[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"tool-content:en:proportion-calculator":3,"glossary:en":56,"published-tools-en":105},{"id":4,"documentId":5,"slug":6,"intro":7,"howTo":8,"longContent":9,"createdAt":10,"updatedAt":11,"publishedAt":12,"locale":13,"name":14,"faq":15,"examples":40,"category":41,"seo":50,"localizations":55,"metaTitle":52,"metaDescription":53},326,"x72qg70xguuwfhiycxt6m0kn","proportion-calculator","\u003Cp>A proportion sets two ratios equal in the form a\u002Fb = c\u002Fd. It holds only when the cross products \u003Cstrong>a × d\u003C\u002Fstrong> and \u003Cstrong>b × c\u003C\u002Fstrong> match. This \u003Cstrong>proportion calculator\u003C\u002Fstrong> takes the three known terms, works the fourth one out of that cross product and shows every line of the working. Filling all four boxes switches it to a check, with a true or false verdict and the value the last term would need.\u003C\u002Fp>","\u003Col>\u003Cli>Type the three terms you know into a, b, c and d, in the order they take in a\u002Fb = c\u002Fd.\u003C\u002Fli>\u003Cli>Leave the fourth box empty to mark the unknown. An x, a capital X or a question mark does the same job. Only one box may stay open.\u003C\u002Fli>\u003Cli>Read the value of x above the working, then follow the steps underneath, from a × d = b × c down to the division that isolates x.\u003C\u002Fli>\u003Cli>Fill all four boxes instead to switch to checking mode, which returns a true or false verdict plus the value d would need for the two ratios to match.\u003C\u002Fli>\u003C\u002Fol>","\u003Ch2 id=\"formula\">Which formula solves each position in the proportion a\u002Fb = c\u002Fd?\u003C\u002Fh2>\n\u003Cp>All four formulas come out of one rule, the cross product \u003Cstrong>a × d = b × c\u003C\u002Fstrong>, which holds whenever the two ratios have the same value. Rearranging that equality once per position gives four divisions, so the missing term is a product of two known values divided by the third.\u003C\u002Fp>\n\u003Ctable>\u003Cthead>\u003Ctr>\u003Cth>Missing term\u003C\u002Fth>\u003Cth>Formula\u003C\u002Fth>\u003Cth>Example\u003C\u002Fth>\u003Cth>Result\u003C\u002Fth>\u003C\u002Ftr>\u003C\u002Fthead>\u003Ctbody>\n\u003Ctr>\u003Ctd>a\u003C\u002Ftd>\u003Ctd>x = (b × c) ÷ d\u003C\u002Ftd>\u003Ctd>x\u002F5 = 8\u002F20\u003C\u002Ftd>\u003Ctd>(5 × 8) ÷ 20 = 2\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>b\u003C\u002Ftd>\u003Ctd>x = (a × d) ÷ c\u003C\u002Ftd>\u003Ctd>3\u002Fx = 9\u002F12\u003C\u002Ftd>\u003Ctd>(3 × 12) ÷ 9 = 4\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>c\u003C\u002Ftd>\u003Ctd>x = (a × d) ÷ b\u003C\u002Ftd>\u003Ctd>2\u002F3 = x\u002F12\u003C\u002Ftd>\u003Ctd>(2 × 12) ÷ 3 = 8\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>d\u003C\u002Ftd>\u003Ctd>x = (b × c) ÷ a\u003C\u002Ftd>\u003Ctd>3\u002F4 = 9\u002Fx\u003C\u002Ftd>\u003Ctd>(4 × 9) ÷ 3 = 12\u003C\u002Ftd>\u003C\u002Ftr>\n\u003C\u002Ftbody>\u003C\u002Ftable>\n\u003Cp>\u003Cstrong>b and d sit under the fraction bar\u003C\u002Fstrong>, so the calculator refuses a zero typed into either one. It also refuses a zero that the algebra produces on its own, the case of \u003Cstrong>0\u002Fx = 3\u002F4\u003C\u002Fstrong> where the cross product forces x to \u003Cstrong>0\u003C\u002Fstrong> and leaves the first ratio without a value.\u003C\u002Fp>\n\u003Ch2 id=\"by-hand\">How to calculate a proportion by hand\u003C\u002Fh2>\n\u003Cp>Multiply across the diagonal, then divide by the term facing the gap. Take 3\u002F4 = 9\u002Fx as an example: cross multiplication rewrites it as 3 × x = 4 × 9, the known side comes to \u003Cstrong>36\u003C\u002Fstrong>, then dividing 36 by the 3 facing x leaves \u003Cstrong>x = 12\u003C\u002Fstrong>. Those lines appear in that same order under the result, below the literal formula \u003Cstrong>x = (b × c) ÷ a\u003C\u002Fstrong>.