[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-670951-105":59,"doc-detail-670951-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","engineering-formula-sheet-reference-math-science-formulas","Engineering Formula Sheet - Reference - Math & Science Formulas","","Engineering Formula Sheet consolidates essential statistics, probability, and geometry relationships for quick review and problem solving. It includes formulas for mean, median, mode, range, standard deviation, and key probability structures such as independent, mutually exclusive, and conditional events. The sheet further provides binomial probability expressions and foundational engineering equations covering right-triangle geometry, solid volumes and surface areas, constants, SI prefixes, temperature conversions, and core mechanics, electricity, fluid, and thermodynamics relationships.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/engineering-formula-sheet-reference-math-science-formulas/670951/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/engineering-formula-sheet-reference-math-science-formulas/670951.png","ImageObject",300,407,{"name":92,"@type":93},"anakgang17","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02","2026-11-01",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What formulas are included for basic statistics measures like mean and standard deviation?","Question",{"text":112,"@type":113},"The sheet lists mean (µ) and the standard deviation (σ) expressions, along with definitions for individual data values and total data values (xi and n). It also includes median and range formulas.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the sheet represent probability for independent, mutually exclusive, and conditional events?",{"text":117,"@type":113},"Independent events use a product form for P(A and B and C) in sequence, mutually exclusive events use an additive form P(A or B)=PA+PB, and conditional probability is given as P(A|D) with companion expressions for related events.",{"name":119,"@type":110,"acceptedAnswer":120},"Which geometry and engineering volume/surface area formulas are provided?",{"text":121,"@type":113},"It covers right-triangle relationships, trapezoid and cube equations, and the general solids set: rectangular prism, right circular cone, pyramid, sphere, cylinder, and irregular prism, each with volume and surface area where applicable.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},670951,1793573030,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143},962090883568,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Engineering Formula Sheet  \nStatistics  \nMean  \n∑ x  \nµ = mean value  \nΣxi = sum of all data values (x 1 , x2 , x3 ,   n = number of data values  \nStandard Deviation  \n√∑~~ ~~(x~~ ~~)~~ ~~  \nσ = standard deviation  \nxi = individual data value ( x 1 , x2 , x3 ,   n = number of data values  \nMode  \nPlace data in ascending order.  \nMode = most frequently occurring value  \nIf two values occur at the maximum frequency the data set is bimodal.  \nIf three or more values occur at the maximum frequency the data set is multi-modal.  \nMedian  \nPlace data in ascending order.  \nIf n is odd, median = central value  \nIf n is even, median = mean of two central values  \nn = number of data values  \nRange  \nRange = xmax-xmin  \nxmax = maximum data value xmin = minimum data value  \n\n| \u003Cbr>Probability |\n| --- |\n|  |\n| Frequency\u003Cbr> xx\u003Cbr> xx\u003Cbr>fx = relative frequency of outcome x nx = number of events with outcome xn = total number of events\u003Cbr>Px = probability of outcome x\u003Cbr>fa = frequency of all events |\n|  |\n| Binomial Probability (order doesn’t matter)\u003Cbr>\u003Cbr>Pk = binomial probability of k successes in n trials p = probability of a success\u003Cbr>q = 1 – p = probability of failure\u003Cbr>k = number of successes\u003Cbr>n = number of trials |\n\nIndependent Events  \nP (A and B and C) = PAPBPC  \nP (A and B and C) = probability of independent events A and B and C occurring in sequence  \nPA = probability of event A  \nMutually Exclusive Events  \nP (A or B) = PA + PB  \nP (A or B) = probability of either mutually exclusive event A or B occurring in a trial  \nPA = probability of event A  \nΣxi = sum of all data values (x 1 , x2 , x3 ,   n = number of