66.8: SI Units
- Page ID
- 91938
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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 \(\PageIndex{1}\): SI base units.
|
Name |
Symbol |
Quantity |
|---|---|---|
|
meter |
m |
length |
|
kilogram |
kg |
mass |
|
second |
s |
time |
|
ampere |
|
electric current |
|
kelvin |
|
temperature |
|
mole |
mol |
amount of substance |
|
candela |
cd |
luminous intensity |
A
KTable \(\PageIndex{2}\): Derived SI units
| Name | Symbol | Definition | Base Units | Quantity |
|---|---|---|---|---|
| radian | \(\mathrm{rad}\) | \(\mathrm{m} / \mathrm{m}\) | - | plane angle |
| steradian | \(\mathrm{sr}\) | \(\mathrm{m}^2 / \mathrm{m}^2\) | - | solid angle |
| newton | \(\mathrm{N}\) | \(\mathrm{kg} \mathrm{m} \mathrm{s}^{-2}\) | \(\(\mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-2}\) | force |
| joule | \(\mathrm{J}\) | \(\mathrm{N} \mathrm{m}\) | \(\mathrm{kg} \mathrm{m}^2 \mathrm{~s}^{-2}\) | energy |
| watt | \(\mathrm{W}\) | \(\mathrm{J} / \mathrm{s}\) | \(\mathrm{kg} \mathrm{m}^2 \mathrm{~s}^{-3}\) | power |
| pascal | \(\mathrm{Pa}\) | \(\mathrm{N} / \mathrm{m}^2\) | \(\mathrm{~kg} \mathrm{~m}^{-1} \mathrm{~s}^{-2}\) | pressure |
| hertz | \(\mathrm{Hz}\) | \(\mathrm{s}^{-1}\) | \(\mathrm{~s}^{-1}\) | frequency |
| coulomb | \(\mathrm{C}\) | \(\mathrm{A} \mathrm{s}\) | \(\mathrm{A} \mathrm{s}^2\) | electric charge |
| volt | \(\mathrm{V}\) | \(\mathrm{J} / \mathrm{C}\) | \(\mathrm{kg} \mathrm{m}^{-1} \mathrm{~A}^{-3}\) | electric potential |
| ohm | \(\Omega\) | \(\mathrm{V} / \mathrm{A}\) | \(\mathrm{kg} \mathrm{m}^2 \mathrm{~A}^{-2} \mathrm{~s}^{-3}\) | electrical resistance |
| siemens | \(\mathrm{S}\) | \(\mathrm{A} / \mathrm{V}\) | \(\mathrm{kg}^{-1} \mathrm{~m}^{-2} \mathrm{~A}^2 \mathrm{~s}^3\) | electrical conductance |
| farad | \(\mathrm{F}\) | \(\mathrm{C} / \mathrm{V}\) | \(\mathrm{kg}^{-1} \mathrm{~m}^{-2} \mathrm{~A}^2 \mathrm{~s}^4\) | capacitance |
| weber | \(\mathrm{Wb}\) | \(\mathrm{V} \mathrm{s}\) | \(\mathrm{kg} \mathrm{m}^2 \mathrm{~A}^{-1} \mathrm{~s}^{-2}\) | magnetic flux |
| tesla | \(\mathrm{T}\) | \(\mathrm{Wb} / \mathrm{m}^2\) | \(\mathrm{~kg} \mathrm{~A}^{-1} \mathrm{~s}^{-2}\) | magnetic induction |
| henry | \(\mathrm{H}\) | \(\mathrm{Wb} / \mathrm{A}\) | \(\mathrm{kg} \mathrm{m}^2 \mathrm{~A}^{-2} \mathrm{~s}^{-2}\) | induction |
| lumen | \(\mathrm{lm}\) | \(\mathrm{cd} \mathrm{sr}\) | \(\mathrm{cd} \mathrm{sr}^{-2}\) | luminous flux |
| lux | \(\mathrm{lx}\) | \(\mathrm{lm} / \mathrm{m}^2\) | \(\mathrm{~cd} \mathrm{sr} \mathrm{m}^{-2}\) | illuminance |
| becquerel | \(\mathrm{Bq}\) | \(\mathrm{s} \mathrm{s}^{-1}\) | \(\mathrm{~s}^{-1}\) | radioactivity |
| gray | \(\mathrm{Gy}\) | \(\mathrm{J} / \mathrm{kg}\) | \(\mathrm{m}^2 \mathrm{~s}^{-2}\) | absorbed dose |
| sievert | \(\mathrm{Sv}\) | \(\mathrm{J} / \mathrm{kg}\) | \(\mathrm{m}^2 \mathrm{~s}^{-2}\) | dose equivalent |
| katal | \(\mathrm{kat}\) | \(\mathrm{mol} / \mathrm{s}\) | \(\mathrm{mol} \mathrm{s}^{-1}\) | catalytic activity |
Table \(\PageIndex{3}\): SI units prefixes.