\u003C\u002Fp>\n\u003Cp>The method holds wherever the gap sits. \u003Cstrong>x\u002F5 = 8\u002F20\u003C\u002Fstrong> leaves the first term open, where the known cross product is 5 × 8 = 40 and the divisor is the 20 sitting opposite it, which lands on \u003Cstrong>x = 2\u003C\u002Fstrong>. A gap in the second box behaves the same way, so \u003Cstrong>3\u002Fx = 9\u002F12\u003C\u002Fstrong> multiplies 3 by 12 before dividing that 36 by the 9 facing it, ending at \u003Cstrong>x = 4\u003C\u002Fstrong>.\u003C\u002Fp>\n\u003Cp>Nothing on the page asks which term to solve for. The calculator reads the empty box as the unknown and treats an \u003Cstrong>x\u003C\u002Fstrong>, a capital X or a question mark the same way. Two empty boxes stop it, since a proportion missing two terms has an unlimited number of answers.\u003C\u002Fp>\n\u003Ch2 id=\"check\">How do you check whether a proportion is true?\u003C\u002Fh2>\n\u003Cp>Filling all four boxes leaves nothing to solve, so the page compares the two cross products and returns a verdict instead. \u003Cstrong>2\u002F3 = 5\u002F7\u003C\u002Fstrong> comes back false, with a × d at \u003Cstrong>14\u003C\u002Fstrong> against \u003Cstrong>15\u003C\u002Fstrong> for b × c, a gap of 1. The same line names the value that would settle it, \u003Cstrong>d = 7.5\u003C\u002Fstrong> in place of the 7, which comes from (3 × 5) ÷ 2.\u003C\u002Fp>\n\u003Cp>The calculator compares the two products with a small tolerance on decimals, which keeps binary rounding, the tiny error a computer makes while storing 0.1, from turning a true proportion into a false verdict. \u003Cstrong>0.1\u002F0.3 = 1\u002F3\u003C\u002Fstrong> comes back true even though 0.1 × 3 evaluates to 0.30000000000000004 in a browser and not to 0.3.\u003C\u002Fp>\n\u003Ch2 id=\"uses\">Which everyday problems are proportions?\u003C\u002Fh2>\n\u003Cp>Flour at \u003Cstrong>250 g for 4 servings\u003C\u002Fstrong> becomes 250\u002F4 = x\u002F6 for a table of six. The \u003Cstrong>375 g\u003C\u002Fstrong> that comes back holds the flour at 62.5 g per serving, a factor of 1.5 that every other quantity in the recipe follows too.\u003C\u002Fp>\n\u003Cp>A wall drawn at 12 cm on a \u003Cstrong>1:50\u003C\u002Fstrong> plan reads 1\u002F50 = 12\u002Fx, which puts the real wall at \u003Cstrong>600 cm\u003C\u002Fstrong>. The rule of three taught at school is this same layout under another name.\u003C\u002Fp>\n\u003Cp>Unit prices and currency amounts at a fixed rate fold into these same four boxes. Turning a single fraction into a decimal or adding two of them belongs to the \u003Ca href=\"\u002Fmath\u002Ffraction-calculator\">fraction calculator\u003C\u002Fa>, while reducing a ratio to its smallest whole numbers is the job of the \u003Ca href=\"\u002Fmath\u002Fratio-calculator\">ratio calculator\u003C\u002Fa>.\u003C\u002Fp>","2026-08-06T07:18:53.981Z","2026-08-19T10:00:02.080Z","2026-08-19T10:00:00.000Z","en","Proportion Calculator",[16,20,24,28,32,36],{"id":17,"question":18,"answer":19},2310,"How do I calculate a proportion?","\u003Cp>Cross multiply first, then divide. In \u003Cstrong>5\u002F8 = x\u002F24\u003C\u002Fstrong> the two known terms on the diagonal are 5 and 24, whose product is \u003Cstrong>120\u003C\u002Fstrong>. Dividing that 120 by the 8 facing the gap gives \u003Cstrong>x = 15\u003C\u002Fstrong>.\u003C\u002Fp>\u003Cp>The three moves stay the same whichever box is empty.\u003C\u002Fp>\u003Col>\u003Cli>Multiply the two known terms that sit on the diagonal.\u003C\u002Fli>\u003Cli>Divide that product by the third known term, the one facing the empty box.\u003C\u002Fli>\u003Cli>Confirm the answer by comparing a × d with b × c, which must come out equal.\u003C\u002Fli>\u003C\u002Fol>",{"id":21,"question":22,"answer":23},2312,"What is the formula for proportion?","\u003Cp>The proportion itself is written \u003Cstrong>a\u002Fb = c\u002Fd\u003C\u002Fstrong>. The working formula behind it is the cross product \u003Cstrong>a × d = b × c\u003C\u002Fstrong>. Isolating whichever term is missing turns that equality into one of four divisions.