3240:
36:
133:
1790:
817:
A systems of quantities relates physical quantities, and due to this dependence, a limited number of quantities can serve as a basis in terms of which the dimensions of all the remaining quantities of the system can be defined. A set of mutually independent quantities may be chosen by convention to
493:
Physical quantities are normally typeset in italics. Purely numerical quantities, even those denoted by letters, are usually printed in roman (upright) type, though sometimes in italics. Symbols for elementary functions (circular trigonometric, hyperbolic, logarithmic etc.), changes in a quantity
1638:
1350:
quantity within some scope of context (not necessarily base quantities) and present in the table below some of the most commonly used symbols where applicable, their definitions, usage, SI units and SI dimensions – where denotes the dimension of
3238:
a web component (custom HTML element) for expressing physical quantities on the web/Internet, featuring self-contained unit conversion, a compact and clean UI, no redundant dual units, and seamless integration across all websites and platforms.
1269:
2601:
1421:
with the unit normal for a surface, since the amount of current passing through the surface is reduced when the current is not normal to the area. Only the current passing perpendicular to the surface contributes to the current passing
1358:
For time derivatives, specific, molar, and flux densities of quantities, there is no one symbol; nomenclature depends on the subject, though time derivatives can be generally written using overdot notation. For generality we use
1667:
2512:
1925:
2733:
1519:
2887:
2180:
2106:
2668:
2300:
2448:
2802:
2028:
1542:
2344:
435:
The multiplication sign is usually left out, just as it is left out between variables in the scientific notation of formulas. The convention used to express quantities is referred to as
2842:
3078:
1415:
749:
are usually used in scientific contexts due to their ease of use, international familiarity and prescription. For example, a quantity of mass might be represented by the symbol
381:
2967:"The concept 'quantity' may be generically divided into, e.g. 'physical quantity', 'chemical quantity', and 'biological quantity', or 'base quantity' and 'derived quantity'."
1385:
needs to be written. For spatial density, current, current density and flux, the notations are common from one context to another, differing only by a change in subscripts.
280:
1207:
2535:
1868:
673:
2225:
430:
335:
728:
in 1822. By convention, physical quantities are organized in a dimensional system built upon base quantities, each of which is regarded as having its own dimension.
303:
1785:{\displaystyle \int X\mathrm {d} ^{n}x\equiv \int X\mathrm {d} V_{n}\equiv \int \cdots \int \int X\mathrm {d} x_{1}\mathrm {d} x_{2}\cdots \mathrm {d} x_{n}}
1096:
are thus, of course, derived from the length, but included for completeness as they occur frequently in many derived quantities, in particular densities.
468:
2459:
2393:
1874:
599:
is a physical quantity that has magnitude but no direction. Symbols for physical quantities are usually chosen to be a single letter of the
3126:
Physics for
Scientists and Engineers: With Modern Physics (6th Edition), P.A. Tipler, G. Mosca, W.H. Freeman and Co, 2008, 9-781429-202657
2694:
1452:
2854:
2131:
2057:
100:
2626:
72:
3072:
2261:
2408:
1633:{\displaystyle \mathrm {d} ^{n}x\equiv \mathrm {d} V_{n}\equiv \mathrm {d} x_{1}\mathrm {d} x_{2}\cdots \mathrm {d} x_{n}}
684:
79:
17:
3034:
634:. Symbols for physical quantities that are vectors are in bold type, underlined or with an arrow above. For example, if
2771:
1982:
842:
819:
53:
3163:
3114:
3104:
2305:
119:
621:
86:
3186:
2921:
2814:
3217:
3194:
3171:
3145:
57:
68:
3152:
3255:
3209:
794:
share extra commonalities beyond their dimension and units allowing their comparison; for example, not all
203:). Quantities that are vectors have, besides numerical value and unit, direction or orientation in space.
2916:
1391:
1080:
Derived quantities are those whose definitions are based on other physical quantities (base quantities).
826:
units and dimensions are listed in the following table. Other conventions may have a different number of
340:
3059:
1264:{\displaystyle \mathbf {A} \equiv A\mathbf {\hat {n}} ,\quad \mathbf {S} \equiv S\mathbf {\hat {n}} }
954:
2596:{\displaystyle \mathbf {F} \cdot \mathbf {\hat {n}} ={\frac {\mathrm {d} \Phi _{F}}{\mathrm {d} A}}}
241:
1377:
respectively. No symbol is necessarily required for the gradient of a scalar field, since only the
795:
785:
153:
1066:
can be written explicitly to emphasize the fact that the quantity involves plane or solid angles.
827:
773:
441:. In formulas, the unit can be treated as if it were a specific magnitude of a kind of physical
216:
46:
1844:
649:
626:
are physical quantities that possess both magnitude and direction and whose operations obey the
383:
is the unit. Conversely, the numerical value expressed in an arbitrary unit can be obtained as:
2605:
Flow of a property though a cross-section/surface boundary per unit cross-section/surface area
1447:
1441:
93:
3009:
2926:
2207:
389:
2931:
1058:, are defined as derived dimensionless quantities in the SI. For some relations, their units
488:
308:
3109:
Essential
Principles of Physics, P.M. Whelan, M.J. Hodgson, 2nd Edition, 1978, John Murray,
3220:
3197:
3174:
3155:
3148:
746:
737:
698:
447:
8:
1530:
977:
835:
781:
777:
715:
172:
1023:
520:
288:
3110:
3100:
3068:
2946:
1650:
1122:
527:
437:
818:
act as such a set, and are called base quantities. The seven base quantities of the
638:
is the speed of a particle, then the straightforward notations for its velocity are
219:
of a physical quantity is expressed as a comparison to a unit of that quantity. The
3123:, G.L. Trigg, 2nd Edition, VHC Publishers, Hans Warlimont, Springer, 2005, pp 12–13
2898:
2745:
2401:
1316:
1000:
594:
588:
459:
International recommendations for the use of symbols for quantities are set out in
3235:
1417:
is a unit vector in the direction of flow, i.e. tangent to a flowline. Notice the
1339:, are used interchangeably in the same context; sometimes they are used uniquely.
