1.3: Calculations, Units, and Unit Conversion
- Page ID
- 102514
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)SI Base Units
| Quantity | Unit | Symbol |
|---|---|---|
| Length | meter | m |
| Mass | kilogram | kg |
| Time | second | s |
| Angle | radian | rad |
| Temperature | kelvin | K |
SI Derived Units
| Quantity | Symbol | Units/Formula |
|---|---|---|
| Acceleration | - | m/s2 |
| Area | - | m2 |
| Density | - | kg/m3 |
| Force | N | kg•m/s² |
| Pressure/Stress | Pa | N/m2 |
| Pressure/Stress | MPa | N/mm² |
| Weight | N | kg•m/s² |
| Work | J | N•m |
SI Prefixes
| Prefix | SI Symbol | Factor |
|---|---|---|
| giga | G | 1,000,000,000 = 109 |
| mega | M | 1,000,000 = 106 |
| kilo | k | 1,000 = 103 |
| milli | m | 0.001 = 10-3 |
| micro | µ | 0.000 001 = 10-6 |
Unit Conversions
The table below shows how to convert units. Open this Excel file or look for the file in your course to access the interactive version that allows you to enter inputs to calculate outputs.
|
Left to right |
These units multiplied by...--> |
..this factor will...--> |
..convert to these units. |
|---|---|---|---|
| Reverse, right to left... | Convert to these units...<-- | <---this factor will... | <---These units divided by... |
| Length | |||
| inches | 2.54 | centimeters | |
| feet | 0.3048 | meters | |
| yards | 0.9144 | meters | |
| miles | 1.609 | kilometers | |
| miles | 5,280 | feet | |
| Area | |||
| square inches | 645.2 | square millimeters | |
| square feet | 0.0929 | square meters | |
| square yards | 0.8361 | square meters | |
| Volume | |||
| cubic inches | 16,387 | cubic millimeters | |
| cubic feet | 0.02832 | cubic meters | |
| cubic yards | 0.7646 | cubic meters | |
| gallons | 0.003785 | cubic meters | |
| Force | |||
| pounds | 4.448 | newtons | |
| kips | 4,448 | newtons | |
| kips | 1,000 | pounds | |
| Tons (short) | 2,000 | pounds | |
| Force per unit length | |||
| pounds per foot | 14.594 | newtons per meter | |
| kips per foot | 14,594 | newtons per meter | |
| Load per unit volume | |||
| pounds per cubic foot | 0.15714 | kilonewtons per cubic meter | |
| Bending moment (torque) | |||
| inch-pounds | 0.113 | newton meters | |
| foot-pounds | 1.356 | newton meters | |
|
Stress, pressure, loading Force per unit area |
|||
| pounds per square inch | 6,895 | pascals | |
| pounds per square inch | 6.895 | kilopascals | |
| pounds per square inch | 0.006895 | megapascals | |
| Mass | |||
| pounds | 0.4536 | kilograms | |
| Moment of Inertia | |||
| inches4 | 416,231 | millimeters4 |