data values  \nConditional Probability  \n\n| ( | ) | ( ) ( | ) |\n| --- | --- |\n|  | ( ) ( | ) ( ) ( | ) |\n\nP (A|D) = probability of event A given event DP(A) = probability of event A occurring P(~A) = probability of event A not occurring  \nP(D|~A) = probability of event D given event A did not occur  \nPLTW, Inc. Engineering Formulas  \n| Right Triangle |  |  |\n| --- | --- | --- |\n| c2 = a2 + b2 | a | \u003Cbr>b |\n| |  |  |\n\nSolid Geometry   \n| Regular Polygons\u003Cbr>\u003Cbr>n = number of sides | \u003Cbr>s\u003Cbr>f |\n| --- | --- |\n\n\n| Trapezoid\u003Cbr>Area = ½(a + b)h | a h\u003Cbr>b |\n| --- | --- |\n\n\n| Cube\u003Cbr>Volume = s3\u003Cbr>Surface Area = 6s2 | s | |\n| --- | --- | --- |\n\n\n| Rectangular Prism |  |  |\n| --- | --- | --- |\n| Volume = wdh\u003Cbr>Surface Area = 2(wd + wh + dh) | h\u003Cbr>w | d |\n\n\n| Right Circular Cone\u003Cbr>\u003Cbr>h\u003Cbr>√ | r |\n| --- | --- |\n\n\n| Pyramid\u003Cbr>\u003Cbr>A = area of base | |\n| --- | --- |\n\n\n| Sphere\u003Cbr>Volume ~~ ~~ r3\u003Cbr>Surface Area = 4 r2 | \u003Cbr>r |\n| --- | --- |\n\n\n| Cylinder\u003Cbr>Volume = r2 h\u003Cbr>Surface Area = 2 r h+2 r2 | \u003Cbr>r\u003Cbr>h |\n| --- | --- |\n\n\n| Irregular Prism\u003Cbr>Volume = Ah\u003Cbr>A = area of base | |\n| --- | --- |\n\nConstants  \ng = 9.8 m/s2 = 32.27 ft/s2 G = 6.67 x 10-11 m3/kg·s2 π = 3.14159  \nPLTW, Inc. Engineering Formulas  \nConversions  \nSI Prefixes  \n\n| Numbers Less Than One |  |  |\n| --- | --- | --- |\n| Power of 10 | Prefix | Abbreviation |\n| 10-1 | deci- | d |\n| 10-2 | centi- | c |\n| 10-3 | milli- | m |\n| 10-6 | micro- | µ |\n| 10-9 | nano- | n |\n| 10-12 | pico- | p |\n| 10-15 | femto- | f |\n| 10-18 | atto- | a |\n| 10-21 | zepto- | z |\n| 10-24 | yocto- | y |\n\n\n| Numbers Greater Than One |  |  |\n| --- | --- | --- |\n| Power of 10 | Prefix | Abbreviation |\n| 101 | deca- | da |\n| 102 | hecto- | h |\n| 103 | kilo- | k |\n| 106 | Mega- | M |\n| 109 | Giga- | G |\n| 1012 | Tera- | T |\n| 1015 | Peta- | P |\n| 1018 | Exa- | E |\n| 1021 | Zetta- | Z |\n| 1024 | Yotta- | Y |\n\nTemperature  \nTK = TC + 273 TR = TF + 460  \nTK = temperature in Kelvin TC = temperature in Celsius TR = temperature in Rankin TF = temperature in Fahrenheit  \nPLTW, Inc. Engineering Formulas  \nEquations (Continued)  \nEnergy: Work  \nW = work F = forced = distance  \nPower  \nP = power E = energy W = work t = time τ = torque  \nrpm = revolutions per minute  \n\n| Efficiency\u003Cbr>y\u003Cbr>Pout = useful power output Pin = total power input |  |\n| --- | --- |\n|  |  |\n| |  |\n\nEnergy: Kinetic  \nK = k","cbCaichQNAIYPKrp","https://ap.wps.com/l/cbCaichQNAIYPKrp","pdf",1106580,"English","# Statistics\n## Mean, Standard Deviation, Mode, Median, Range\n## Probability, Binomial Probability\n## Independent, Mutually Exclusive, Conditional Probability\n# Solid Geometry\n## Right Triangle\n## Regular Polygons and Trapezoid\n## Cube, Rectangular Prism, Cone, Pyramid, Sphere, Cylinder, Irregular Prism\n# Constants and Conversions\n## SI Prefixes\n## Temperature Conversions\n# Engineering Equations\n## Energy and Power\n## Fluid Mechanics and Mechanics\n## Electricity and Thermodynamics\n## Section Properties and Centroid","[{\"question\":\"What formulas are included for basic statistics measures like mean and standard deviation?\",\"answer\":\"The sheet lists mean (µ) and the standard deviation (σ) expressions, along with definitions for individual data values and total data values (xi and n). It also includes median and range formulas.\"},{\"question\":\"How does the sheet represent probability for independent, mutually exclusive, and conditional events?\",\"answer\":\"Independent events use a product form for P(A and B and C) in sequence, mutually exclusive events use an additive form P(A or B)=PA+PB, and conditional probability is given as P(A|D) with companion expressions for related events.\"},{\"question\":\"Which geometry and engineering volume/surface area formulas are provided?\",\"answer\":\"It covers right-triangle relationships, trapezoid and cube equations, and the general solids set: rectangular prism, right circular cone, pyramid, sphere, cylinder, and irregular prism, each with volume and surface area where applicable.\"}]","Engineering Formula Sheet - Reference - Math & Science Formulas | PDF",25]