\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>x = (b × c) ÷ d\u003C\u002Fstrong> when a is the missing term\u003C\u002Fli>\u003Cli>\u003Cstrong>x = (a × d) ÷ c\u003C\u002Fstrong> when b is missing\u003C\u002Fli>\u003Cli>\u003Cstrong>x = (a × d) ÷ b\u003C\u002Fstrong> when c is missing\u003C\u002Fli>\u003Cli>\u003Cstrong>x = (b × c) ÷ a\u003C\u002Fstrong> when d is missing\u003C\u002Fli>\u003C\u002Ful>\u003Cp>The denominators b and d take any value except zero, since a fraction with zero underneath has no value.\u003C\u002Fp>",{"id":25,"question":26,"answer":27},2313,"Is there an easy way to solve proportions?","\u003Cp>Scaling one ratio into the other is quicker than cross multiplication whenever the numbers divide evenly. In \u003Cstrong>3\u002F4 = 9\u002Fx\u003C\u002Fstrong> the step from 3 to 9 is a \u003Cstrong>factor of 3\u003C\u002Fstrong>. Applying that same factor to the 4 gives \u003Cstrong>12\u003C\u002Fstrong> with no division at the end.\u003C\u002Fp>\u003Cp>The same trick runs down the columns. From \u003Cstrong>2\u002F3 = x\u002F12\u003C\u002Fstrong> the two denominators jump by a factor of 4, so 2 × 4 gives \u003Cstrong>x = 8\u003C\u002Fstrong>. A pair like 7\u002F13 = x\u002F31 leaves no whole factor in either direction. The cross product still answers it at \u003Cstrong>16.6923076923\u003C\u002Fstrong>.\u003C\u002Fp>",{"id":29,"question":30,"answer":31},2314,"How do you calculate a proportion in statistics?","\u003Cp>Divide the count by the total. A proportion in statistics is a share of a group. The sample proportion p-hat is written \u003Cstrong>p̂ = x ÷ n\u003C\u002Fstrong>, where x counts the individuals showing a trait and n counts everyone measured. A survey finding 37 smokers among 200 people gives 37 ÷ 200 = \u003Cstrong>0.185\u003C\u002Fstrong>, which reads as 18.5 percent.\u003C\u002Fp>\u003Cp>Filling the missing term of an equation is a different job, so the sample proportion is not what this page works out. The four boxes still turn it into a percentage, since \u003Cstrong>x\u002F100 = 37\u002F200\u003C\u002Fstrong> resolves to \u003Cstrong>18.5\u003C\u002Fstrong>. The \u003Ca href=\"\u002Fmath\u002Fpercentage-calculator\">percentage calculator\u003C\u002Fa> reaches the same figure in one step. Standard error and confidence intervals around a sample proportion belong to a statistics tool of their own.\u003C\u002Fp>",{"id":33,"question":34,"answer":35},2315,"Can this work as a golden proportion calculator?","\u003Cp>Only as a scaling step. The golden proportion is the fixed number \u003Cstrong>1.618\u003C\u002Fstrong>, written 1.6180339887 when the decimals matter. Entering 1.618 and 1 as the known ratio scales any length by it, so a side of 10 cm written \u003Cstrong>1.618\u002F1 = x\u002F10\u003C\u002Fstrong> comes back as \u003Cstrong>16.18\u003C\u002Fstrong>.\u003C\u002Fp>\u003Cp>Producing that number on its own is outside what these four boxes do, as is measuring the golden proportion of a face or a logo. Tools built for that compare distances read off an image against 1.618 and report how far each one strays.\u003C\u002Fp>",{"id":37,"question":38,"answer":39},2316,"Can more than one box be left empty?","\u003Cp>No, one unknown is the limit. Two empty boxes would leave an unlimited number of matching pairs, so the calculator stops there and asks for exactly one gap.\u003C\u002Fp>\u003Cp>The calculator refuses a zero in \u003Cstrong>b or d\u003C\u002Fstrong> straight away, those two positions sitting under the fraction bar. It refuses a zero that only shows up in the answer as well, which is why \u003Cstrong>0\u002Fx = 3\u002F4\u003C\u002Fstrong> returns an error in place of x = 0.