[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"tool-content:en:braille-translator":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},332,"l295dumqfpompgsg47dl1d3r","braille-translator","\u003Cp>This \u003Cstrong>braille translator\u003C\u002Fstrong> turns English text into Unicode braille cells and reads braille back into English, one cell per letter. It works in \u003Cstrong>grade 1 (uncontracted) braille\u003C\u002Fstrong>, marks digits with the number sign ⠼ and capitals with the capital indicator ⠠, then shows which of the six dots each cell raises.\u003C\u002Fp>","\u003Col>\n\u003Cli>Type English in the box or paste braille cells copied from somewhere else. The field takes up to 2000 characters.\u003C\u002Fli>\n\u003Cli>Leave Direction on automatic detection. Set it to English to braille or Braille to English when an input mixes the two.\u003C\u002Fli>\n\u003Cli>Read the result under the box. The Grade 1 badge confirms that the tool applied no grade 2 contraction.\u003C\u002Fli>\n\u003Cli>Open the cell-by-cell panel to see the six-dot pattern behind each character. Anything listed as unsupported passed through untranslated.\u003C\u002Fli>\n\u003C\u002Fol>","\u003Ch2>Why this braille translator stops at grade 1\u003C\u002Fh2>\n\u003Cp>\u003Cstrong>Grade 1 braille\u003C\u002Fstrong>, also called uncontracted braille, spells a word out letter by letter, so one printed letter becomes one cell. Grade 2 sits on top of that system and swaps common words and letter groups for \u003Cstrong>contractions\u003C\u002Fstrong> that run into the hundreds.\u003C\u002Fp>\n\u003Cp>Those contractions depend on position. A \u003Cstrong>b\u003C\u002Fstrong> standing on its own means the word \u003Cem>but\u003C\u002Fem>, while the same b inside a word stays a plain letter. Dozens of letter groups work that way, so a table covering half of them turns out cells that read as a different word. The tool therefore handles \u003Cstrong>grade 1 only\u003C\u002Fstrong> and puts a Grade 1 badge on every result.\u003C\u002Fp>\n\n\u003Ch2>The braille alphabet, cell by cell\u003C\u002Fh2>\n\u003Cp>A cell holds six dot positions, numbered 1 to 3 down the left column and 4 to 6 down the right. Raising any combination of them gives 63 patterns, of which the 26 below carry the letters. The \u003Cstrong>braille alphabet\u003C\u002Fstrong> runs in decades of ten: a to j stay inside the top four positions, k to t repeat those ten shapes with \u003Cstrong>dot 3\u003C\u002Fstrong> added while the rest add dots 3 and 6 to the first five.\u003C\u002Fp>\n\n\u003Ctable>\n\u003Cthead>\u003Ctr>\u003Cth scope=\"col\">Letter\u003C\u002Fth>\u003Cth scope=\"col\">Cell\u003C\u002Fth>\u003Cth scope=\"col\">Dots\u003C\u002Fth>\u003Cth scope=\"col\">Letter\u003C\u002Fth>\u003Cth scope=\"col\">Cell\u003C\u002Fth>\u003Cth scope=\"col\">Dots\u003C\u002Fth>\u003C\u002Ftr>\u003C\u002Fthead>\n\u003Ctbody>\n\u003Ctr>\u003Ctd>a\u003C\u002Ftd>\u003Ctd>⠁\u003C\u002Ftd>\u003Ctd>1\u003C\u002Ftd>\u003Ctd>n\u003C\u002Ftd>\u003Ctd>⠝\u003C\u002Ftd>\u003Ctd>1-3-4-5\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>b\u003C\u002Ftd>\u003Ctd>⠃\u003C\u002Ftd>\u003Ctd>1-2\u003C\u002Ftd>\u003Ctd>o\u003C\u002Ftd>\u003Ctd>⠕\u003C\u002Ftd>\u003Ctd>1-3-5\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>c\u003C\u002Ftd>\u003Ctd>⠉\u003C\u002