{"id":42500,"date":"2025-02-01T07:56:52","date_gmt":"2025-02-01T06:56:52","guid":{"rendered":"https:\/\/www.schwiizerfranke.com\/?p=42500"},"modified":"2026-10-29T12:05:04","modified_gmt":"2026-10-29T11:05:04","slug":"dreisatz-rechner","status":"publish","type":"post","link":"https:\/\/www.schwiizerfranke.com\/en\/dreisatz-rechner","title":{"rendered":"Online rule of three calculator with step-by-step solution + simple explanation"},"content":{"rendered":"<p class=\"wp-block-paragraph\">With the rule of three calculator, you can easily solve any rule of three problem online: simply enter three values and you\u2019ll see the result, along with the step-by-step calculation and the formula.<\/p>\n\n\n\n<div id=\"sf-dreisatz-tool\" style=\"min-height:980px;\"><\/div>\n<script src=\"https:\/\/tools.schwiizerfranke.com\/dreisatz-rechner\/embed.js\" defer><\/script>\n\n\n\n<p class=\"wp-block-paragraph\">The rule of three, also known as the three-term rule, is a method of calculation that allows you to determine a fourth value from three known values. You\u2019ll need it when shopping, for recipes, when calculating wages, or when working with percentages. Here, you\u2019ll find a simple explanation of the rule of three, complete with a formula, table and examples. And if you\u2019re in a hurry, the rule of three calculator above will work out any problem with three values for you and help you work out any ratio.<\/p>\n\n\n\n<div class=\"wp-block-group sf-keypoints is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"sf-keypoints__t wp-block-paragraph\">The most important facts at a glance<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Three values known, one unknown:<\/strong> That is where the name \u2018rule of three\u2019 comes from. The calculation is carried out in three steps, the three \u2018s\u00e4tze\u2019.<\/li>\n\n\n\n<li><strong>Proportional:<\/strong> The more, the more. Formula: x = b \u00f7 a \u00d7 c.<\/li>\n\n\n\n<li><strong>Inversely proportional:<\/strong> The more, the less. Formula: x = a \u00d7 b \u00f7 c.<\/li>\n\n\n\n<li><strong>Tip:<\/strong> Always work out the figure for 1 piece, 1 hour or 1 % first. Then the rest is easy.<\/li>\n\n\n\n<li><strong>Percentage:<\/strong> The rule of three is the basis of all percentage calculations. 100 % is the base value.<\/li>\n<\/ul>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Quick guide to the rule of three calculator<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Here\u2019s how to use the online rule of three calculator to work out the rule of three. Simply enter your problem as a sentence, exactly as it appears in your workbook:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Known ratio:<\/strong> For example, \u00abIf 12 apples cost CHF 3.60\u00bb. Units such as \u2018apples\u2019 or \u2018CHF\u2019 are optional, but they make the calculation easier to follow. The same applies to the euro.<\/li>\n\n\n\n<li><strong>Ratio to be calculated:<\/strong> \u00ab\u2026then there are 8 apples\u2026\u00bb. The result appears straight away, without having to click \u00abCalculate\u00bb.<\/li>\n\n\n\n<li><strong>Method of calculation:<\/strong> Choose \u2018proportional\u2019 (the more, the more) or \u2018inversely proportional\u2019 (the more, the less). More apples cost more, so it\u2019s proportional.<\/li>\n\n\n\n<li><strong>Calculation method:<\/strong> On the right, you can see the three equations as they appear in the exercise book, with the \u00f7 and \u00d7 symbols and the formula. Under \u00abGraph\u00bb, you can see the problem represented as a straight line or a curve.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">With \u00abCopy working\u00bb, you can copy the solution as text, for example for your homework. With \u00abShare with classmates\u00bb, you can send a link that opens your specific exercise. The templates \u2018Shopping\u2019, \u2018Time &amp; Work\u2019, \u2018Recipes\u2019, \u2018Percentages\u2019, \u2018Speed\u2019 and \u2018Salary\u2019 show you typical examples.<\/p>\n\n\n\n<div class=\"wp-block-group sf-tip is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>Free of charge and without an app:<\/strong> The rule of three calculator runs directly in your browser, on your mobile and on your computer. No download, no registration, no adverts in the calculator.<\/p>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\">What is a rule of three?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A rule of three is a <a href=\"https:\/\/de.wikipedia.org\/wiki\/Dreisatz\" target=\"_blank\" rel=\"noopener\">mathematical calculation<\/a>, in which you compare three known quantities to determine a fourth. The best-known application is calculating percentages.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">There are two explanations for the name. Either it comes from the fact that three values are known, or from the fact that the calculation is carried out in three steps, as we learn at school:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Known ratio:<\/strong> 12 apples cost CHF 3.60.