\u003C\u002Fp>",[],{"id":42,"documentId":43,"uid":44,"name":45,"tagline":46,"hubContent":47,"createdAt":48,"updatedAt":48,"publishedAt":49,"locale":13},15,"s8cujbpmiszotf6zdbotc2p0","math","Math","Calculators for school, work and everyday numbers","\u003Cp>Every calculator in this category computes live as you type and shows the formula behind the result. Grades, percentages, fractions, ratios or volumes: you see the answer and the reasoning, so you can trust the number you copy. Each tool also documents its edge cases, because a calculator you cannot verify is just a guess with confidence.\u003C\u002Fp>","2026-07-17T11:46:54.883Z","2026-07-17T12:01:48.544Z",{"id":51,"metaTitle":52,"metaDescription":53,"keywords":54,"metaRobots":54,"structuredData":54,"metaViewport":54,"canonicalURL":54},556,"Proportion Calculator: Solve a\u002Fb = c\u002Fd for Any Term","Free proportion calculator that solves a\u002Fb = c\u002Fd for the missing term. Leave one box empty to get x, the cross products and every step of the working.",null,[],[57,69,81,93],{"id":58,"documentId":59,"slug":60,"term":61,"definition":62,"relatedTools":63,"createdAt":66,"updatedAt":67,"publishedAt":68,"locale":13},17,"o1ljpluv6app6z9rrhst4gfn","cubic-yard","Cubic yard","\u003Cp>A \u003Cstrong>cubic yard\u003C\u002Fstrong> is the volume of a cube measuring 3 x 3 x 3 feet, which equals 27 cubic feet or about \u003Cstrong>0.7646 m³\u003C\u002Fstrong>. It is the standard unit for ordering bulk materials in the United States: ready-mix concrete, topsoil, gravel, sand and mulch are all priced and delivered by the cubic yard, often shortened to \"yard\" on a quote.\u003C\u002Fp>\u003Cp>For scale, a typical 12 x 10 ft patio slab poured 4 inches thick contains 40 cubic feet, which is 40 \u002F 27 = 1.48 cubic yards of concrete. A standard ready-mix truck carries 8 to 10 cubic yards, so that whole slab uses less than a fifth of one load.\u003C\u002Fp>\u003Cp>How big is a cubic yard in practice? The cube stands 3 feet on each side, roughly counter height, and holds about 14 full wheelbarrow loads of material. Spread out, one cubic yard covers close to 100 square feet at a depth of 3 inches, the usual layer for mulch or a gravel path.\u003C\u002Fp>",[64,65],"math\u002Fconcrete-calculator","math\u002Fvolume-calculator","2026-07-18T14:23:56.812Z","2026-08-02T10:00:01.228Z","2026-08-02T10:00:00.000Z",{"id":70,"documentId":71,"slug":72,"term":73,"definition":74,"relatedTools":75,"createdAt":78,"updatedAt":79,"publishedAt":80,"locale":13},16,"mdw0ypy9f3z1nioxaxnl9rvr","password-entropy","Entropy (passwords)","\u003Cp>\u003Cstrong>Entropy\u003C\u002Fstrong> measures how unpredictable a password is, expressed in bits. Each additional bit doubles the number of guesses an attacker needs. For a randomly generated password, it follows a simple formula: entropy = length × log2 of the alphabet size, so both the length and the variety of characters raise the score.\u003C\u002Fp>\u003Cp>A random 16-character password drawn from the 94 printable ASCII symbols reaches 16 × log2(94), about \u003Cstrong>105 bits\u003C\u002Fstrong>. At 10 billion guesses per second, exhausting that space would take on the order of 10^14 years, while a 6-character password from the same alphabet peaks at 39 bits and falls in about a minute.\u003C\u002Fp>\u003Cp>Written as a formula, \u003Cstrong>E = L × log2(N)\u003C\u002Fstrong>: the entropy equals the length L multiplied by the base-2 logarithm of N, the number of possible symbols per character. Current guidance treats 75 to 80 bits as the comfortable minimum for accounts that matter, a level a random 12-character password mixing all character types already clears.\u003C\u002Fp>",[76,77],"generator\u002Fpassword-generator","generator\u002Fusername-generator","2026-07-18T14:23:55.755Z","2026-08-01T10:00:01.360Z","2026-08-01T10:00:00.000Z",{"id":42,"documentId":82,"slug":83,"term":84,"definition":85,"relatedTools":86,"createdAt":90,"updatedAt":91,"publishedAt":92,"locale":13},"ypkfs6wnfljm03ge2b1ztiwv","percentage-point","Percentage point","\u003Cp>A \u003Cstrong>percentage point\u003C\u002Fstrong> is the unit used to express the arithmetic difference between two percentages. It compares rates by subtraction, while \"percent\" compares them by division: the two measures answer different questions and can differ wildly for the same change.