[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-300759-105":59,"doc-detail-300759-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","pltw-engineering-formula-sheet-v2026-02","PLTW Engineering Formula Sheet - v2026 .02","","PLTW Engineering Formula Sheet v2026 .02 consolidates key STEM reference formulas for common engineering problem solving. It covers statistics essentials such as mean, median, range, mode, and standard deviation, then expands to probability topics including relative frequency, binomial probability, independent events, mutually exclusive events, and conditional probability. Geometry and unit fundamentals follow, featuring right-triangle trigonometry, solid geometry volumes and surface areas, physical constants, conversions, defined units, SI prefixes, and core equations for mass/weight, temperature conversions, energy, and power.",{"@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":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/pltw-engineering-formula-sheet-v2026-02/300759/",{"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/pltw-engineering-formula-sheet-v2026-02/300759.png","ImageObject",300,407,{"name":92,"@type":93},"Franzy","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-09-19",true,{"@type":102,"interactionType":103,"userInteractionCount":46},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What statistical measures and formulas are included in the sheet?","Question",{"text":112,"@type":113},"The sheet provides formulas for population and sample mean, median, range, mode, and standard deviation.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which probability concepts and equations are covered?",{"text":117,"@type":113},"It includes relative frequency, binomial probability, independent events, mutually exclusive events, and conditional probability.",{"name":119,"@type":110,"acceptedAnswer":120},"How does the sheet support engineering calculations involving geometry and units?",{"text":121,"@type":113},"It lists right-triangle relationships, solid geometry volume/surface area formulas, constants, unit conversions, defined units, SI prefixes, and common physics equations for mass/weight, temperature, work, and power.","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},300759,1789777135,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":46,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":41,"preview_page_count":4},2336478945519,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","PLTW Engineering Formula Sheet v2026 .02  \n\n| \u003Cbr>1.0 Statistics |\n| --- |\n| Mean\u003Cbr>μ = σxNi (1.1a) തx = σnxi (1.1b)\u003Cbr>µ = population mean\u003Cbr>തx = sample mean\u003Cbr>Σxi = sum of all data values (x 1 , x2 , x3 ,   ) N = size of population\u003Cbr>n = size of sample |\n\nMedian  \n\n| Place data in ascending order.\u003Cbr>If N is odd, median = central value\u003Cbr>If N is even, median = mean of two central values | (1.2) |\n| --- | --- |\n\nN = size of population  \nRange (1.5)  \n\n| Range = xmax-xmin | (1.3) |\n| --- | --- |\n\nxmax = maximum data value xmin = minimum data value  \nMode  \nPlace data in ascending order.  \nMode = most frequently occurring value (1 .4)  \nIf two values occur with maximum frequency the data set is bimodal.  \nIf three or more values occur with maximum frequency the data set is multi-modal.  \nStandard Deviation  \n\n| σ = ටσሺx~~i~~N-~~ ~~μሻ2 (Population) | (1.5a) |\n| --- | --- |\n| s = ටσሺxn~~i ~~‒-~~ ~~ഥx1ሻ2 (Sample) | (1.5b) |\n\nσ = population standard deviations = sample standard deviation  \nxi = individual data value ( x 1 , x2 , x3 ,   )  \n􀟤 = population mean തx = sample mean N = size of population n = size of sample  \n2.0 Probability  \nFrequency  \n\n| fx = nn~~x~~ | (2 . 