21: Appendix E—Useful Formulas
- Page ID
- 31591
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Length Conversions
to miles (mi) = km × 0.62
= nmi÷1.151
= ft÷5,280
to kilometers (km) = mi × 1.61
= nmi×1.852
= ft÷3,281
to nautical miles (nmi) = mi ÷ 1.51
= km÷1.852
= ft÷6,076
to feet (ft) = mi × 5,280
= km×3,281
= nmi×6,076
Area Conversions
to square miles (mi2) = km2 ÷ 2.59
= nmi2 × 1.324
to square kilometers (km2) = mi2 × 2.59
= nmi2 × 3.43
to square nautical miles (nmi2) = mi2 ÷ 1.324
= km2 ÷ 3.43
Volume Conversions
to gallons (gal) = m3 × 264.2
= L÷3.785
to cubic meters (m3) = gal ÷ 264.2
= L÷1,000
to liters (L) = gal × 3.785
= m3 × 1,000
Pressure Conversions
to atmospheres (atm) = mb ÷ 1,013
= in. Hg÷29.92
= lb/in2 ÷ 14.7
= Pa÷101,300
to millibars (mb) = atm × 1,013
= in. Hg×33.864
= lb/in2 × 68.948
= Pa÷100
to inches of Mercury (in. Hg) = atm × 29.92
= mb÷33.864
= lb/in2 × 2.036
= Pa÷3,386
to Pascals (Pa) = atm × 101,300
= mb×100
= in. Hg×3,386
= lb/in2 × 6,895
Speed Conversions
to miles per hour (mph) = knots × 1.151
= km/hr÷1.609
= ft/s÷1.467
= m/s×2.237
to nautical miles per hour (knots) = mph ÷ 1.151
= km/hr÷1.852
= ft/s÷1.688
= m/s×1.944
to kilometers per hour (km/hr) = mph × 1.609
= knots×1.852
= ft/s×1.097
= m/s×3.6
to feet per second (f/s) = mph × 1.467
= km/hr÷1.097
= knots×1.688
= m/s×3.281
to meters per second (m/s) = mph ÷ 2.237
= knots÷1.944
= km/hr÷3.6
= ft/s÷3.281
Temperature
To convert degrees Fahrenheit (°F) to degrees Celsius (°C): (°F – 32) ÷ 1.8
To convert degrees Celsius (°C) to degrees Fahrenheit (°F): (°C × 1.8) + 32)