[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"tool-content:en:rounding-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},312,"y2h7g6prtoj03ji7psb2g3zc","rounding-calculator","\u003Cp>Rounding \u003Cstrong>2.675 to the nearest hundredth gives 2.68\u003C\u002Fstrong>. That is what this \u003Cstrong>rounding calculator\u003C\u002Fstrong> returns where a spreadsheet or a pocket calculator shows 2.67. The difference comes from what a machine stores for 2.675, a value beginning \u003Cstrong>2.67499999999999982\u003C\u002Fstrong> that sits below the halfway mark and pulls any result computed from it down. Here the arithmetic runs on the decimal digits as typed, so \u003Cstrong>every exact tie survives\u003C\u002Fstrong>. Choose a place between \u003Cstrong>thousand and thousandth\u003C\u002Fstrong> then one of the \u003Cstrong>six rounding modes\u003C\u002Fstrong>, with the deciding digit marked in the breakdown.\u003C\u002Fp>","\u003Col>\u003Cli>Type the number as text, decimals included, since the field keeps 2.675 exactly as typed instead of normalising it to a float.\u003C\u002Fli>\u003Cli>Pick the target place, from thousand down to thousandth. The badge beside the result gives the matching step, 0.01 at the hundredth.\u003C\u002Fli>\u003Cli>Pick one of the six modes and read the highlighted digit in the breakdown. It is the first digit dropped. The sentence under it names the rule that applied.\u003C\u002Fli>\u003Cli>Check the two neighbours framing the value to see which way it moved, then set the significant figures field between 1 and 15 when precision is counted that way.\u003C\u002Fli>\u003C\u002Fol>","\u003Ch2 id=\"six-modes\">What are the six rounding modes?\u003C\u002Fh2>\u003Cp>Two calculators can disagree on 2.5 without either one being broken. They apply different \u003Cstrong>tie-breaking rules\u003C\u002Fstrong>. A tie, meaning a discarded part that measures exactly half a step of the rounding grid, only comes up for three of the six modes. The rows below cover an exact tie (2.5 and 2.675), a negative value that swaps ceiling and floor (-2.5) and a value nowhere near a tie (3.14159).\u003C\u002Fp>\u003Ctable>\u003Cthead>\u003Ctr>\u003Cth scope=\"col\">Number\u003C\u002Fth>\u003Cth scope=\"col\">Place\u003C\u002Fth>\u003Cth scope=\"col\">Half up\u003C\u002Fth>\u003Cth scope=\"col\">Half down\u003C\u002Fth>\u003Cth scope=\"col\">Half to even\u003C\u002Fth>\u003Cth scope=\"col\">Ceiling\u003C\u002Fth>\u003Cth scope=\"col\">Floor\u003C\u002Fth>\u003Cth scope=\"col\">Truncate\u003C\u002Fth>\u003C\u002Ftr>\u003C\u002Fthead>\u003Ctbody>\u003Ctr>\u003Cth scope=\"row\">2.5\u003C\u002Fth>\u003Ctd>Integer\u003C\u002Ftd>\u003Ctd>3\u003C\u002Ftd>\u003Ctd>2\u003C\u002Ftd>\u003Ctd>2\u003C\u002Ftd>\u003Ctd>3\u003C\u002Ftd>\u003Ctd>2\u003C\u002Ftd>\u003Ctd>2\u003C\u002Ftd>\u003C\u002Ftr>\u003Ctr>\u003Cth scope=\"row\">-2.5\u003C\u002Fth>\u003Ctd>Integer\u003C\u002Ftd>\u003Ctd>-3\u003C\u002Ftd>\u003Ctd>-2\u003C\u002Ftd>\u003Ctd>-2\u003C\u002Ftd>\u003Ctd>-2\u003C\u002Ftd>\u003Ctd>-3\u003C\u002Ftd>\u003Ctd>-2\u003C\u002Ftd>\u003C\u002Ftr>\u003Ctr>\u003Cth scope=\"row\">2.675\u003C\u002Fth>\u003Ctd>Hundredth\u003C\u002Ftd>\u003Ctd>2.68\u003C\u002Ftd>\u003Ctd>2.67\u003C\u002Ftd>\u003Ctd>2.68\u003C\u002Ftd>\u003Ctd>2.68\u003C\u002Ftd>\u003Ctd>2.67\u003C\u002Ftd>\u003Ctd>2.67\u003C\u002Ftd>\u003C\u002Ftr>\u003Ctr>\u003Cth scope=\"row\">3.14159\u003C\u002Fth>\u003Ctd>Tenth\u003C\u002Ftd>\u003Ctd>3.1\u003C\u002Ftd>\u003Ctd>3.1\u003C\u002Ftd>\u003Ctd>3.1\u003C\u002Ftd>\u003Ctd>3.2\u003C\u002Ftd>\u003Ctd>3.1\u003C\u002Ftd>\u003Ctd>3.1\u003C\u002Ftd>\u003C\u002Ftr>\u003C\u002Ftbody>\u003C\u002Ftable>\u003Cp>Half up sends a tie away from zero, half down sends it toward zero and half to even sends it to whichever neighbour ends in an even digit. The other three never consult the deciding digit: ceiling moves toward positive infinity, floor moves toward negative infinity and truncate drops the surplus digits while keeping the sign.\u003C\u002Fp>\u003Cp>For a price carried to the cent or a school exercise, \u003Cstrong>half up\u003C\u002Fstrong> is the answer people expect. For a column of figures that will be summed, \u003Cstrong>half to even\u003C\u002Fstrong> keeps the total closest to the exact sum. Learning \u003Cstrong>how to round on a calculator\u003C\u002Fstrong> is largely a matter of knowing which of these six rules the machine at hand applies.