Ftd>\u003Ctd>1-4\u003C\u002Ftd>\u003Ctd>p\u003C\u002Ftd>\u003Ctd>⠏\u003C\u002Ftd>\u003Ctd>1-2-3-4\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>d\u003C\u002Ftd>\u003Ctd>⠙\u003C\u002Ftd>\u003Ctd>1-4-5\u003C\u002Ftd>\u003Ctd>q\u003C\u002Ftd>\u003Ctd>⠟\u003C\u002Ftd>\u003Ctd>1-2-3-4-5\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>e\u003C\u002Ftd>\u003Ctd>⠑\u003C\u002Ftd>\u003Ctd>1-5\u003C\u002Ftd>\u003Ctd>r\u003C\u002Ftd>\u003Ctd>⠗\u003C\u002Ftd>\u003Ctd>1-2-3-5\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>f\u003C\u002Ftd>\u003Ctd>⠋\u003C\u002Ftd>\u003Ctd>1-2-4\u003C\u002Ftd>\u003Ctd>s\u003C\u002Ftd>\u003Ctd>⠎\u003C\u002Ftd>\u003Ctd>2-3-4\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>g\u003C\u002Ftd>\u003Ctd>⠛\u003C\u002Ftd>\u003Ctd>1-2-4-5\u003C\u002Ftd>\u003Ctd>t\u003C\u002Ftd>\u003Ctd>⠞\u003C\u002Ftd>\u003Ctd>2-3-4-5\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>h\u003C\u002Ftd>\u003Ctd>⠓\u003C\u002Ftd>\u003Ctd>1-2-5\u003C\u002Ftd>\u003Ctd>u\u003C\u002Ftd>\u003Ctd>⠥\u003C\u002Ftd>\u003Ctd>1-3-6\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>i\u003C\u002Ftd>\u003Ctd>⠊\u003C\u002Ftd>\u003Ctd>2-4\u003C\u002Ftd>\u003Ctd>v\u003C\u002Ftd>\u003Ctd>⠧\u003C\u002Ftd>\u003Ctd>1-2-3-6\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>j\u003C\u002Ftd>\u003Ctd>⠚\u003C\u002Ftd>\u003Ctd>2-4-5\u003C\u002Ftd>\u003Ctd>w\u003C\u002Ftd>\u003Ctd>⠺\u003C\u002Ftd>\u003Ctd>2-4-5-6\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>k\u003C\u002Ftd>\u003Ctd>⠅\u003C\u002Ftd>\u003Ctd>1-3\u003C\u002Ftd>\u003Ctd>x\u003C\u002Ftd>\u003Ctd>⠭\u003C\u002Ftd>\u003Ctd>1-3-4-6\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>l\u003C\u002Ftd>\u003Ctd>⠇\u003C\u002Ftd>\u003Ctd>1-2-3\u003C\u002Ftd>\u003Ctd>y\u003C\u002Ftd>\u003Ctd>⠽\u003C\u002Ftd>\u003Ctd>1-3-4-5-6\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>m\u003C\u002Ftd>\u003Ctd>⠍\u003C\u002Ftd>\u003Ctd>1-3-4\u003C\u002Ftd>\u003Ctd>z\u003C\u002Ftd>\u003Ctd>⠵\u003C\u002Ftd>\u003Ctd>1-3-5-6\u003C\u002Ftd>\u003C\u002Ftr>\n\u003C\u002Ftbody>\n\u003C\u002Ftable>\n\u003Cp>Only the w breaks that logic. French had no w when Louis Braille drew up the code, so the letter came in later and its cell ⠺ looks unrelated to the ones around it.\u003C\u002Fp>\n\n\u003Ch2>Writing numbers and capitals in braille\u003C\u002Fh2>\n\u003Cp>Digits reuse the first ten letters. A \u003Cstrong>number sign ⠼\u003C\u002Fstrong> (dots 3-4-5-6) opens the sequence, after which a to j stand for 1 to 9 and 0. Take the year 1809 as an example: it comes out as ⠼⠁⠓⠚⠊, where ⠁ is 1, ⠓ is 8, ⠚ is 0 and ⠊ is 9, for \u003Cstrong>five cells\u003C\u002Fstrong> in all.\u003C\u002Fp>\n\u003Cp>Number mode survives a period and a comma, which keeps \u003Cstrong>3.14\u003C\u002Fstrong> (⠼⠉⠲⠁⠙) and \u003Cstrong>1,000\u003C\u002Fstrong> (⠼⠁⠂⠚⠚⠚) reading as one value each. A reader would take a letter straight after a digit as another digit, so a \u003Cstrong>letter sign ⠰\u003C\u002Fstrong> (dots 5-6) closes the number and 1st comes out as ⠼⠁⠰⠎⠞.\u003C\u002Fp>\n\u003Cp>Capitals take the \u003Cstrong>capital indicator ⠠\u003C\u002Fstrong> (dot 6) in front of the letter it applies to. Hello, World! becomes ⠠⠓⠑⠇⠇⠕⠂⠀⠠⠺⠕⠗⠇⠙⠖, which is \u003Cstrong>15 cells\u003C\u002Fstrong> counting the space between the words. Decoding is more forgiving than encoding here, since two capital indicators in a row mean a whole word in capitals and ⠠⠠⠉⠁⠞ comes back as CAT.