<\/li>\n\n\n\n<li><strong>Ratio to a unit:<\/strong> 1 apple costs CHF 0.30.<\/li>\n\n\n\n<li><strong>Ratio to be calculated:<\/strong> 8 apples cost CHF 2.40.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">How is the rule of three calculated?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The rule of three is always worked out in three steps. You set the known values in proportion, reduce the result to a single unit, and then multiply by the value you are looking for.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example:<\/strong> If 12 apples cost CHF 3.60, how much do 8 apples cost?<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>12 apples cost CHF 3.60.<\/li>\n\n\n\n<li>Calculate the price per apple: CHF 3.60 \u00f7 12 = CHF 0.30.<\/li>\n\n\n\n<li>Multiply by the quantity required: CHF 0.30 \u00d7 8 = CHF 2.40.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">So 8 apples cost CHF 2.40.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Rule of three formula<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">If you summarise these three steps, you get the rule of three formula. a and b are the known ratio, c is the new value and x is the result:<\/p>\n\n\n\n<p class=\"sf-formel wp-block-paragraph\"><strong>Proportional: x = b \u00f7 a \u00d7 c<\/strong><\/p>\n\n\n\n<p class=\"sf-formel wp-block-paragraph\"><strong>Inversely proportional: x = a \u00d7 b \u00f7 c<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In this example, that means: x = 3.60 \u00f7 12 \u00d7 8 = 2.40. The calculator shows you this formula with your figures in the calculation history.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Rule of three table<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Many people learn the rule of three using a table. This allows you to see at a glance how both sides change. For the apples, it looks like this:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Step<\/th><th>Apples<\/th><th>Price<\/th><\/tr><\/thead><tbody><tr><td>1st sentence<\/td><td>12<\/td><td>CHF 3.60<\/td><\/tr><tr><td>2nd sentence (\u00f7 12)<\/td><td>1<\/td><td>CHF 0.30<\/td><\/tr><tr><td>3rd set (\u00d7 8)<\/td><td>8<\/td><td>CHF 2.40<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">In a proportional problem, you carry out the same calculation on both the left and the right. In an inversely proportional problem, you do the opposite on the right: if you divide on the left, you multiply on the right.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Cross calculation (St Andrew\u2019s Cross)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Instead of using three equations, you can also work out proportional problems using the cross-multiplication method. You write the values one below the other and multiply them in a cross-multiplication format: 3.60 \u00d7 8 = 28.80, then you divide by 12. Result: 2.40. This is the same calculation as the formula, just written differently.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The rule of three formulas and everyday examples<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In theory, the rule of three seems more dry than it actually is. It quickly becomes clear when you look at some examples.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Formula proportional rule of three<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2018Proportional\u2019 means that the first value is in the same ratio to the second as the third is to the fourth. In mathematics, this is referred to as a proportional relationship. If one value doubles, the other also doubles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example:<\/strong> 3 kg of potatoes cost CHF 5. How much do 2 kg cost?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3 kg = CHF 5<\/li>\n\n\n\n<li>1 kg = CHF 5 \u00f7 3 = CHF 1.67<\/li>\n\n\n\n<li>2 kg = CHF 5 \u00f7 3 \u00d7 2 = <strong>CHF 3.33<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">When working on problems like these, carry on calculating using the unrounded intermediate value wherever possible, otherwise a rounding error will occur. The calculator does this automatically.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Formula antiproportional rule of three<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Inverse proportionality is the opposite: the more of one, the less of the other. If one value doubles, the other is halved.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example:<\/strong> Travelling at 50 km\/h, you\u2019ll reach your destination in 4 hours. How long will it take you at 100 km\/h?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>50 km\/h = 4 hours<\/li>\n\n\n\n<li>1 km\/h = 4 \u00d7 50 = 200 hours<\/li>\n\n\n\n<li>100 km\/h = 200 \u00f7 100 = <strong>2 hours<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">A second example: 3 painters take 12 days to paint a house. 4 painters take 3 \u00d7 12 \u00f7 4 = 9 days.