\u003C\u002Fp>\u003Ch2 id=\"nearest-tenth\">How do you round to the nearest tenth?\u003C\u002Fh2>\u003Cp>A stopwatch reading of 3.14159 seconds comes back as \u003Cstrong>3.1\u003C\u002Fstrong> at the tenth, since the hundredths digit is 4 and everything past it is discarded. Nudge that digit up to 6 and 3.16 climbs to 3.2. Set the place list to tenth and the page works as a \u003Cstrong>round to the nearest tenth calculator\u003C\u002Fstrong>, with the hundredths digit highlighted in the breakdown.\u003C\u002Fp>\u003Cp>The same reading moves one column right for the hundredth, where the thousandths digit decides and 2.675 lands on \u003Cstrong>2.68\u003C\u002Fstrong> under half up. That column separates a cent kept from a cent lost.\u003C\u002Fp>\u003Ch2 id=\"bankers-rounding\">What is banker's rounding?\u003C\u002Fh2>\u003Cp>Add 0.5, 1.5, 2.5 and 3.5 together and the exact total is 8. Round each one to a whole number with half up and the total becomes \u003Cstrong>10\u003C\u002Fstrong>, because all four ties moved in the same direction. Half to even, the rule usually called \u003Cstrong>banker's rounding\u003C\u002Fstrong>, sends each tie to whichever neighbour ends in an even digit: 0.5 falls to 0, 1.5 climbs to 2, 2.5 falls to 2 and 3.5 climbs to 4, for the \u003Cstrong>exact total of 8\u003C\u002Fstrong>.\u003C\u002Fp>\u003Cp>That behaviour is the default of the \u003Cstrong>IEEE 754\u003C\u002Fstrong> standard, the specification every mainstream processor follows for floating-point arithmetic. Each language then picks its own rule on top of it, which is why one rounds a tie differently from the next.\u003C\u002Fp>\u003Cul>\u003Cli>Python's built-in round() and .NET's Math.Round use half to even, so round(2.5) returns 2.\u003C\u002Fli>\u003Cli>JavaScript's Math.round sends a tie toward positive infinity, which makes Math.round(-2.5) equal to -2.\u003C\u002Fli>\u003Cli>Excel's ROUND moves a tie away from zero, so ROUND(-2.5, 0) returns -3.\u003C\u002Fli>\u003C\u002Ful>\u003Ch2 id=\"float-trap\">Why does a calculator round 2.675 to 2.67?\u003C\u002Fh2>\u003Cp>The digits 2.675 have no exact equivalent in binary. A calculator stores them in a \u003Cstrong>double\u003C\u002Fstrong>, the 64-bit floating-point type behind almost every spreadsheet cell, so what it holds is \u003Cstrong>2.67499999999999982\u003C\u002Fstrong>. That value sits below the tie, which leaves a rounding rule reading it no option but to go down. The same trap catches any \u003Cstrong>round off calculator\u003C\u002Fstrong> that multiplies by 100 first, turning 1.005 into 1.00 and 8.575 into 8.57.\u003C\u002Fp>\u003Cp>Nothing on this page passes through a float. The engine cuts the digit string at the target position, reads the first discarded digit, then carries the increment leftward through the digits it kept, so that \u003Cstrong>9.99 rounded to one decimal comes out as 10.0\u003C\u002Fstrong> and every finite decimal stays exact.\u003C\u002Fp>\u003Cp>On a single invoice line the gap is one cent. Repeat it over a few hundred lines and the reconciliation stops matching, which is the usual reason someone goes looking for a decimal type such as Python's \u003Cstrong>Decimal\u003C\u002Fstrong>.\u003C\u002Fp>\u003Ch2 id=\"significant-figures\">What is the difference between decimal places and significant figures?\u003C\u002Fh2>\u003Cp>A lab reading of \u003Cstrong>0.00045678\u003C\u002Fstrong> carries eight decimal places and five significant figures, because counting starts at the first non-zero digit. Asked for three significant figures, it comes back as \u003Cstrong>0.000457\u003C\u002Fstrong>, a value that still needs six decimal places to write out. That gap is what makes significant figures the working unit for very small measurements.\u003C\u002Fp>\u003Cp>Rounding 9.99 to two significant figures pushes the carry through both nines and gives \u003Cstrong>10\u003C\u002Fstrong> with no trailing zero, since writing 10.0 would claim a third significant figure the measurement never had. The field accepts \u003Cstrong>1 to 15 significant figures\u003C\u002Fstrong>.