1) |\n| --- | --- |\n\nfx = relative frequency of outcome x  \nnx = number of events with outcome xn = total number of events  \nBinomial Probability (order doesn’t matter)  \n\n| n!(pk )(qn-k ) Pk =  k!(n-k)!  | (2.2) |\n| --- | --- |\n\nPk = binomial probability of k successes in n trials p = probability of a success  \nq = 1 – p = probability of failure  \nk = number of successes  \nn = number of trials  \nIndependent Events  \n\n| P (A and B and C) = PAPBPC | (2 .3) |\n| --- | --- |\n\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  \n\n| P (A or B) = PA + PB | (2.4) |\n| --- | --- |\n\nP (A or B) = probability of either mutually exclusive event A or B occurring in a trial  \nPA = probability of event A  \nConditional Probability  \n\n| 􀜲ሺ􀜣ȁ􀜦ሻ = 􀯉ሺ􀮺ሻ~~ ~~∙􀯉൫~~􀜦~~􀯉หሺ􀮺ሻ~~􀜣~~൯+∙~~ ~~􀯉ሺ􀯉ሺ􀮽~ȁ􀮺􀮺ሻሻ~~ ~~∙~~ ~~􀯉ሺ􀮽ȁ~􀮺ሻ | (2.5) |\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  \n© 2026 Project Lead The Way, Inc. PLTW Engineering Formula Sheet  \nEES IED POE DE CEA AE ES CIM EDD 1  \n| Right Triangle |  |  |  |\n| --- | --- | --- | --- |\n| c2 = a2 + b2 sin θ = ac cos θ = bc tan θ = ab | (3.4)\u003Cbr>(3.5)\u003Cbr>(3.6)\u003Cbr>(3.7) | a | |\n\n4.0 Solid Geometry  \n| Trapezoid\u003Cbr>Area = ½(a + b)h (3.16) | a\u003Cbr>hb |\n| --- | --- |\n\n\n| Cube\u003Cbr>Volume = s3 (4 . 1)\u003Cbr>Surface Area = 6s2 (4 .2) | s | |\n| --- | --- | --- |\n\nRectangular Prism  \nVolume = wdh (4 .3) h  \nSurface Area = 2(wd + wh + dh) (4 .4) w d  \n\n| Right Circular Cone\u003Cbr>Volume = πr~~ ~~23h\u003Cbr>h\u003Cbr>(4.5)\u003Cbr>Total Surface Area = π r2 + π rඥ r2 +h2\u003Cbr>(4.6) | r |\n| --- | --- |\n\n\n| Pyramid\u003Cbr>Volume = Ah3 (4.7)\u003Cbr>A = area of base | |\n| --- | --- |\n\n© 2026 Project Lead The Way, Inc. PLTW Engineering Formula Sheet  \nSphere  \nVolume = 43 π r3 (4.8)  \nSurface Area = 4 π r2 (4 .9)  \n| Cylinder\u003Cbr>Volume = π r2 h (4 . 10)\u003Cbr>Surface Area = 2 π r h+2 π r2 (4 . 11) | \u003Cbr>r\u003Cbr>h |\n| --- | --- |\n\n\n| Irregular Prism\u003Cbr>Volume = Ah (4.12)\u003Cbr>A = area of base | |\n| --- | --- |\n\n5.0 Constants  \ng = -9.81 m/s2 = -32.17 ft/s2 G = 6.67 x 10-11 m3/kg·s2 π = 3.14159  \nEES IED POE DE CEA AE ES CIM EDD 2  \n6.0 Conversions  \nMass/Weight (6.1)  \n1 kg = 2.205 lbm  \n1 slug = 32.2 lbm  \n1 ton = 2000 lb  \n1 lb = 16 oz  \nTemperature Unit Equivalents (6.6)  \n*Use equation in section 9.0 to convert  \nΔ1 K = Δ 1 ºC = Δ 1.8 ºF  \n= Δ 1.8 ºR  \nForce (6 .7)  \n1 N = 0.225 lb  \n1 kip = 1,000 lb  \nPressure (6 .8)  \n1 atm = 1.01325 bar = 33.9 ft H2O  \n= 29.92 in. Hg = 760 mm Hg = 101,325 Pa  \n= 14.7 psi 1psi = 2.31 ft of H2O  \nPower (6 .9)  \n1 W = 3.412 Btu/h = 0.00134 hp = 14.34 cal/min = 0.7376 ft·lbf/s  \n1 hp = 550 ft∙lb/sec  \nEnergy (6.","cbCaikI8g72lXjTb","https://ap.wps.com/l/cbCaikI8g72lXjTb","pdf",1279790,12,"English","# 1.0 Statistics\n# 2.0 Probability\n# 3.0 Right Triangle\n# 4.0 Solid Geometry\n# 5.0 Constants\n# 6.0 Conversions\n# 7.0 Defined Units\n# 8.0 SI Prefixes\n# 9.0 Equations","[{\"question\":\"What statistical measures and formulas are included in the sheet?\",\"answer\":\"The sheet provides formulas for population and sample mean, median, range, mode, and standard deviation.\"},{\"question\":\"Which probability concepts and equations are covered?\",\"answer\":\"It includes relative frequency, binomial probability, independent events, mutually exclusive events, and conditional probability.\"},{\"question\":\"How does the sheet support engineering calculations involving geometry and units?\",\"answer\":\"It lists right-triangle relationships, solid geometry volume/surface area formulas, constants, unit conversions, defined units, SI prefixes, and common physics equations for mass/weight, temperature, work, and power.\"}]","PLTW Engineering Formula Sheet - v2026 .02 | PDF"]