\u003C\u002Fp>\u003Cp>Example: an interest rate that moves from 5% to 7% rises by \u003Cstrong>2 percentage points\u003C\u002Fstrong> (7 - 5 = 2), but by 40 percent in relative terms (2 ÷ 5 × 100 = 40). Saying \"the rate went up 2%\" would be wrong on both counts: the correct phrasings are \"up 2 points\" or \"up 40%\".\u003C\u002Fp>\u003Cp>The standard abbreviation is \u003Cstrong>pp\u003C\u002Fstrong>, sometimes just \"points\", as in \"unemployment fell by 0.5 pp\". Confusing percent with percentage points remains the classic trap: a party moving from 20% to 30% in the polls gains 10 percentage points, yet grows by 50 percent, and headlines regularly pick the wrong figure.\u003C\u002Fp>",[87,88,89],"math\u002Fpercentage-calculator","math\u002Faverage-calculator","finance\u002Fcalcul-remise","2026-07-18T14:23:54.573Z","2026-07-31T10:00:01.940Z","2026-07-31T10:00:00.000Z",{"id":94,"documentId":95,"slug":96,"term":97,"definition":98,"relatedTools":99,"createdAt":102,"updatedAt":103,"publishedAt":104,"locale":13},14,"g3okb797ekrz0kkpm36mfjwc","weighted-average","Weighted average","\u003Cp>A \u003Cstrong>weighted average\u003C\u002Fstrong> is an average where each value counts in proportion to an assigned importance, called its weight, instead of counting equally. Each value is multiplied by its weight, the products are added, and the sum is divided by the total of the weights. Class grades, GPAs, and stock indexes are all weighted averages.\u003C\u002Fp>\u003Cp>Example: scores of 92, 85, and 88 with weights of 30, 30, and 40 give (92 x 30 + 85 x 30 + 88 x 40) \u002F 100 = \u003Cstrong>88.3\u003C\u002Fstrong>. The plain average of the same scores is 88.33, but if the heaviest score dropped to 78, the weighted average would fall to 84.3 while the plain average only fell to 85.\u003C\u002Fp>\u003Cp>The weighted average formula in plain words: multiply each value by its weight, add up the products, then divide by the sum of the weights. In a spreadsheet the whole calculation fits in one cell, since Excel's SUMPRODUCT function multiplies and adds in a single pass: SUMPRODUCT of the values and weights, divided by SUM of the weights.\u003C\u002Fp>",[88,100,101],"math\u002Fgrade-calculator","math\u002Fgpa-calculator","2026-07-18T14:23:53.329Z","2026-07-30T10:00:01.216Z","2026-07-30T10:00:00.000Z",{"slugs":106},[107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,6,151,152,153,154,155,156,157,158,159,160,161],"age-calculator","average-calculator","cd-calculator","concrete-calculator","cursive-font-generator","date-calculator","fantasy-name-generator","final-grade-calculator","fraction-calculator","glitch-text-generator","gpa-calculator","grade-calculator","hex-converter","hours-calculator","interest-calculator","military-time-converter","roman-numeral-converter","password-generator","binary-converter","celsius-to-fahrenheit-converter","kg-to-lbs-converter","percentage-calculator","word-counter","tip-calculator","morse-code-translator","username-generator","ratio-calculator","sales-tax-calculator","small-text-generator","mm-to-inches-converter","volume-calculator","timer","square-footage-calculator","stair-calculator","roof-pitch-calculator","board-foot-calculator","aspect-ratio-calculator","rounding-calculator","random-letter-generator","mulch-calculator","fence-calculator","upside-down-text-generator","acreage-calculator","gravel-calculator","paint-calculator","tile-calculator","braille-translator","quadratic-formula-calculator","gcf-calculator","probability-calculator","hex-to-rgb-converter","uuid-generator","standard-deviation-calculator","lcm-calculator","caesar-cipher"]