3213:
3190:
3167:
2397:
1837:
1075:
812:
776:
is not necessarily sufficient for quantities to be comparable; for example, both
616:
166:
3120:
1536:
1312:
725:
604:
600:
464:
3038:, Firmin Didot, Paris, 1822. (In this book, Fourier introduces the concept of
2507:{\displaystyle \Phi _{F}=\iint _{S}\mathbf {F} \cdot \mathrm {d} \mathbf {A} }
3249:
2977:
2897:
has a moment about a point or axes, often relates to tendency of rotation or
762:
460:
3054:
2452:
2197:
758:
697:
can be used to describe more general physical properties. For example, the
631:
3160:
533:π for the ratio of a circle's circumference to its diameter, 3.14159265...
471:. For example, the recommended symbol for the physical quantity "mass" is
1418:
1195:
1152:
Angular position, angle of rotation (can be treated as vector or scalar)
1055:
1051:
987:
212:
157:
3183:
2941:
2680:
Current density (sometimes called flux density in transport mechanics)
1920:{\displaystyle {\dot {q}}\equiv {\frac {\mathrm {d} q}{\mathrm {d} t}}}
1319:
are associated with many quantities. Sometimes different terms such as
3232:
online calculation and scripting tool supporting physical quantities.
1063:
442:
3141:
35:
3224:
3201:
3178:
2936:
1382:
941:
754:
548:, representing differences (finite or otherwise) in the quantities
475:, and the recommended symbol for the quantity "electric charge" is
200:
132:
2728:{\displaystyle I=\iint \mathbf {J} \cdot \mathrm {d} \mathbf {S} }
2672:
Rate of flow of property through a cross-section/surface boundary
1199:
1036:
137:
3206:
3055:
1342:
To clarify these effective template-derived quantities, we use
1307:
Important and convenient derived quantities such as densities,
1093:
1059:
1010:
964:
918:
877:
694:
627:
3010:"ISO 80000-1:2009(en) Quantities and units — Part 1: General"
2737:
Rate of flow of property per unit cross-section/surface area
1514:{\displaystyle X\equiv X\left(x_{1},x_{2}\cdots x_{n}\right)}
895:
2882:{\displaystyle \mathbf {m} =\mathbf {r} \times \mathbf {q} }
2517:
Flow of a property though a cross-section/surface boundary.
2175:{\displaystyle q_{n}={\frac {\mathrm {d} q}{\mathrm {d} n}}}
2101:{\displaystyle q_{m}={\frac {\mathrm {d} q}{\mathrm {d} m}}}
1308:
1302:
1089:
1088:
Important applied base units for space and time are below.
931:
908:
701:
possesses magnitude, direction, and orientation qualities.
177:
1378:
831:
3229:
2663:{\displaystyle I={\frac {\mathrm {d} q}{\mathrm {d} t}}}
2295:{\displaystyle q=\int q_{\lambda }\mathrm {d} \lambda }
2256:
Two definitions are used, for frequency and wavelength:
1433:
The calculus notations below can be used synonymously.
823:
743:
784:
have dimension of square length per time (in units of
199:
is the numerical value and kg is the unit symbol (for
2857:
2817:
2774:
2697:
2629:
2538:
2462:
2411:
2349:
Amount of property per unit wavelength or frequency.
2308:
2264:
2210:
2134:
2060:
1985:
1877:
1847:
1670:
1545:
1455:
1394:
1210:
652:
392:
343:
311:
291:
244:
2443:{\displaystyle q=\iiint F\mathrm {d} A\mathrm {d} t}
2229:
Rate of change of property with respect to position
502:, are also recommended to be printed in roman type.
152:) is a property of a material or system that can be
60:. Unsourced material may be challenged and removed.
2881:
2836:
2796:
2727:
2662:
2595:
2506:
2442:
2338:
2294:
2219:
2174:
2100:
2022:
1919:
1862:
1784:
1632:
1513:
1409:
1263:
667:
424:
375:
329:
297:
274:
3050:
3048:
2797:{\displaystyle \mathbf {m} =\mathbf {r} \wedge q}
2553:
2023:{\displaystyle q=\int \rho _{n}\mathrm {d} V_{n}}
1401:
1255:
1228:
3247:
1929:Rate of change of property with respect to time
2339:{\displaystyle q=\int q_{\nu }\mathrm {d} \nu }
1198:(Magnitude of surface area, directed normal to
3045:
3014:International Organization for Standardization
801:
704:
689:Scalar and vector quantities are the simplest
3004:
3002:
3000:
2998:
2996:
1069:
164:, which is the algebraic multiplication of a
3056:International Bureau of Weights and Measures
2035:(length, area, volume or higher dimensions)
399:
393:
318:
312:
257:
251:
160:. A physical quantity can be expressed as a
27:Measurable property of a material or system
454:
2993:
2837:{\displaystyle \mathbf {m} =\mathbf {r} q}
2184:Amount of property per mole of substance
724:of a physical quantity was introduced by
120:Learn how and when to remove this message
3097:The observational foundations of physics
1303:Densities, flows, gradients, and moments
742:There is often a choice of unit, though
131:
1430:the (tangential) plane of the surface.
