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Engineering Formula SheetStatisticsModeMeanPlace data in ascending order.Mode most frequently occurring value xµ mean valueΣxi sum of all data values (x1, x2, x3, n number of data values (xMedianPlace data in ascending order.If n is odd, median central valueIf n is even, median mean of two central valuesStandard Deviation If two values occur at the maximum frequency thedata set is bimodal.If three or more values occur at the maximumfrequency the data set is multi-modal.)n number of data valuesσ standard deviationxi individual data value ( x1, x2, x3, Rangen number of data valuesxmax maximum data valuexmin minimum data valueRange xmax - xminProbabilityIndependent EventsP (A and B and C) PAPBPCFrequencyP (A and B and C) probability of independentevents A and B and C occurring in sequencePA probability of event AxxxxMutually Exclusive Eventsfx relative frequency of outcome xnx number of events with outcome xn total number of eventsPx probability of outcome xfa frequency of all eventsBinomial Probability (order doesn’t matter)P (A or B) PA PBP (A or B) probability of either mutually exclusiveevent A or B occurring in a trialPA probability of event AΣxi sum of all data values (x1, x2, x3, n number of data valuesConditional ProbabilityPk binomial probability of k successes in n trialsp probability of a successq 1 – p probability of failurek number of successesn number of trialsPLTW, Inc.( )( )( )( )( )( )( )P (A D) probability of event A given event DP(A) probability of event A occurringP( A) probability of event A not occurringP(D A) probability of event D given event A did not occurEngineering FormulasIED POEDECEAAEBECIM EDD1

Plane GeometryEllipseRectangle2bCirclePerimeter 2a 2bArea ab2aBTriangleParallelogramhArea bha b c – 2bc·cos A222b a c – 2ac·cos B222c a b – 2ab·cos CC2ch2AbsRegular PolygonsRight Triangle2a2b2Area ½ bhf2c a bcan number of sidesθbahTrapezoidArea ½(a b)hhhbhSolid GeometryCubeSpheres3Volume s2Surface Area 6sr3sVolume rSurface Area 4sr2Rectangular PrismCylinderrhVolume wdhSurface Area 2(wd wh dh)dwh2Volume r hSurface Area 2r h 2r2Right Circular ConehIrregular Prismr hVolume AhA area of basePyramidhA area of basePLTW, Inc.Constants2g 9.8 m/s 32.27 ft/s-1132G 6.67 x 10 m /kg·sπ 3.14159Engineering FormulasIED POEDE2CEAAEBECIM EDD2

ConversionsMassAreaForce21 acre 4047 m2 43,560 ft2 0.00156 mi1 kg 2.205 lbm1 slug 32.2 lbm1 ton 2000 lbm1N1 kipEnergy 0.225 lbf 1,000 lbf1J 0.239 cal-4 9.48 x 10 Btu 0.7376 ft·lbf1kW h 3,600,000 JPressureLengthVolume1m1 km1 in.1 mi1 yd 3.28 ft 0.621 mi 2.54 cm 5280 ft 3 ft1L1mL1 atm 0.264 gal3 0.0353 ft 33.8 fl oz3 1 cm 1 cc1psiTemperature UnitEquivalentsTime1d1h1 min1 yr1K 24 h 60 min 60 s 365 d 1 ºC 1.8 ºF 1.8 ºR 1.01325 bar 33.9 ft H2O 29.92 in. Hg 760 mm Hg 101,325 Pa 14.7 psi 2.31 ft of H2ODefined Units1J1N1 Pa1V1W1W1 Hz1F1HPower1WSee below fortemperature calculation 3.412 Btu/h 0.00134 hp 14.34 cal/min 0.7376 ft·lbf/s 1 N·m 1 kg·m / s2 1 N / m2 1W/A 1J/s 1V/A 1 s-1 1 A·s / V 1 V·s / VSI PrefixesNumbers Less Than OnePower of ozeptoyocto-EquationsMass and WeightNumbers Greater Than OnePower of 11024dcmµnpfazyTemperatureTK TC 273M VDmTR TF 460W mgTF PLTW, Inc.dahkMGTPEZYForc

Engineering Formula Sheet Probability Conditional Probability Binomial Probability (order doesn’t matter) P k ( binomial probability of k successes in n trials p probability of a success –p probability of failure k number of successes n number of trials Independent Events P (A and B and C) P A P B P C

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