row</strong>.</p><p>Using 22.5 lb and two-foot row spacing gives approximately:</p><ul><li><p><strong>Potatoes:</strong> 2.24 kg/m&#178;</p></li><li><p><strong>Dry beans:</strong> 0.55 kg/m&#178;</p></li></ul><p>For food energy I used fixed USDA FoodData Central records:</p><ul><li><p><strong><a href="https://fdc.nal.usda.gov/food-details/170027/nutrients">Whole raw russet potatoes</a>:</strong> 79 kcal/100 g</p></li><li><p><strong><a href="https://fdc.nal.usda.gov/food-details/175199/nutrients">Dry mature pinto beans</a>:</strong> 347 kcal/100 g</p></li></ul><p>That works out to roughly:</p><p><strong>Potatoes: 1,771 kcal/m&#178;</strong></p><p><strong>Dry beans: 1,906 kcal/m&#178;</strong></p><p>With 70% of the growing area in potatoes and 30% in beans:</p><p><strong>~1,811 kcal per cultivated m&#178; before losses.</strong></p><p>I then apply a 10% post-harvest-loss assumption.</p><p>That&#8217;s an assumption, not a universal agricultural constant. I left it explicit in the model so it can be changed.</p><p>After that haircut:</p><p><strong>~1,630 kcal/m&#178;/year.</strong></p><p>Divide 730,000 by that and the first answer is:</p><p><strong>~448 m&#178;.</strong></p><p>At first glance, a 500 m&#178; backyard seems to pass.</p><p>It doesn&#8217;t.</p><h2>500 m&#178; of backyard is not 500 m&#178; of crops</h2><p>The 448 m&#178; figure is <strong>cultivated soil</strong>.</p><p>A real growing area also needs some combination of paths, access, compost, working space, irrigation equipment, storage, shaded edges and other non-producing area.</p><p>There is no universal percentage, so instead of pretending there is one, I tested several.</p><p>If productive beds occupy:</p><ul><li><p><strong>80% of the site:</strong> 448 m&#178; cultivated requires about <strong>560 m&#178; total</strong></p></li><li><p><strong>60%:</strong> about <strong>746 m&#178; total</strong></p></li><li><p><strong>40%:</strong> about <strong>1,119 m&#178; total</strong></p></li></ul><p>I&#8217;ll use 60% as the middle scenario below.</p><p>That isn&#8217;t supposed to describe a &#8220;typical&#8221; backyard. It&#8217;s simply one visible assumption that can be changed.</p><p>A <strong>500 m&#178; total backyard</strong> at 60% cultivation gives:</p><p><strong>300 m&#178; of crops.</strong></p><p>At the average-yield assumptions:</p><p><strong>300 &#215; 1,630 &#8776; 489,000 kcal/year.</strong></p><p>That&#8217;s about:</p><h2><strong>67% of one person&#8217;s annual reference calories.</strong></h2><p>Not 67% of a family&#8217;s calories.</p><p>Not nutritional self-sufficiency.</p><p>Just 67% of the 730,000-calorie target for one person.</p><p>And remember what was planted to get there:</p><p><strong>70% potatoes and 30% dry beans.</strong></p><p>The calculation is already trying quite hard to win.</p><h2>Then the harvest gets worse</h2><p>The average yield is doing a lot of work.</p><p>Weather, soil, pests, water, cultivar and growing skill all move crop yields around.</p><p>Utah State also publishes planning values 25% and 50% below its average yields, so I ran those without changing anything else.</p><p>For the same 500 m&#178; property:</p><ul><li><p><strong>Extension-average yield:</strong> about <strong>67%</strong> of the annual calorie target</p></li><li><p><strong>25% below average:</strong> about <strong>50%</strong></p></li><li><p><strong>50% below average:</strong> about <strong>33.5%</strong></p></li></ul><p>If instead we ask how much total garden footprint is required to reach the full 730,000 calories:</p><ul><li><p><strong>Extension average:</strong> about <strong>746 m&#178;</strong></p></li><li><p><strong>25% below average:</strong> about <strong>995 m&#178;</strong></p></li><li><p><strong>50% below average:</strong> about <strong>1,493 m&#178;</strong></p></li></ul><p>For four adult-equivalents, those figures become approximately:</p><ul><li><p><strong>2,985 m&#178;</strong></p></li><li><p><strong>3,980 m&#178;</strong></p></li><li><p><strong>5,970 m&#178;</strong></p></li></ul><p>That&#8217;s where the word <em>backyard</em> starts becoming misleading.</p><p>We&#8217;re getting closer to a small agricultural system.</p><h2>But the bean number may actually be too generous</h2><p>There is another wrinkle.</p><p>The Utah State home-garden bean figure, when converted using the row spacing above, implies almost <strong>4,900 lb/acre</strong> of dry beans.</p><p>That&#8217;s aggressive.</p><p><a href="https://extension.umn.edu/nutrient-management/dried-edible-bean-fertilizer-guidelines">University of Minnesota dry-bean guidance</a> uses yield-goal bands extending through roughly <strong>2,900+ lb/acre</strong>.