14:
3248:
3061:The International System of Units (SI)
753:, and could be expressed in the units
1810:
1807:
1804:
1801:
1798:
176:. For example, the physical quantity
3081:from the original on 18 October 2021
2032:Amount of property per unit n-space
58:adding citations to reliable sources
29:
1410:{\displaystyle \mathbf {\hat {t}} }
24:
3089:
2716:
2650:
2640:
2583:
2571:
2566:
2495:
2464:
2433:
2425:
2329:
2285:
2211:
2162:
2152:
2088:
2078:
2006:
1907:
1897:
1768:
1750:
1735:
1702:
1679:
1616:
1598:
1583:
1565:
1548:
843:International System of Quantities
820:International System of Quantities
806:
607:, and are printed in italic type.
369:
366:
363:
360:
357:
25:
3267:
3130:
2237:Spectral quantity (for EM waves)
2110:Amount of property per unit mass
376:{\displaystyle =\mathrm {metre} }
227:is expressed as the product of a
3035:Théorie analytique de la chaleur
2875:
2867:
2859:
2827:
2819:
2784:
2776:
2721:
2708:
2550:
2540:
2500:
2487:
1398:
1252:
1239:
1225:
1212:
34:
1426:the surface, no current passes
1237:
235:} (a pure number) and a unit :
45:needs additional citations for
3026:
2970:
2961:
2927:List of radiometric quantities
2922:List of photometric quantities
822:(ISQ) and their corresponding
659:
419:
413:
350:
344:
275:{\displaystyle Z=\{Z\}\times }
269:
263:
13:
1:
3042:for the physical quantities.)
2986:
709:
482:
206:
1836:Rate of change of quantity,
705:Dimensions, units, and kind
451:for more on this treatment.
7:
3184:Physical Measure C# library
2917:List of physical quantities
2910:
802:Base and derived quantities
509:Real numbers, such as 1 or
337:is the numerical value and
10:
3272:
1863:{\displaystyle {\dot {q}}}
1073:
1070:General derived quantities
810:
788:). Quantities of the same
735:
713:
685:Tensor physical quantities
682:
678:
668:{\displaystyle {\vec {u}}}
614:
610:
586:
582:
577:
486:
3119:Encyclopedia of Physics,
2390:Two definitions are used:
1937:Quantity spatial density
1107:
1104:
1101:
955:Thermodynamic temperature
855:
852:
849:
3136:Computer implementations
2954:
2375:Flux, flow (synonymous)
2220:{\displaystyle \nabla q}
1083:
1050:The angular quantities,
796:dimensionless quantities
498:or operators like d in d
455:Symbols and nomenclature
425:{\displaystyle \{Z\}=Z/}
774:Dimensional homogeneity
768:
731:
330:{\displaystyle \{Z\}=2}
223:of a physical quantity
184:, can be quantified as
2883:
2838:
2798:
2729:
2664:
2597:
2508:
2444:
2340:
2296:
2221:
2192:Quantity gradient (if
2176:
2102:
2024:
1921:
1864:
1786:
1634:
1515:
1411:
1265:
798:are of the same kind.
669:
426:
377:
331:
299:
276:
141:
2932:Philosophy of science
2893:Quantity at position
2884:
2839:
2799:
2730:
2665:
2598:
2509:
2445:
2341:
2297:
2222:
2177:
2103:
2025:
1969:-space density, here
1965:No common symbol for
1922:
1865:
1829:Amount of a property
1787:
1635:
1516:
1412:
1388:For current density,
1266:
1074:Further information:
670:
489:Mathematical notation
487:Further information:
427:
378:
332:
305:be "2 metres"; then,
300:
277:
135:
2855:
2815:
2772:
2695:
2627:
2536:
2460:
2409:
2306:
2262:
2208:
2132:
2058:
1983:
1875:
1845:
1668:
1543:
1453:
1392:
1208:
1174:Area, cross-section
738:Units of measurement
699:Cauchy stress tensor
650:
448:Dimensional analysis
390:
341:
309:
289:
242:
54:improve this article
3256:Physical quantities
3161:Physical Quantities
3099:, Cambridge, 1994.
3040:physical dimensions
2942:Observable quantity
2394:Transport mechanics
1951:= surface density (
978:Amount of substance
866:(Common) symbol(s)
846:
838:systems of units).
782:thermal diffusivity
778:kinematic viscosity
716:Dimension (physics)
173:unit of measurement
69:"Physical quantity"
18:Physical quantities
3212:2014-01-01 at the
3189:2014-01-01 at the
3166:2014-01-01 at the
2879:
2834:
2794:
2725:
2660:
2593:
2504:
2440:
2336:
2292:
2217:
2172:
2098:
2044:Specific quantity
2020:
1959:= linear density (
1943:= volume density (
1917:
1860:
1782:
1630:
1511:
1407:
1379:nabla/del operator
1261:
1202:plane of surface)
1024:Luminous intensity
841:
665:
521:natural logarithms
422:
373:
327:
295:
272:
142:
3236:physical-quantity
3074:978-92-822-2272-0
3032:Fourier, Joseph.