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Example: Calculating a salary using the rule of three<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Working 42 hours a week, you earn CHF 1,260 a week, and you\u2019re reducing your hours to 35. Calculated proportionally: CHF 1,260 \u00f7 42 \u00d7 35 = <strong>CHF 1,050<\/strong>. That\u2019s CHF 30 per hour. You can see how much you\u2019ll take home in the <a href=\"https:\/\/www.schwiizerfranke.com\/en\/brutto-netto-rechner-schweiz\/\">Gross-net calculator<\/a>, your hourly wage of <a href=\"https:\/\/www.schwiizerfranke.com\/en\/stundenlohn-berechnen-schweiz\/\">Hourly Wage Calculator<\/a>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Example: Converting a recipe<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A recipe for 4 people requires 500 g of flour. For 6 people, you calculate 500 \u00f7 4 \u00d7 6 = <strong>750 g<\/strong>. This applies to all ingredients in the same proportions.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">When do you need the rule of three?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">You always need to use the rule of three when two quantities are in a fixed ratio and you want to convert one of the values. Typical examples:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Shopping:<\/strong> How much do 350 g of strawberries cost if you know the price per kilo?<\/li>\n\n\n\n<li><strong>Work and time:<\/strong> How much longer does it take for more people to do the same job?<\/li>\n\n\n\n<li><strong>Wages:<\/strong> How much do you earn if you work more or fewer hours?<\/li>\n\n\n\n<li><strong>Travel:<\/strong> How much petrol do you need for a longer journey? There\u2019s also the <a href=\"https:\/\/www.schwiizerfranke.com\/en\/benzinkosten-berechnen-schweiz\/\">Petrol cost calculator<\/a>.<\/li>\n\n\n\n<li><strong>Percentages:<\/strong> Discount, VAT or interest.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Important: The rule of three is only accurate if the ratio is truly fixed. If there is a volume discount or fixed costs such as a standing charge, it will give an incorrect result.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Rule of three in percentage calculation<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The rule of three is particularly useful for calculating percentages. First, you work out 1 % and then multiply by the percentage you are looking for. 100 % is always the base value.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example:<\/strong> A television costs CHF 800 and has been reduced by 30 %. How much does it cost now?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>100 % = CHF 800<\/li>\n\n\n\n<li>1 % = CHF 800 \u00f7 100 = CHF 8<\/li>\n\n\n\n<li>70 % = CHF 8 \u00d7 70 = <strong>CHF 560<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Using the rule of three, you can work out all three figures in a percentage calculation:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Wanted<\/th><th>Example<\/th><th>Result<\/th><\/tr><\/thead><tbody><tr><td>Percentage<\/td><td>30 % at CHF 800<\/td><td>\u00a3240<\/td><\/tr><tr><td>Percentage<\/td><td>CHF 240 out of CHF 800<\/td><td>30 %<\/td><\/tr><tr><td>Base value (reverse)<\/td><td>70 % cost CHF 560<\/td><td>CHF 800<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">In the rule of three calculator for percentages, select the \u00abPercentages\u00bb template. For pure percentage problems, the <a href=\"https:\/\/www.schwiizerfranke.com\/en\/prozentrechner\/\">Percentage calculator<\/a> even faster, for the VAT on the <a href=\"https:\/\/www.schwiizerfranke.com\/en\/mwst-rechner-schweiz\/\">VAT calculator<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Double rule of three<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In a double or compound rule of three, two quantities change at the same time. You simply work it out as two rules of three in succession.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example:<\/strong> 3 machines produce 120 parts in 4 hours. How many parts can 5 machines produce in 6 hours?<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Calculate for 1 machine and 1 hour: 120 \u00f7 3 \u00f7 4 = 10 parts.<\/li>\n\n\n\n<li>Extrapolate to 5 machines and 6 hours: 10 \u00d7 5 \u00d7 6 = <strong>300 pieces<\/strong>.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">In the rule of three calculator, you first enter the number of machines (3 machines = 120 parts, then 5 machines = 200 parts) and use the result to work out the hours (4 hours = 200 parts, then 6 hours = 300 parts).<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The Rule of Three in Excel<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">If a, b and c are in cells A2, B2 and C2, the Excel formula for the proportional rule is <code>=B2\/A2*C2<\/code>. For the inverse-proportional rule of three, you write <code>=A2*B2\/C2<\/code>. This way, you can convert entire lists in one go.