1284:"The system of quantities, including the relations among them the quantities used as the basis of the units of the SI, is named the International System of Quantities, denoted 'ISQ', in all languages. It should be realized, however, that ISQ is simply a convenient notation to assign to the essentially infinite and continually evolving and expanding system of quantities and equations on which all of modern science and technology rests. ISQ is a shorthand notation for the 'system of quantities on which the SI is based', which was the phrase used for this system in ISO 31."
53:
1787:
1832:
1163:) and for a power quantity. It is not defined for ratios of quantities of other kinds. Within the ISQ, all levels are treated as derived quantities of dimension 1. Several units for levels are defined by the SI and classified as "non-SI units accepted for use with the SI units". An example of level is
1310:
makes no mention of it ("The conventional symbolic representation of the dimension of a base quantity is a single upper case letter in roman (upright) type.") whereas the secondary source BIPM JCGM 200:2012 does ("The conventional symbolic representation of the dimension of a base quantity is a
1225:. Working jointly, ISO and IEC have formalized parts of the ISQ by giving information and definitions concerning quantities, systems of quantities, units, quantity and unit symbols, and coherent unit systems, with particular reference to the ISQ. ISO/IEC 80000 defines physical
694:
73:
is a subset of those quantities, where no base quantity can be expressed in terms of the others, but where every quantity in the system can be expressed in terms of the base quantities. Within this constraint, the set of base quantities is chosen by convention. There are seven
580:
The conventional symbolic representation of the dimension of a derived quantity is the product of powers of the dimensions of the base quantities according to the definition of the derived quantity. The dimension of a quantity is denoted by
584:
897:
81:
The dimension of a physical quantity does not include magnitude or units. The conventional symbolic representation of the dimension of a base quantity is a single upper-case letter in
1159:
of the ratio of the quantity with a stated reference value of that quantity. Within the ISQ it is differently defined for a root-power quantity (also known by the deprecated term
835:
1065:
942:
735:
405:
787:
1020:
981:
534:
466:
344:
283:
222:
161:
509:
568:
is a quantity in a system of quantities that is defined in terms of only the base quantities of that system. The ISQ defines many derived quantities and corresponding
35:
and in modern science in general. It includes basic quantities such as length and mass and the relationships between those quantities. This system underlies the
1108:
441:
380:
319:
258:
197:
136:
1110:. Such a quantity can be regarded as a derived quantity in the form of the ratio of two quantities of the same dimension. The named dimensionless units "
1480:
1396:
689:{\displaystyle {\mathsf {L}}^{a}{\mathsf {M}}^{b}{\mathsf {T}}^{c}{\mathsf {I}}^{d}{\mathsf {\Theta }}^{e}{\mathsf {N}}^{f}{\mathsf {J}}^{g}}
1516:
49:(which also defines many other quantities used in science and technology), first completed in 2009 and subsequently revised and expanded.
1325:
The associated quantity symbol, the SI unit name and SI unit symbol are given here for reference only; they do not form part of the ISQ.
1234:
1233:
and also includes many other quantities in modern science and technology. The name "International System of
Quantities" is used by the
1297:, in which it is proposed that the quantities and equations used with the SI will be known as the International System of Quantities."
1146:
1429:
848:
1488:
1874:
1509:
1454:(3rd ed.). International Bureau of Weights and Measures (BIPM):Joint Committee for Guides in Metrology. 2012
1374:
700:
may be omitted if its exponent is zero. For example, in the ISQ, the quantity dimension of velocity is denoted
1355:(1st ed.), Switzerland: ISO (the International Organization for Standardization), 2009-11-15, p. vi
1260:
1238:
1230:
1217:, first completed in 2009 but subsequently revised and expanded, which replaced standards published in 1992,
36:
1864:
1842:
1801:
1140:
800:
1502:
1255:
1199:
1180:
1090:(a term that is still commonly used); all its dimensional exponents are zero and its dimension symbol is
1033:
910:
703:
386:
758:
994:
955:
1699:
1416:
358:
1444:
515:
447:
325:
264:
203:
142:
1118:" (sr) are acceptable for distinguishing dimensionless quantities of different kind, respectively
487:
1811:
1835:
1086:
1350:
1816:
1452:
International vocabulary of metrology – Basic and general concepts and associated terms (VIM)
1869:
1559:
1250:
1164:
555:
8:
1726:
1195:
419:
1751:
1188:
1093:
480:
426:
365:
304:
243:
182:
121:
52:
1484:
1425:
1424:(9th ed.), International Bureau of Weights and Measures, Dec 2022, p. 145,
70:
39:(SI) but does not itself determine the units of measurement used for the quantities.
1664:
697:
297:
82:
559:
1858:
1214:
1080:
46:
1525:
1265:
1211:
1026:
569:
104:
43:
1392:
1741:
1307:
1123:
1119:
470:
78:. The symbols for them, as for other quantities, are written in italics.
696:, where the dimensional exponents are positive, negative, or zero. The
86:
56:
Metrological dependencies between the base units of the SI system
1682:
1494:
1156:
1115:
751:
1306:
The status of the requirement for sans-serif is not as clear, since
1654:
1226:
1222:
903:
841:
226:
28:
1187:, corresponding to a factor of 2 in frequency (precisely) and the
1771:
1546:
1293:"The revised harmonized standard will be known as ISO/IEC 80000,
1168:
538:
32:
16:
System of quantities used in science and their interrelationships
737:. The following table lists some quantities defined by the ISQ.