2947:Specific quantity
2908:
2907:
2658:
2591:
2556:
2170:
2096:
1915:
1887:
1857:
1664:-space volume is
1529:The differential
1404:
1300:
1299:
1258:
1231:
1123:position (vector)
1048:
1047:
691:tensor quantities
662:
438:quantity calculus
298:{\displaystyle Z}
285:For example, let
146:physical quantity
130:
129:
122:
104:
16:(Redirected from
3263:
3207:Ethical Measures
3083:
3082:
3067:(9th ed.),
3066:
3052:
3043:
3030:
3024:
3023:
3021:
3020:
3006:
2980:
2974:
2968:
2965:
2899:potential energy
2888:
2886:
2885:
2880:
2878:
2870:
2862:
2843:
2841:
2840:
2835:
2830:
2822:
2803:
2801:
2800:
2795:
2787:
2779:
2734:
2732:
2731:
2726:
2724:
2719:
2711:
2669:
2667:
2666:
2661:
2659:
2657:
2653:
2647:
2643:
2637:
2602:
2600:
2599:
2594:
2592:
2590:
2586:
2580:
2579:
2578:
2569:
2563:
2558:
2557:
2549:
2543:
2513:
2511:
2510:
2505:
2503:
2498:
2490:
2485:
2484:
2472:
2471:
2449:
2447:
2446:
2441:
2436:
2428:
2402:particle physics
2345:
2343:
2342:
2337:
2332:
2327:
2326:
2301:
2299:
2298:
2293:
2288:
2283:
2282:
2226:
2224:
2223:
2218:
2181:
2179:
2178:
2173:
2171:
2169:
2165:
2159:
2155:
2149:
2144:
2143:
2107:
2105:
2104:
2099:
2097:
2095:
2091:
2085:
2081:
2075:
2070:
2069:
2029:
2027:
2026:
2021:
2019:
2018:
2009:
2004:
2003:
1926:
1924:
1923:
1918:
1916:
1914:
1910:
1904:
1900:
1894:
1889:
1888:
1880:
1869:
1867:
1866:
1861:
1859:
1858:
1850:
1802:Typical symbols
1796:
1795:
1791:
1789:
1788:
1783:
1781:
1780:
1771:
1763:
1762:
1753:
1748:
1747:
1738:
1715:
1714:
1705:
1688:
1687:
1682:
1639:
1637:
1636:
1631:
1629:
1628:
1619:
1611:
1610:
1601:
1596:
1595:
1586:
1578:
1577:
1568:
1557:
1556:
1551:
1520:
1518:
1517:
1512:
1510:
1506:
1505:
1504:
1492:
1491:
1479:
1478:
1416:
1414:
1413:
1408:
1406:
1405:
1397:
1270:
1268:
1267:
1262:
1260:
1259:
1251:
1242:
1233:
1232:
1224:
1215:
1099:
1098:
1001:Electric current
847:
845:base quantities
840:
674:
672:
671:
666:
664:
663:
655:
589:Scalar (physics)
515:
514:
469:IUPAC green book
431:
429:
428:
423:
412:
382:
380:
379:
374:
372:
336:
334:
333:
328:
304:
302:
301:
296:
281:
279:
278:
273:
194:
125:
118:
114:
111:
105:
103:
62:
38:
30:
21:
3271:
3270:
3266:
3265:
3264:
3262:
3261:
3260:
3246:
3245:
3214:Wayback Machine
3191:Wayback Machine
3168:Wayback Machine
3133:
3092:
3090:Further reading
3087:
3086:
3075:
3064:
3058:(20 May 2019),
3053:
3046:
3031:
3027:
3018:
3016:
3008:
3007:
2994:
2989:
2984:
2983:
2975:
2971:
2966:
2962:
2957:
2913:
2874:
2866:
2858:
2856:
2853:
2852:
2851:, equivalently
2844:
2826:
2818:
2816:
2813:
2812:
2783:
2775:
2773:
2770:
2769:
2720:
2715:
2707:
2696:
2693:
2692:
2649:
2648:
2639:
2638:
2636:
2628:
2625:
2624:
2582:
2581:
2574:
2570:
2565:
2564:
2562:
2548:
2547:
2539:
2537:
2534:
2533:
2499:
2494:
2486:
2480:
2476:
2467:
2463:
2461:
2458:
2457:
2456:
2432:
2424:
2410:
2407:
2406:
2405:
2398:nuclear physics
2391:
2382:
2367:
2360:
2357:
2328:
2322:
2318:
2307:
2304:
2303:
2302:
2284:
2278:
2274:
2263:
2260:
2259:
2257:
2252:
2248:
2244:
2209:
2206:
2205:
2161:
2160:
2151:
2150:
2148:
2139:
2135:
2133:
2130:
2129:
2125:
2118:Molar quantity
2087:
2086:
2077:
2076:
2074:
2065:
2061:
2059:
2056:
2055:
2051:
2033:
2014:
2010:
2005:
1999:
1995:
1984:
1981:
1980:
1974:
1906:
1905:
1896:
1895:
1893:
1879:
1878:
1876:
1873:
1872:
1849:
1848:
1846:
1843:
1842:
1838:time derivative
1808:Meaning, usage
1776:
1772:
1767:
1758:
1754:
1749:
1743:
1739:
1734:
1710:
1706:
1701:
1683:
1678:
1677:
1669:
1666:
1665:
1624:
1620:
1615:
1606:
1602:
1597:
1591:
1587:
1582:
1573:
1569:
1564:
1552:
1547:
1546:
1544:
1541:
1540:
1500:
1496:
1487:
1483:
1474:
1470:
1469:
1465:
1454:
1451:
1450:
1396:
1395:
1393:
1390:
1389:
1371:
1364:
1321:current density
1305:
1250:
1249:
1238:
1223:
1222:
1211:
1209:
1206:
1205:
1086:
1078:
1076:SI derived unit
1072:
1033:
857:
815:
813:Base quantities
809:
807:Base quantities
804:
771:
740:
734:
718:
712:
707:
687:
683:Main category:
681:
654:
653:
651:
648:
647:
619:
617:Vector quantity
613:
591:
585:
580:
519:e, the base of
512:
510:
491:
485:
457:
408:
391:
388:
387:
356:
342:
339:
338:
310:
307:
306:
290:
287:
286:
243:
240:
239:
229:numerical value
215:, any value or
209:
192:
167:numerical value
126:
115:
109:
106:
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
3269:
3259:
3258:
3244:
3243:
3233:
3227:
3204:
3181:
3158:
3138:
3137:
3132:
3131:External links
3129:
3128:
3127:
3124:
3117:
3107:
3095:Cook, Alan H.