</p><p>They aren&#8217;t directly equivalent production systems, so I don&#8217;t think it makes sense to quietly replace one number with the other and pretend the result has become more scientific.</p><p>But it tells us something useful:</p><p><strong>The main result isn&#8217;t being created by choosing a pessimistic bean yield.</strong></p><p>Quite the opposite.</p><p>If I substitute 2,900 lb/acre while leaving everything else alone, the middle land requirement moves from roughly:</p><p><strong>746 m&#178; &#8594; 857 m&#178; per person.</strong></p><p>So the 746 m&#178; result is better thought of as a fairly favorable test than an alarmist one.</p><div><hr></div><h2>Check the model</h2><p>If you want to inspect the assumptions or replace them with your own local yields and available area, the spreadsheet is here:</p><div class="file-embed-wrapper" data-component-name="FileToDOM"><div class="file-embed-container-reader"><div class="file-embed-container-top"><image class="file-embed-thumbnail-default" src="https://substackcdn.com/image/fetch/$s_!0Cy0!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack.com%2Fimg%2Fattachment_icon.svg"></image><div class="file-embed-details"><div class="file-embed-details-h1">Backyard Food Evidence Model V3</div><div class="file-embed-details-h2">40.7KB &#8729; XLSX file</div></div><a class="file-embed-button wide" href="https://plotarithmetic.substack.com/api/v1/file/a5cfe83d-2fc6-46e4-b019-1b8da311bfba.xlsx"><span class="file-embed-button-text">Download</span></a></div><a class="file-embed-button narrow" href="https://plotarithmetic.substack.com/api/v1/file/a5cfe83d-2fc6-46e4-b019-1b8da311bfba.xlsx"><span class="file-embed-button-text">Download</span></a></div></div><p></p><p>If you&#8217;re more interested in the practical side - how to turn a backyard into a productive system rather than just model the calories - <strong><a href="https://independentbackyard.com/my-book/#aff=aboel3z">The Self-Sufficient Backyard</a></strong> goes much further into that problem.</p><div><hr></div><h2>Land isn&#8217;t the only constraint</h2><p>Once I had the calorie calculation, I started looking at the other inputs.</p><p>Water is an obvious one.</p><p><a href="https://extension.umn.edu/gardening-minnesota/watering-vegetable-garden">University of Minnesota Extension</a> uses roughly <strong>one inch of water per week from rainfall plus irrigation</strong> as a useful vegetable-garden benchmark.</p><p>One inch over one square metre is about 25.4 litres.</p><p>Our hypothetical 500 m&#178; property has 300 m&#178; under cultivation in the middle scenario.</p><p>If there were a 16-week period where rainfall supplied none of that requirement and irrigation had to replace the whole inch:</p><p><strong>300 &#215; 25.4 &#215; 16 &#8776; 122,000 litres</strong></p><p>That&#8217;s deliberately an upper bound.</p><p>It is <strong>not</strong> a prediction that a 300 m&#178; garden normally consumes 122,000 litres of irrigation water.</p><p>But it exposes something that isn&#8217;t obvious when looking only at crop yield.</p><p>You can reduce one dependency by creating another.</p><p>Growing more food locally can mean less dependence on purchased food while making these things more important:</p><ul><li><p>water</p></li><li><p>irrigation</p></li><li><p>soil fertility</p></li><li><p>seed</p></li><li><p>tools</p></li><li><p>pest control</p></li><li><p>preservation</p></li><li><p>storage</p></li><li><p>time</p></li></ul><p>So there are at least two different ideas hiding inside the word <em>self-sufficient</em>.</p><p>One is:</p><blockquote><p>I produce a useful amount of what I consume.</p></blockquote><p>The other is:</p><blockquote><p>I can keep producing it when the systems around me stop supplying inputs.</p></blockquote><p>Those are different engineering problems.</p><h2>I also found a data trap</h2><p>I originally included corn and winter squash in the main calorie model.</p><p>Then I noticed a problem.</p><p>Agricultural yield tables and nutrition databases don&#8217;t necessarily describe the same mass.</p><p>A yield figure for corn may describe harvested ears.</p><p>A food-composition value may describe edible kernels.</p><p>Multiplying one directly by the other quietly assumes the cob, husk and discarded material have the same calorie density as the part being eaten.</p><p>They don&#8217;t.</p><p>Squash can have a similar issue between harvested fruit and edible flesh.</p><p>So I removed both from the headline calculation.</p><p>The main result now stays with:</p><p><strong>potato tuber yield &#8594; whole raw potato nutrition</strong></p><p>and:</p><p><strong>dry bean seed yield &#8594; dry mature bean nutrition</strong></p><p>It&#8217;s less varied, but the arithmetic is cleaner.