| Prefix | Symbol | Definition | English |
|---|---|---|---|
| yotta- | \(\mathrm{Y}\) | \(10^{24}\) | septillion |
| zetta- | \(\mathrm{Z}\) | \(10^{21}\) | sextillion |
| exa- | \(\mathrm{E}\) | \(10^{18}\) | quintillion |
| peta- | \(\mathrm{P}\) | \(10^{15}\) | quadrillion |
| tera- | \(\mathrm{T}\) | \(10^{12}\) | trillion |
| giga- | \(\mathrm{G}\) | \(10^9\) | billion |
| mega- | \(\mathrm{M}\) | \(10^6\) | million |
| kilo- | \(\mathrm{k}\) | \(10^3\) | thousand |
| hecto- | \(\mathrm{h}\) | \(10^2\) | hundred |
| deka- | \(\mathrm{da}\) | \(10^1\) | ten |
| deci- | \(\mathrm{d}\) | \(10^{-1}\) | tenth |
| centi- | \(\mathrm{c}\) | \(10^{-2}\) | hundredth |
| milli- | \(\mathrm{m}\) | \(10^{-3}\) | thousandth |
| micro- | \(\mu\) | \(10^{-6}\) | millionth |
| nano- | \(\mathrm{n}\) | \(10^{-9}\) | billionth |
| pico- | \(\mathrm{p}\) | \(10^{-12}\) | trillionth |
| femto- | \(\mathrm{f}\) | \(10^{-15}\) | quadrillionth |
| atto- | \(\mathrm{a}\) | \(10^{-18}\) | quintillionth |
| zepto- | \(\mathrm{z}\) | \(10^{-21}\) | sextillionth |
| yocto- | \(\mathrm{y}\) | \(10^{-24}\) | septillionth |
Table \(\PageIndex{4}\): Prefixes for computer use only
| Prefix | Symbol | Definition | |
|---|---|---|---|
| yobi- | \(\mathrm{Yi} \) | \(2^{80} \) | =1,208,925,819,614,629,174,706,176 |
| zebi- | \(\mathrm{Zi} \) | \(2^{70} \) | =1,180,591,620,717,411,303,424 |
| exbi- | \(\mathrm{Ei} \) | \(2^{60} \) | =1,152,921,504,606,846,976 |
| pebi- | \(\mathrm{Pi} \) | \(2^{50} \) | =1,125,899,906,842,624 |
| tebi- | \(\mathrm{Ti} \) | \(2^{40} \) | =1,099,511,627,776 |
| gibi- | \(\mathrm{Gi} \) | \(2^{30} \) | =1,073,741,824 |
| mebi- | \(\mathrm{Mi} \) | \(2^{20} \) | =1,048,576 |
| kibi- | \(\mathrm{Ki} \) | \(2^{10} \) | =1,024 |