3091:
3088:
3085:
3084:
3073:
3044:
3025:
2991:
2990:
2988:
2985:
2982:
2981:
2969:
2959:
2958:
2956:
2953:
2952:
2951:
2950:
2949:
2944:
2934:
2929:
2924:
2919:
2912:
2909:
2906:
2905:
2902:
2891:
2890:
2889:
2877:
2873:
2869:
2865:
2861:
2845:
2833:
2829:
2825:
2821:
2793:
2790:
2786:
2782:
2778:
2758:
2749:
2742:
2741:
2738:
2735:
2723:
2718:
2714:
2710:
2706:
2703:
2700:
2690:
2681:
2677:
2676:
2673:
2670:
2656:
2652:
2646:
2642:
2635:
2632:
2622:
2613:
2609:
2608:
2606:
2603:
2589:
2585:
2577:
2573:
2568:
2561:
2555:
2552:
2546:
2542:
2531:
2526:
2522:
2521:
2518:
2515:
2502:
2497:
2493:
2489:
2483:
2479:
2475:
2470:
2466:
2439:
2435:
2431:
2427:
2423:
2420:
2417:
2414:
2388:
2380:
2376:
2372:
2371:
2365:
2355:
2350:
2347:
2335:
2331:
2325:
2321:
2317:
2314:
2311:
2291:
2287:
2281:
2277:
2273:
2270:
2267:
2254:
2250:
2246:
2242:
2238:
2234:
2233:
2230:
2227:
2216:
2213:
2203:
2201:
2189:
2188:
2185:
2182:
2168:
2164:
2158:
2154:
2147:
2142:
2138:
2127:
2123:
2119:
2115:
2114:
2111:
2108:
2094:
2090:
2084:
2080:
2073:
2068:
2064:
2053:
2049:
2045:
2041:
2040:
2037:
2030:
2017:
2013:
2008:
2002:
1998:
1994:
1991:
1988:
1978:
1972:
1938:
1934:
1933:
1930:
1927:
1913:
1909:
1903:
1899:
1892:
1886:
1883:
1870:
1856:
1853:
1840:
1833:
1832:
1830:
1827:
1822:
1817:
1813:
1812:
1809:
1806:
1803:
1800:
1794:
1793:
1779:
1775:
1770:
1766:
1761:
1757:
1752:
1746:
1742:
1737:
1733:
1730:
1727:
1724:
1721:
1718:
1713:
1709:
1704:
1700:
1697:
1694:
1691:
1686:
1681:
1676:
1673:
1627:
1623:
1618:
1614:
1609:
1605:
1600:
1594:
1590:
1585:
1581:
1576:
1572:
1567:
1563:
1560:
1555:
1550:
1537:volume element
1509:
1503:
1499:
1495:
1490:
1486:
1482:
1477:
1473:
1468:
1464:
1461:
1458:
1403:
1400:
1369:
1362:
1304:
1301:
1298:
1297:
1294:
1291:
1282:
1278:
1277:
1274:
1271:
1257:
1254:
1248:
1245:
1241:
1236:
1230:
1227:
1221:
1218:
1214:
1203:
1192:
1191:
1188:
1185:
1175:
1171:
1170:
1165:
1162:
1153:
1149:
1148:
1145:
1142:
1125:
1118:
1117:
1114:
1110:
1109:
1106:
1103:
1085:
1082:
1071:
1068:
1046:
1045:
1042:
1039:
1034:
1031:
1026:
1020:
1019:
1016:
1013:
1008:
1003:
997:
996:
993:
990:
985:
980:
974:
973:
970:
967:
962:
957:
951:
950:
947:
944:
939:
934:
928:
927:
924:
921:
916:
911:
905:
904:
901:
898:
893:
880:
874:
873:
870:
867:
864:
860:
859:
854:
851:
811:Main article:
808:
805:
803:
800:
770:
767:
736:Main article:
733:
730:
726:Joseph Fourier
720:The notion of
714:Main article:
711:
708:
706:
703:
680:
677:
661:
658:
615:Main article:
612:
609:
605:Greek alphabet
587:Main article:
584:
581:
579:
576:
575:
574:
560:
534:
531:
524:
517:
484:
481:
465:IUPAP red book
456:
453:
433:
432:
421:
418:
415:
411:
407:
404:
401:
398:
395:
371:
368:
365:
362:
359:
355:
352:
349:
346:
326:
323:
320:
317:
314:
294:
283:
282:
271:
268:
265:
262:
259:
256:
253:
250:
247:
208:
205:
128:
127:
42:
40:
33:
26:
9:
6:
4:
3:
2:
3268:
3257:
3254:
3253:
3251:
3242:
3237:
3234:
3231:
3228:
3226:
3222:
3219:
3215:
3211:
3208:
3205:
3203:
3199:
3196:
3192:
3188:
3185:
3182:
3180:
3176:
3173:
3169:
3165:
3162:
3159:
3157:
3154:
3150:
3147:
3143:
3140:
3139:
3135:
3134:
3125:
3122:
3118:
3116:
3115:0-7195-3382-1
3112:
3108:
3106:
3105:0-521-45597-9
3102:
3098:
3094:
3093:
3080:
3076:
3070:
3063:
3062:
3057:
3051:
3049:
3041:
3037:
3036:
3029:
3015:
3011:
3005:
3003:
3001:
2999:
2997:
2992:
2979:
2978:Hodge duality
2973:
2964:
2960:
2948:
2945:
2943:
2940:
2939:
2938:
2935:
2933:
2930:
2928:
2925:
2923:
2920:
2918:
2915:
2914:
2903:
2900:
2896:
2892:
2871:
2863:
2850:
2846:
2831:
2823:
2810:
2806:
2805:
2804:
2791:
2788:
2780:
2767:
2763:
2759:
2757:
2753:
2750:
2747:
2744:
2743:
2739:
2736:
2712:
2704:
2701:
2698:
2691:
2689:
2685:
2682:
2679:
2678:
2674:
2671:
2654:
2644:
2633:
2630:
2623:
2621:
2617:
2614:
2611:
2610:
2607:
2604:
2587:
2575:
2559:
2544:
2532:
2530:
2527:
2525:Flux density
2524:
2523:
2519:
2516:
2514:
2491:
2481:
2477:
2473:
2468:
2454:
2450:
2437:
2429:
2421:
2418:
2415:
2412:
2403:
2399:
2395:
2389:
2387:
2383:
2377:
2374:
2373:
2370:
2368:
2358:
2351:
2348:
2346:
2333:
2323:
2319:
2315:
2312:
2309:
2289:
2279:
2275:
2271:
2268:
2265:
2255:
2253:
2239:
2236:
2235:
2231:
2228:
2214:
2204:
2202:
2199:
2195:
2191:
2190:
2186:
2183:
2166:
2156:
2145:
2140:
2136:
2128:
2126:
2120:
2117:
2116:
2112:
2109:
2092:
2082:
2071:
2066:
2062:
2054:
2052:
2046:
2043:
2042:
2038:
2036:
2031:
2015:
2011:
2000:
1996:
1992:
1989:
1986:
1979:
1977:
1975:
1968:
1962:
1958:
1954:
1950:
1946:
1942:
1939:
1936:
1935:
1931:
1928:
1911:
1901:
1890:
1884:
1881:
1871:
1854:
1851:
1841:
1839:
1835:
1834:
1831:
1828:
1826:
1823:
1821:
1818:
1815:
1814:
1797:
1777:
1773:
1764:
1759:
1755:
1744:
1740:
1731:
1728:
1725:
1722:
1719:
1716:
1711:
1707:
1698:
1695:
1692:
1689:
1684:
1674:
1671:
1663:
1659:
1655:
1653:
1648:
1647:
1643:
1642:
1641:
1625:
1621:
1612:
1607:
1603:
1592:
1588:
1579:
1574:
1570:
1561:
1558:
1553:
1538:
1535:
1533:
1528:
1527:
1522:
1507:
1501:
1497:
1493:
1488:
1484:
1480:
1475:
1471:
1466:
1462:
1459:
1456:
1449:
1446:
1444:
1439:
1434:
1431:
1429:
1425:
1420:
1386:
1384:
1380:
1376:
1372:
1365:
1356:
1354:
1349:
1346:to stand for
1345:
1340:
1338:
1334:
1330:
1326:
1322:
1318:
1314:
1310:
1295:
1292:
1290:
1286:
1283:
1280:
1279:
1275:
1272:
1246:
1243:
1234:
1219:
1216:
1204:
1201:
1197:
1194:
1193:
1189:
1186:
1183:
1179:
1176:
1173:
1172:
1169:
1166:
1163:
1161:
1157:
1154:
1151:
1150:
1146:
1143:
1141:
1137:
1133:
1129:
1126:
1124:
1120:
1119:
1115:
1112:
1111:
1100:
1097:
1095:
1091:
1081:
1077:
1067:
1065:
1061:
1057:
1053:
1043:
1040:
1038:
1035:
1030:
1027:
1025:
1022:
1021:
1017:
1014:
1012:
1009:
1007:
1004:
1002:
999:
998:
994:
991:
989:
986:
984:
981:
979:
976:
975:
971:
968:
966:
963:
961:
958:
956:
953:
952:
948:
945:
943:
940:
938:
935:
933:
930:
929:
925:
922:
920:
917:
915:
912:
910:
907:
906:
902:
899:
897:
894:
892:
888:
884:
881:
879:
876:
875:
871:
868:
865:
862:
861:
848:
844:
839:
837:
833:
829:
825:
821:
814:
799:
797:
793:
792:
787:
783:
779:
775:
766:
764:
760:
756:
752:
748:
745:
739:
729:
727:
723:
717:
702:
700:
696:
692:
686:
676:
656:
645:
641:
637:
633:
629:
625:
624:
618:
608:
606:
602:
598:
597:
590:
573:
569:
565:
561:
559:
555:
551:
547:
543:
539:
535:
532:
529:
525:
522:
518:
508:
507:
506:
503:
501:
497:
490:
480:
478:
474:
470:
466:
462:
461:ISO/IEC 80000
452:
450:
449:
444:
440:
439:
416:
409:
405:
402:
396:
386:
385:
384:
353:
347:
324:
321:
315:
292:
266:
260:
254:
248:
245:
238:
237:
236:
234:
230:
226:
222:
218:
214:
204:
202:
198:
191:
187:
183:
179:
175:
174:
169:
168:
163:
159:
155:
151:
147:
139:
136:Ampèremetre (
134:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
3096:
3060:
3039:
3033:
3028:
3017:. Retrieved
3013:
2972:
2963:
2894:
2848:
2808:
2765:
2761:
2760:
2755:
2751:
2748:of quantity
2687:
2683:
2619:
2615:
2528:
2453:Vector field
2451:
2392:
2385:
2378:
2363:
2361:
2353:
2258:
2240:
2198:scalar field
2193:
2121:
2047:
2034:
1970:
1966:
1964:
1960:
1956:
1952:
1948:
1944:
1940:
1824:
1819:
1661:
1657:
1651:
1645:
1644:
1531:
1526:Differential
1525:
1524:
1523:
1442:
1437:
1435:
1432:
1427:
1423:
1387:
1374:
1367:
1360:
1357:
1352:
1347:
1343:
1341:
1336:
1332:
1328:
1325:flux density
1324:
1320:
1306:
1288:
1284:
1181:
1177:
1167:
1159:
1155:
1139:
1135:
1131:
1127:
1113:Description
1087:
1079:
1049:
1028:
1005:
982:
959:
936:
913:
890:
886:
882:
816:
790:
789:
772:
750:
741:
721:
719:
693:, which are
690:
688:
643:
639:
635:
632:vector space
622:
620:
595:
592:
571:
567:
563:
557:
553:
549:
545:
541:
537:
504:
499:
495:
492:
476:
472:
458:
446:
436:
434:
284:
232:
228:
224:
220:
210:
196:
189:
185:
181:
171:
165:
161:
149:
145:
143:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
3230:Engineer JS
3216:project in
3193:project in
3170:project in
3144:project in
3121:R.G. Lerner
1811:Dimensions
1805:Definition
1419:dot product
1196:Vector area
1108:Dimensions
1056:solid angle
1052:plane angle
494:like Δ in Δ
213:ISO 80000-1
158:measurement
148:(or simply
3019:2023-05-12
2987:References
2847:3D vector
1976:is used.
1200:tangential
1121:(Spatial)
830:(e.g. the
828:base units
710:Dimensions
505:Examples:
483:Typography
211:Following
207:Components
195:kg, where
154:quantified
110:March 2022
80:newspapers
3225:Code Plex
3202:Code Plex
3179:Code Plex
2872:×
2789:∧
2713:⋅
2705:∬
2572:Φ
2554:^
2545:⋅
2492:⋅
2478:∬
2465:Φ
2419:∭
2334:ν
2324:ν
2316:∫
2290:λ
2280:λ
2272:∫
2212:∇
1997:ρ
1993:∫
1891:≡
1885:˙
1855:˙
1816:Quantity
1799:Quantity
1765:⋯
1729:∫
1726:∫
1723:⋯
1720:∫
1717:≡
1696:∫
1693:≡
1672:∫
1660:over the
1613:⋯
1580:≡
1562:≡
1494:⋯
1460:≡
1445:-variable
1402:^
1333:frequency
1256:^
1244:≡
1229:^
1217:≡
1102:Quantity
1064:steradian
856:Dimension
850:Quantity
761:(lb), or
755:kilograms
722:dimension
660:→
528:imaginary
443:dimension
261:×
217:magnitude
180:, symbol
3250:Category
3221:Language
3210:Archived
3198:Language
3187:Archived
3175:Language
3164:Archived
3156:Language
3149:Language
3079:archived
2937:Quantity
2911:See also
2764:-vector
2612:Current
1654:integral
1652:multiple
1646:Integral
1448:function
1317:currents
1116:Symbols
1105:SI unit
942:kilogram
863:Name(s)
853:SI unit
467:and the
201:kilogram
150:quantity
2807:scalar
1521:, then
1424:through
1337:current
1281:Volume
1037:candela
872:Symbol
858:symbol
763:daltons
695:tensors
679:Tensors
623:Vectors
611:Vectors
583:Scalars
578:Support
566:, sinh
526:i, the
511:√
138:Ammeter
94:scholar
3153:Delphi
3142:DEVLIB
3113:
3103:
3071:
2746:Moment
2520:TL, L
1955:= 2),
1947:= 3),
1649:: The
1534:-space
1373:, and
1309:fluxes
1094:volume
1060:radian
1011:ampere
965:kelvin
919:second
878:Length
765:(Da).