</p><p>I&#8217;d rather discard a useful-looking number than keep one I can&#8217;t explain.</p><h2>What about getting more than one crop from the same land?</h2><p>Fair objection.</p><p>A square metre doesn&#8217;t necessarily produce only one crop in a year.</p><p>A longer growing season, succession planting, protected growing or different varieties can raise annual output.</p><p>So I also ran a deliberately favorable case:</p><ul><li><p>extension-average yields</p></li><li><p>only 5% post-harvest loss</p></li><li><p>25% more effective annual land use through succession</p></li><li><p>80% of the total site under cultivation</p></li></ul><p>Under that combination, the requirement falls to roughly:</p><p><strong>424 m&#178; of total plot per adult-equivalent.</strong></p><p>That&#8217;s dramatically better than the middle case.</p><p>It&#8217;s also still around:</p><p><strong>1,700 m&#178; for four adult-equivalents</strong></p><p>before asking whether the food being produced forms a complete diet.</p><p>Better technique matters.</p><p>It just doesn&#8217;t make the land constraint disappear.</p><h2>Calories are the easy part</h2><p>There is a more fundamental problem with everything above.</p><p>People don&#8217;t eat calories. They eat food.</p><p>The potato-and-bean model says nothing about whether the resulting diet supplies appropriate:</p><ul><li><p>fats</p></li><li><p>amino acids</p></li><li><p>vitamins</p></li><li><p>minerals</p></li><li><p>variety</p></li><li><p>palatability</p></li></ul><p>Nor does it model crop rotation or all the inputs required to maintain production over time.</p><p>That&#8217;s intentional.</p><p>I wanted to answer the easiest version of the question first.</p><p>Give the land calorie-dense crops.</p><p>Ignore dietary variety.</p><p>Ignore many secondary constraints.</p><p>Use relatively favorable yields.</p><p>Then ask whether the land works.</p><p>If the easy version already needs hundreds of square metres per person, adding the rest of the food system is unlikely to make the required infrastructure smaller.</p><h2>A 500 m&#178; backyard is still useful</h2><p>None of this means a 500 m&#178; property is too small to matter.</p><p>Quite the opposite.</p><p>Under the middle assumptions, 300 m&#178; of cultivated ground produces the equivalent of roughly:</p><p><strong>489,000 calories.</strong></p><p>That&#8217;s substantial.</p><p>And calorie replacement isn&#8217;t necessarily the best way to value a garden anyway.</p><p>A smaller amount of land devoted to expensive or highly perishable foods may have more household value than trying to replace cheap commodity calories.</p><p>Herbs, berries, tomatoes and greens may be poor choices if the objective is:</p><p><code>kcal/m&#178;</code></p><p>while being excellent choices if the objective is:</p><p><code>quality / freshness / price / availability / enjoyment</code></p><p>The spreadsheet is answering one question.</p><p>It isn&#8217;t declaring the correct way to garden.</p><h2>So can 500 m&#178; grow a year&#8217;s worth of calories?</h2><p>Under the middle assumptions here:</p><h2><strong>No.</strong></h2><p>A 500 m&#178; total plot with 60% of its area cultivated reaches about:</p><p><strong>67% of one 2,000-kcal adult-equivalent year.</strong></p><p>With a harvest 25% below the extension average:</p><p><strong>~50%.</strong></p><p>At 50% below average:</p><p><strong>~33.5%.</strong></p><p>The model requires approximately:</p><p><strong>746 m&#178;</strong></p><p>of gross garden footprint to hit the calorie target in the extension-average case.</p><p>And there is reason to consider even that favorable: the dry-bean yield used in the main calculation is aggressive.</p><p>Using the lower bean-yield cross-check moves the result toward:</p><p><strong>857 m&#178;.</strong></p><p>The exact boundary isn&#8217;t what I find interesting.</p><p>The distinction is.</p><p>A backyard can make a household <strong>meaningfully less dependent</strong> on the larger food system without making it <strong>independent</strong> of that system.</p><p>Those are not the same achievement.</p><p>Once water, storage, seed, fertility, labor and nutritional completeness are added, self-sufficiency stops looking like a gardening slogan.</p><p>It starts looking like infrastructure.</p><div><hr></div><h3>If you&#8217;re actually planning one</h3><p>The spreadsheet above is the useful part if you want to replace my assumptions with your own area and local yields.</p><p>For the practical side rather than the calorie model, <strong><a href="https://independentbackyard.com/my-book/#aff=aboel3z">The Self-Sufficient Backyard</a></strong> goes much further into actually organizing a productive backyard system.</p>]]></content:encoded></item></channel></rss>