\u003C\u002Fp>\n\n\u003Ch2>How to translate braille to English\u003C\u002Fh2>\n\u003Cp>Pasting cells into the same box is all it takes to go the other way. The tool reads the direction from the input. Any string holding at least one cell from the \u003Cstrong>Unicode Braille Patterns\u003C\u002Fstrong> block (U+2800 to U+28FF) goes back to English while anything else goes to braille. The Direction menu forces one side when an input mixes the two.\u003C\u002Fp>\n\u003Cp>⠓⠑⠇⠇⠕ ⠺⠕⠗⠇⠙ comes back as \u003Cstrong>hello world\u003C\u002Fstrong>, with the empty cell ⠀ and an ordinary space both accepted as a word break. Decoding walks the same table backwards, so a cell belonging to grade 2 or to eight-dot braille, which adds two dots under the standard six, gets flagged as unsupported rather than turned into a guess.\u003C\u002Fp>\n\n\u003Ch2>Characters the braille translator leaves untranslated\u003C\u002Fh2>\n\u003Cp>Accented letters, currency signs, @, % and emoji have no cell in the covered set. They travel through the output untouched and appear in a list under the result, which turns café into ⠉⠁⠋é with the é flagged. The tool leaves them in place rather than swapping in an \u003Cstrong>approximate cell\u003C\u002Fstrong>, since a plausible wrong cell is harder to spot than a character that stayed behind.\u003C\u002Fp>\n\u003Cp>Punctuation is where this table departs from printed braille on purpose. Printed braille gives dots 2-3-6 to both the question mark and the opening double quote; the tool keeps those dots for \u003Cstrong>?\u003C\u002Fstrong> and writes both double quotes with dots 3-5-6. One cell per character is what lets a decode return the original line. The tool retranslates its own output and reports whether the round trip landed back on the input.\u003C\u002Fp>\n\n\u003Ctable>\n\u003Cthead>\u003Ctr>\u003Cth scope=\"col\">Sign\u003C\u002Fth>\u003Cth scope=\"col\">Cell\u003C\u002Fth>\u003Cth scope=\"col\">Dots\u003C\u002Fth>\u003C\u002Ftr>\u003C\u002Fthead>\n\u003Ctbody>\n\u003Ctr>\u003Ctd>Number sign\u003C\u002Ftd>\u003Ctd>⠼\u003C\u002Ftd>\u003Ctd>3-4-5-6\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>Capital indicator\u003C\u002Ftd>\u003Ctd>⠠\u003C\u002Ftd>\u003Ctd>6\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>Letter sign\u003C\u002Ftd>\u003Ctd>⠰\u003C\u002Ftd>\u003Ctd>5-6\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>Space\u003C\u002Ftd>\u003Ctd>⠀\u003C\u002Ftd>\u003Ctd>empty cell\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>Comma ,\u003C\u002Ftd>\u003Ctd>⠂\u003C\u002Ftd>\u003Ctd>2\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>Semicolon ;\u003C\u002Ftd>\u003Ctd>⠆\u003C\u002Ftd>\u003Ctd>2-3\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>Colon :\u003C\u002Ftd>\u003Ctd>⠒\u003C\u002Ftd>\u003Ctd>2-5\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>Period .\u003C\u002Ftd>\u003Ctd>⠲\u003C\u002Ftd>\u003Ctd>2-5-6\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>Exclamation !\u003C\u002Ftd>\u003Ctd>⠖\u003C\u002Ftd>\u003Ctd>2-3-5\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>Question mark ?