759:pounds
757:(kg),
628:axioms
596:scalar
570:, log
568:γ
564:α
463:, the
445:: see
193:
170:and a
96:
89:
82:
75:
67:
3065:(PDF)
2955:Notes
2196:is a
1963:= 1)
1440:is a
1381:∇ or
1313:flows
1084:Space
896:metre
869:Name
747:units
646:, or
630:of a
601:Latin
530:unit,
221:value
162:value
101:JSTOR
87:books
3241:Demo
3151:and
3111:ISBN
3101:ISBN
3069:ISBN
2976:via
1383:grad
1335:and
1329:rate
1323:and
1184:, Ω
1168:None
1164:rad
1092:and
1090:Area
1062:and
1054:and
1006:i, I
992:mol
988:mole
932:Mass
909:Time
834:and
791:kind
780:and
769:Kind
732:Unit
562:sin
556:and
178:mass
73:news
3223:at
3200:at
3177:at
2740:TL
2362:T (
2352:L (
2249:, q
2245:, q
2200:).
1656:of
1539:is
1436:If
1348:any
1041:cd
946:kg
836:MKS
832:CGS
786:m/s
603:or
544:, d
540:, Δ
156:by
56:by
3252::
3218:C#
3195:C#
3172:C#
3146:C#
3077:,
3047:^
3012:.
2995:^
2904:L
2901:.
2811::
2768::
2754:,
2686:,
2675:T
2618:,
2455::
2404::
2396:,
2384:,
2369:)
2232:L
2187:N
2113:M
2039:L
1932:T
1640:,
1428:in
1366:,
1355:.
1331:,
1327:,
1315:,
1311:,
1296:L
1293:m
1287:,
1276:L
1273:m
1190:L
1187:m
1180:,
1158:,
1147:L
1144:m
1138:,
1134:,
1130:,
1044:J
1018:I
1015:A
995:N
972:Θ
969:K
949:M
926:T
923:s
903:L
900:m
889:,
885:,
824:SI
744:SI
675:.
642:,
593:A
552:,
479:.
144:A
3022:.
2895:r
2876:q
2868:r
2864:=
2860:m
2849:q
2832:q
2828:r
2824:=
2820:m
2809:q
2792:q
2785:r
2781:=
2777:m
2766:q
2762:k
2756:M
2752:m
2722:S
2717:d
2709:J
2702:=
2699:I
2688:J
2684:j
2655:t
2651:d
2645:q
2641:d
2634:=
2631:I
2620:I
2616:i
2588:A
2584:d
2576:F
2567:d
2560:=
2551:n
2541:F
2529:F
2501:A
2496:d
2488:F
2482:S
2474:=
2469:F
2438:t
2434:d
2430:A
2426:d
2422:F
2416:=
2413:q
2400:/
2386:F
2381:F
2379:Φ
2366:ν
2364:q
2359:)
2356:λ
2354:q
2330:d
2320:q
2313:=
2310:q
2286:d
2276:q
2269:=
2266:q
2251:λ
2247:ν
2243:v
2241:q
2215:q
2194:q
2167:n
2163:d
2157:q
2153:d
2146:=
2141:n
2137:q
2124:n
2122:q
2093:m
2089:d
2083:q
2079:d
2072:=
2067:m
2063:q
2050:m
2048:q
2016:n
2012:V
2007:d
2001:n
1990:=
1987:q
1973:n
1971:ρ
1967:n
1961:n
1957:λ
1953:n
1949:σ
1945:n
1941:ρ
1912:t
1908:d
1902:q
1898:d
1882:q
1852:q
1825:q
1820:q
1792:.
1778:n
1774:x
1769:d
1760:2
1756:x
1751:d
1745:1
1741:x
1736:d
1732:X
1712:n
1708:V
1703:d
1699:X
1690:x
1685:n
1680:d
1675:X
1662:n
1658:X
1626:n
1622:x
1617:d
1608:2
1604:x
1599:d
1593:1
1589:x
1584:d
1575:n
1571:V
1566:d
1559:x
1554:n
1549:d
1532:n
1508:)
1502:n
1498:x
1489:2
1485:x
1481:,
1476:1
1472:x
1467:(
1463:X
1457:X
1443:n
1438:X
1399:t
1375:F
1370:n
1368:q
1363:m
1361:q
1353:q
1344:q
1289:V
1285:τ
1253:n
1247:S
1240:S
1235:,
1226:n
1220:A
1213:A
1182:S
1178:A
1160:θ
1156:θ
1140:d
1136:a
1132:R
1128:r
1032:v
1029:I
983:n
960:T
937:m
914:t
891:r
887:x
883:l
751:m
657:u
644:u
640:u
636:u
572:x
558:z
554:y
550:x
546:z
542:y
538:x
536:δ
523:,
516:,
513:2
500:x
496:y
477:Q
473:m
420:]
417:Z
414:[
410:/
406:Z
403:=
400:}
397:Z
394:{
370:e
367:r
364:t
361:e
358:m
354:=
351:]
348:Z
345:[
325:2
322:=
319:}
316:Z
313:{
293:Z
270:]
267:Z
264:[
258:}
255:Z
252:{
249:=
246:Z
233:Z
231:{
225:Z
197:n
190:n
188:=
186:m
182:m
140:)
123:)
117:(
112:)
108:(
98:·
91:·
84:·
77:·
50:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