\u003C\u002Fp>","2026-08-04T07:29:50.385Z","2026-08-12T10:00:02.632Z","2026-08-12T10:00:00.000Z","en","Rounding Calculator",[16,20,24,28,32,36],{"id":17,"question":18,"answer":19},2236,"How do you round to the nearest hundredth?","\u003Cp>Keep two digits after the decimal point and let the thousandths digit decide. Under half up, 2.675 gives \u003Cstrong>2.68\u003C\u002Fstrong> while 2.674 gives \u003Cstrong>2.67\u003C\u002Fstrong>, since the deciding digit there is 4. The hundredth is the cent, the place where a price, a tax line or an interest amount all stop.\u003C\u002Fp>",{"id":21,"question":22,"answer":23},2237,"Is banker's rounding better than rounding half up?","\u003Cp>Neither rule is more accurate on a single value. Half up moves every tie upward, which adds a small positive bias to any long total, while \u003Cstrong>half to even\u003C\u002Fstrong> splits ties between the two directions and cancels that drift. Rounding 0.5, 1.5, 2.5 and 3.5 to whole numbers gives \u003Cstrong>10\u003C\u002Fstrong> under half up against the exact \u003Cstrong>8\u003C\u002Fstrong> under banker's rounding. Use half up for a figure a person reads on an invoice. Use half to even for a column that gets summed, the rule the IEEE standard and most statistical software settle ties with.\u003C\u002Fp>",{"id":25,"question":26,"answer":27},2238,"Why does my calculator round 2.675 to 2.67?","\u003Cp>The number 2.675 has no exact binary form. A calculator stores it in a \u003Cstrong>double\u003C\u002Fstrong>, the 64-bit float type used almost everywhere, so what it holds is \u003Cstrong>2.67499999999999982\u003C\u002Fstrong>. That value sits below the halfway point, which sends any rounding applied to it downward. The same trap catches 1.005 and 8.575, both coming back one cent short of the expected 1.01 and 8.58. Rounding the typed digits avoids it. In code the fix is a decimal type such as Python's \u003Cstrong>Decimal\u003C\u002Fstrong>, Java's BigDecimal or a SQL NUMERIC column.\u003C\u002Fp>",{"id":29,"question":30,"answer":31},2239,"Does this round calculator work with negative numbers?","\u003Cp>Type a leading minus sign and the six modes carry on as usual. Negative values are where they separate most, since rounding \u003Cstrong>-2.5\u003C\u002Fstrong> to the nearest integer returns \u003Cstrong>-3\u003C\u002Fstrong> under half up and floor while the four other modes all return \u003Cstrong>-2\u003C\u002Fstrong>. Ceiling always moves toward positive infinity whatever the sign it starts from, which is what makes it swap roles with floor on negative values.\u003C\u002Fp>",{"id":33,"question":34,"answer":35},2240,"What is the difference between truncating and rounding down?","\u003Cp>Truncate cuts the surplus digits and keeps the sign, so it always moves toward zero, while floor always moves toward negative infinity. On positive values the two agree, since 2.9 becomes 2 either way. On negative values they part company, with -2.9 giving \u003Cstrong>-2\u003C\u002Fstrong> under truncate against \u003Cstrong>-3\u003C\u002Fstrong> under floor. Truncate is also what a cast to an integer does in C, Java and Go, which is worth remembering before running one on a value that can go negative.\u003C\u002Fp>",{"id":37,"question":38,"answer":39},2241,"How do you round to the nearest hundred or thousand?","\u003Cp>The place selector reaches above the decimal point as well as below, covering ten, hundred and thousand. Rounding \u003Cstrong>1250 to the nearest hundred\u003C\u002Fstrong> gives \u003Cstrong>1300\u003C\u002Fstrong> under half up, 1200 under half to even and 1200 under truncate, because the discarded 50 is an exact tie. At the nearest thousand the same value drops to \u003Cstrong>1000\u003C\u002Fstrong> under half up, the discarded 250 falling below half a step.\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},542,"Rounding Calculator: 6 Modes, Thousand to Thousandth","A rounding calculator for the nearest tenth, hundredth or thousand, comparing six modes. Exact decimals, so 2.675 gives 2.68 where a float gives 2.67.",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},[107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,6,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161],"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","random-letter-generator","mulch-calculator","fence-calculator","upside-down-text-generator","acreage-calculator","gravel-calculator","proportion-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"]