\u003C\u002Ftd>\u003Ctd>⠦\u003C\u002Ftd>\u003Ctd>2-3-6\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>Apostrophe '\u003C\u002Ftd>\u003Ctd>⠄\u003C\u002Ftd>\u003Ctd>3\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>Hyphen -\u003C\u002Ftd>\u003Ctd>⠤\u003C\u002Ftd>\u003Ctd>3-6\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>Double quote \"\u003C\u002Ftd>\u003Ctd>⠴\u003C\u002Ftd>\u003Ctd>3-5-6\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>Opening bracket (\u003C\u002Ftd>\u003Ctd>⠐⠣\u003C\u002Ftd>\u003Ctd>5 then 1-2-6\u003C\u002Ftd>\u003C\u002Ftr>\n\u003Ctr>\u003Ctd>Closing bracket )\u003C\u002Ftd>\u003Ctd>⠐⠜\u003C\u002Ftd>\u003Ctd>5 then 3-4-5\u003C\u002Ftd>\u003C\u002Ftr>\n\u003C\u002Ftbody>\n\u003C\u002Ftable>\n\n\u003Ch2>What letter-for-letter braille translation is good for\u003C\u002Fh2>\n\u003Cp>The output is a run of Unicode characters, ready to copy into a document or a message. Producing an embosser file is a separate craft that depends on line breaks counted in cells and on the contraction rules of grade 2. A transcriber checks that kind of work before anything reaches paper.\u003C\u002Fp>\n\u003Cp>For learning the alphabet or checking a braille string found somewhere, a letter-for-letter braille translation sits at the right level. Anything meant to be read under the fingers by someone who reads braille every day calls for grade 2 and a human pass.\u003C\u002Fp>","2026-08-06T07:18:46.119Z","2026-08-22T10:00:02.111Z","2026-08-22T10:00:00.000Z","en","Braille Translator",[16,20,24,28,32,36],{"id":17,"question":18,"answer":19},2344,"How does a braille translator work?","\u003Cp>It walks the text one character at a time and looks each one up in a table that pairs a letter with a \u003Cstrong>six-dot cell\u003C\u002Fstrong>. Two indicators carry the rest of the information. The \u003Cstrong>number sign ⠼\u003C\u002Fstrong> tells a reader that a to j now mean 1 to 9 and 0. The \u003Cstrong>capital indicator ⠠\u003C\u002Fstrong> raises the single letter that follows it. Decoding runs the same table backwards, cell by cell.\u003C\u002Fp>",{"id":21,"question":22,"answer":23},2345,"What are the features of a braille translator?","\u003Cp>This one covers the \u003Cstrong>26 letters\u003C\u002Fstrong>, digits, the space and nine punctuation marks, plus brackets written across two cells. The tool adds four things around that translation.\u003C\u002Fp>\n\u003Cul>\n\u003Cli>automatic direction detection, with a manual override;\u003C\u002Fli>\n\u003Cli>a dot-by-dot view of each cell, matching what would sit under a fingertip;\u003C\u002Fli>\n\u003Cli>a list of the characters it left untranslated, so nothing gets substituted in silence;\u003C\u002Fli>\n\u003Cli>a cell count, a copy button and a .txt download.\u003C\u002Fli>\n\u003C\u002Ful>",{"id":25,"question":26,"answer":27},2346,"When was the braille translator invented?","\u003Cp>The writing system came first. \u003Cstrong>Louis Braille\u003C\u002Fstrong>, born in 1809, worked out the six-dot cell around 1824 and published the code in \u003Cstrong>1829\u003C\u002Fstrong>, in a treatise that also covered music. Machine transcription arrived far later and carries no single invention date. It grew out of braille typewriters, then out of software, once braille cells reached character encoding.