Appendix B: Conversion Factors
- Page ID
- 7934
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Table B1 - Length
| m | cm | km | |
|---|---|---|---|
| 1 meter | 1 | 102 | 10-3 |
| 1 centimeter | 10-2 | 1 | 10-5 |
| 1 kilometer | 103 | 105 | 1 |
| 1 inch | 2.540 x 10-2 | 2.540 | 2.540 x 10-5 |
| 1 foot | 0.3048 | 30.48 | 3.048 x 10-4 |
| 1 mile | 1609 | 1.609 x 104 | 1.609 |
| 1 angstrom | 10-10 | 10-8 | 10-13 |
| 1 fermi | 10-15 | 10-13 | 10-18 |
| 1 light-year | 9.460 x 1015 | 9.460 x 1017 | 9.460 x 1012 |
| in | ft | mi | |
|---|---|---|---|
| 1 meter | 39.37 | 3.281 | 6.214 x 10−4 |
| 1 centimeter | 0.3937 | 3.281 x 10−2 | 6.214 x 10−6 |
| 1 kilometer | 3.937 x 104 | 3.281 x 10−4 | 0.6214 |
| 1 inch | 1 | 8.333 x 10−2 | 1.578 x 10−5 |
| 1 foot | 12 | 1 | 1.894 x 10−4 |
| 1 mile | 6.336 x 104 | 5280 | 1 |
Area
1 cm2 = 0.155 in2
1 m2 = 104 cm2 = 10.76 ft2
1 in2 = 6.452 cm2
1 ft2 = 144 in2 = 0.0929 m2
Volume
1 liter = 1000 cm3 = 10−3 m3 = 0.03531 ft3 = 61.02 in3
1 ft3 = 0.02832 m3 = 28.32 liters = 7.477 gallons
1 gallon = 3.788 liters
Table B2 - Time
| s | min | h | day | yr | |
|---|---|---|---|---|---|
| 1 second | 1 | 1.667 x 10-2 | 2.778 x 10-4 | 1.157 x 10-5 | 3.169 x 10-8 |
| 1 minute | 60 | 1 | 1.667 x 10-2 | 6.944 x 10-4 | 1.901 x 10-6 |
| 1 hour | 3600 | 60 | 1 | 4.167 x 10-2 | 1.141 x 10-4 |
| 1 day | 8.640 x 104 | 1440 | 24 | 1 | 2.738 x 10-3 |
| 1 year | 3.156 x 107 | 5.259 x 105 | 8.766 x 103 | 365.25 | 1 |
Table B3 - Speed
| m/s | cm/s | ft/s | mi/h | |
|---|---|---|---|---|
| 1 meter/second | 1 | 102 | 3.281 | 2.237 |
| 1 centimeter/second | 10-2 | 1 | 3.281 x 10−2 | 2.237 x 10−2 |
| 1 foot/second | 0.3048 | 30.48 | 1 | 0.6818 |
| 1 mile/hour | 0.4470 | 44.70 | 1.467 | 1 |
Acceleration
1 m/s2 = 100 cm/s2 = 3.281 ft/s2
1 cm/s2 = 0.01 m/s2 = 0.03281 ft/s2
1 ft/s2 = 0.3048 m/s2 = 30.48 cm/s2
1 mi/h • s = 1.467 ft/s2
Table B4 - Mass
| kg | g | slug | u | |
|---|---|---|---|---|
| 1 kilogram | 1 | 103 | 6.852 x 10-2 | 6.024 x 1026 |
| 1 gram | 10-3 | 1 | 6.852 x 10-5 | 6.024 x 1023 |
| 1 slug | 14.59 | 1.459 x 104 | 1 | 8.789 x 1027 |
| 1 atomic mass unit | 1.661 x 10-27 | 1.661 x 10-24 | 1.138 x 10-28 | 1 |
| 1 metric ton | 1000 |
Table B5 - Force
| N | dyne | lb | |
|---|---|---|---|
| 1 newton | 1 | 105 | 0.2248 |
| 1 dyne | 10-5 | 1 | 2.248 x 10-6 |
| 1 pound | 4.448 | 4.448 x 105 | 1 |
Table B6 - Pressure
*Where the acceleration due to gravity is 9.80665 m/s2 and the temperature is 0 °C
| Pa | dyne/cm2 | atm | cm Hg | lb/in2 | |
|---|---|---|---|---|---|
| 1 pascal | 1 | 10 | 9.869 x 10−6 | 7.501 x 10−4 | 1.450 x 10−4 |
| 1 dyne/ centimeter2 | 0.1 | 1 | 9.869 x 10−7 | 7.501 x 10−5 | 1.450 x 10−5 |
| 1 atmosphere | 1.013 x 105 | 1.013 x 106 | 1 | 76 | 14.70 |
| 1 centimeter mercury* | 1.333 x 103 | 1.333 x 104 | 1.316 x 10-2 | 1 | 0.1934 |
| 1 pound/inch2 | 6.895 x 103 | 6.895 x 104 | 6.805 x 10-2 | 5.171 | 1 |
| 1 bar | 105 | ||||
| 1 torr | 1 (mm Hg) |
Table B7 - Work, Energy, Heat
| J | erg | ft • lb | eV | cal | Btu | |
|---|---|---|---|---|---|---|
| 1 joule | 1 | 107 | 0.7376 | 6.242 x 1018 | 0.2389 | 9.481 x 10-4 |
| 1 erg | 10-7 | 1 | 7.376 x 10-8 | 6.242 x 1011 | 2.389x 10-8 | 9.481 x 10-11 |
| 1 foot-pound | 1.356 | 1.356 x 107 | 1 | 8.464 x 1018 | 0.3239 | 1.285 x 10-3 |
| 1 electron-volt | 1.602 x 10-19 | 1.602 x 10-12 | 1.182 x 10-19 | 1 | 3.827 x 10-20 | 1.519 x 10-22 |
| 1 calorie | 4.186 | 4.186 x 107 | 3.088 | 2.613 x 1019 | 1 | 3.968 x 10-3 |
| 1 British thermal unit | 1.055 x 103 | 1.055 x 1010 | 7.779 x 102 | 6.585 x 1021 | 2.520 x 102 | 1 |
| 1 kilowatt-hour | 3.600 x 106 |
Power
1 W = 1 J/s
1 hp = 746 W = 550 ft • lb/s
1 Btu/h = 0.293 W
Angle
1 rad = 57.30° = \(\frac{180^{o}}{\pi}\)
1° = 0.01745 rad = \(\frac{\pi}{180\; rad}\)
1 revolution = 360° = 2\(\pi\) rad
1 rev/min (rpm) = 0.1047 rad/s
Contributors and Attributions
Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).