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">You can find more calculators for everyday life and personal finances in the <a href=\"https:\/\/www.schwiizerfranke.com\/en\/rechner\/\">Computer Overview<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">FAQ<\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list\">\n<div id=\"faq-question-ds-1\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question\">How do you use the rule of three?<\/h3>\n<div class=\"rank-math-answer\">\n\n<p>Solving a rule problem involves three steps: write down the known ratio, convert it to a single unit, and multiply by the value you are looking for. Example: 12 apples cost CHF 3.60, 1 apple costs CHF 0.30, 8 apples cost CHF 2.40.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-ds-2\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question\">What is the rule of three?<\/h3>\n<div class=\"rank-math-answer\">\n\n<p>Proportional: x = b \u00f7 a \u00d7 c. Inversely proportional: x = a \u00d7 b \u00f7 c. Here, a and b are the known values and c is the new value.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-ds-3\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question\">How can I tell whether it is proportional or inversely proportional?<\/h3>\n<div class=\"rank-math-answer\">\n\n<p>Ask yourself: Does one value increase when the other increases? If so, they are proportional (the more of one, the more of the other). If it decreases, they are inversely proportional (the more of one, the less of the other); for example, more workers, fewer days.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-ds-4\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question\">How do you calculate percentages using the rule of three?<\/h3>\n<div class=\"rank-math-answer\">\n\n<p>100 % is the base value. First work out 1 % by dividing by 100, then multiply by the percentage you\u2019re looking for. 30 % of CHF 800 is CHF 8 \u00d7 30 = CHF 240.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-ds-5\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question\">What is a double rule of three?<\/h3>\n<div class=\"rank-math-answer\">\n\n<p>In the double rule of three, two quantities change at the same time, for example, the number of machines and the number of hours. You work it out by performing two rules of three in succession.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-ds-6\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question\">What is the English term for \u2018rule of three\u2019?<\/h3>\n<div class=\"rank-math-answer\">\n\n<p>The rule of three is called \u00abrule of three\u00bb in English. \u00abDirect proportion\u00bb means proportional, and \u00abinverse proportion\u00bb means anti-proportional.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-ds-7\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question\">Does the rule of three calculator cost anything?<\/h3>\n<div class=\"rank-math-answer\">\n\n<p>No, the rule of three calculator is free of charge. It works in your browser on your mobile and computer, without the need for an app or registration.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Mit dem Dreisatz Rechner l\u00f6st du jeden Dreisatz einfach online: drei Werte eingeben, schon siehst du das Ergebnis mit Rechenweg und Formel. Der Dreisatz, auch 3-Satz oder 3satz genannt, ist eine Rechnung, mit der du aus drei bekannten Werten einen vierten bestimmst. Du brauchst ihn beim Einkaufen, f\u00fcr Rezepte, beim Lohn oder in der Prozentrechnung. [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":42501,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_wp_convertkit_post_meta":{"form":"-1","landing_page":"","tag":"0","restrict_content":"0"},"footnotes":""},"categories":[468],"tags":[1115,1113,1119,1114,211,1117,1116,1118],"class_list":["post-42500","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-rechner","tag-antiproportional","tag-dreisatz","tag-finanzrechner-schweiz-schule","tag-proportional","tag-rechner","tag-schule","tag-schueler","tag-unterricht"],"_links":{"self":[{"href":"https:\/\/www.schwiizerfranke.com\/en\/wp-json\/wp\/v2\/posts\/42500","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.schwiizerfranke.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.schwiizerfranke.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.schwiizerfranke.com\/en\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/www.schwiizerfranke.com\/en\/wp-json\/wp\/v2\/comments?post=42500"}],"version-history":[{"count":3,"href":"https:\/\/www.schwiizerfranke.com\/en\/wp-json\/wp\/v2\/posts\/42500\/revisions"}],"predecessor-version":[{"id":48851,"href":"https:\/\/www.schwiizerfranke.com\/en\/wp-json\/wp\/v2\/posts\/42500\/revisions\/48851"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.schwiizerfranke.com\/en\/wp-json\/wp\/v2\/media\/42501"}],"wp:attachment":[{"href":"https:\/\/www.schwiizerfranke.com\/en\/wp-json\/wp\/v2\/media?parent=42500"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.schwiizerfranke.com\/en\/wp-json\/wp\/v2\/categories?post=42500"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.schwiizerfranke.com\/en\/wp-json\/wp\/v2\/tags?post=42500"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}