\u003C\u002Fp>",{"id":29,"question":30,"answer":31},2347,"Can this tool translate grade 2 braille?","\u003Cp>No. That limit is deliberate. Grade 2 shortens common words and letter groups with \u003Cstrong>several hundred contractions\u003C\u002Fstrong> whose use depends on position inside a word. A partial table would output cells that a reader decodes as a different word, so the tool stays at \u003Cstrong>grade 1\u003C\u002Fstrong> and says so on every result.\u003C\u002Fp>",{"id":33,"question":34,"answer":35},2348,"How do numbers work in braille?","\u003Cp>Put a \u003Cstrong>number sign ⠼\u003C\u002Fstrong> in front, then reuse a to j for 1 to 9 and 0. So 1809 becomes \u003Cstrong>⠼⠁⠓⠚⠊\u003C\u002Fstrong> and 3.14 becomes ⠼⠉⠲⠁⠙, since a period inside a number keeps number mode open. A letter after a digit needs the \u003Cstrong>letter sign ⠰\u003C\u002Fstrong> to close the number, which makes 1st ⠼⠁⠰⠎⠞.\u003C\u002Fp>",{"id":37,"question":38,"answer":39},2349,"Is this braille ready to emboss?","\u003Cp>Treat the output as text. An embossed page depends on line breaks counted in cells and on the \u003Cstrong>contraction rules of grade 2\u003C\u002Fstrong>, with a transcriber checking that kind of file before it reaches paper. Copy the result into a document or use it to learn the alphabet. Embosser jobs belong to grade 2 software.\u003C\u002Fp>",[],{"id":42,"documentId":43,"uid":44,"name":45,"tagline":46,"hubContent":47,"createdAt":48,"updatedAt":48,"publishedAt":49,"locale":13},17,"cwqkpsjkc7q41an8ek8nu8kk","string","Text & String","Count, clean, convert and transform text","\u003Cp>These tools count, convert and restyle text without sending a single character to a server. The counter gives writers real numbers to work against; the Morse translator and the Unicode generators (small, glitch, cursive) turn plain text into something you can paste anywhere. Every transformation is explained, including where exotic Unicode breaks.\u003C\u002Fp>","2026-07-17T11:46:55.682Z","2026-07-17T12:01:48.595Z",{"id":51,"metaTitle":52,"metaDescription":53,"keywords":54,"metaRobots":54,"structuredData":54,"metaViewport":54,"canonicalURL":54},562,"Braille Translator: English to Braille and Back (Grade 1)","Free braille translator. Type English to get Unicode braille cells or paste braille to read it back. Grade 1 uncontracted, with the dots of every cell.",null,[],[57,68,80,93],{"id":42,"documentId":58,"slug":59,"term":60,"definition":61,"relatedTools":62,"createdAt":65,"updatedAt":66,"publishedAt":67,"locale":13},"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>",[63,64],"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":69,"documentId":70,"slug":71,"term":72,"definition":73,"relatedTools":74,"createdAt":77,"updatedAt":78,"publishedAt":79,"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>",[75,76],"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":81,"documentId":82,"slug":83,"term":84,"definition":85,"relatedTools":86,"createdAt":90,"updatedAt":91,"publishedAt":92,"locale":13},15,"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},[107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,6,154,155,156,157,158,159,160,161],"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","proportion-calculator","paint-calculator","tile-calculator","quadratic-formula-calculator","gcf-calculator","probability-calculator","hex-to-rgb-converter","uuid-generator","standard-deviation-calculator","lcm-calculator","caesar-cipher"]