1716:
1689:
1605:
1595:
1311:
single upper case letter in roman (upright) sans-serif type.").
1218:
1184:
1111:
987:
575:
409:
348:
287:
114:
1237:(CGPM) to describe the system of quantities that underlie the
1629:
793:
165:
1669:
1639:
1580:
948:
236:
175:
1352:
ISO 80000-1:2009 Quantities and units. Part 1: General
1096:
1036:
997:
958:
913:
892:{\displaystyle {\mathsf {L}}^{-1}{\mathsf {MT}}^{-2}}
851:
803:
761:
706:
587:
518:
490:
450:
429:
389:
368:
328:
307:
267:
246:
206:
185:
145:
124:
1709:
1345:
1343:
1341:
1102:
1059:
1014:
975:
936:
891:
829:
781:
729:
688:
528:
503:
460:
435:
399:
374:
338:
313:
277:
252:
216:
191:
155:
130:
1210:The system is formally described in a multi-part
1194:The ISQ recognizes another logarithmic quantity,
42:The system is formally described in a multi-part
1856:
1338:
1174:
1481:National Institute of Standards and Technology
1397:International Organization for Standardization
1510:
1375:"NIST Special Publication 330 – 2008 edition"
576:Dimensional expression of derived quantities
1385:
1072:
1517:
1503:
1321:
1319:
1317:
1235:General Conference on Weights and Measures
1129:
51:
1314:
1147:Power, root-power, and field quantities
1857:
1524:
1372:
1043:
1040:
1001:
962:
920:
917:
875:
872:
855:
813:
810:
807:
765:
713:
710:
675:
661:
647:
633:
619:
605:
591:
521:
453:
392:
331:
270:
209:
148:
1498:
1198:, for which the coherent unit is the
549:
830:{\displaystyle {\mathsf {LMT}}^{-2}}
1060:{\displaystyle {\mathsf {LT}}^{-2}}
937:{\displaystyle {\mathsf {LT}}^{-1}}
730:{\displaystyle {\mathsf {LT}}^{-1}}
400:{\displaystyle {\mathsf {\Theta }}}
13:
1807:International System of Quantities
1477:International System of Units (SI)
1469:
782:{\displaystyle {\mathsf {T}}^{-1}}
60:
21:International System of Quantities
14:
1886:
1418:The International System of Units
1015:{\displaystyle {\mathsf {L}}^{3}}
976:{\displaystyle {\mathsf {L}}^{2}}
746:Expression in SI base dimensions
1831:
1830:
1785:
1205:
1191:, corresponding to a factor 10.
1155:of a quantity is defined as the
1475:B. N. Taylor, Ambler Thompson,
1373:Taylor, Barry N. (April 2008),
1437:
1409:
1366:
1300:
1287:
1278:
1:
1332:
1261:International System of Units
1239:International System of Units
529:{\displaystyle {\mathsf {J}}}
461:{\displaystyle {\mathsf {N}}}
339:{\displaystyle {\mathsf {I}}}
278:{\displaystyle {\mathsf {T}}}
217:{\displaystyle {\mathsf {M}}}
156:{\displaystyle {\mathsf {L}}}
37:International System of Units
1802:History of the metric system
1175:Other logarithmic quantities
1141:Level (logarithmic quantity)
512:
504:{\displaystyle I_{\text{v}}}
484:
444:
423:
383:
362:
322:
301:
261:
240:
200:
179:
139:
118:
7:
1256:List of physical quantities
1244:
1229:that are measured with the
1200:natural unit of information
1181:logarithmic frequency ratio
1084:is historically known as a
10:
1891:
1144:
1138:
553:
27:) is a standard system of
1825:
1794:
1783:
1700:thermodynamic temperature
1545:
1540:
1532:
359:thermodynamic temperature
1271:
1134:
1073:Dimensionless quantities
1875:International standards
1817:Systems of measurement
1130:Logarithmic quantities
1104:
1087:dimensionless quantity
1061:
1016:
977:
938:
893:
831:
783:
731:
690:
530:
505:
462:
437:
401:
376:
340:
315:
279:
254:
218:
193:
157:
132:
57:
1145:Further information:
1105:
1062:
1017:
978:
939:
894:
832:
784:
732:
691:
531:
506:
463:
438:
402:
377:
341:
316:
280:
255:
219:
194:
158:
133:
101:Symbol for dimension
69:of a given system of
55:
1295:Quantities and Units
1251:Dimensional analysis
1165:sound pressure level
1094:
1034:
995:
956:
911:
849:
801:
759:
704:
585:
556:Dimensional analysis
516:
488:
448:
427:
387:
366:
326:
305:
265:
244:
204:
183:
143:
122:
98:Symbol for quantity
1865:Physical quantities
1727:amount of substance
1196:information entropy
1167:, with the unit of
420:amount of substance
76:ISQ base quantities
71:physical quantities
1752:luminous intensity
1526:SI base quantities
1393:"ISO 80000-3:2019"
1215:ISO/IEC 80000
1100:
1057:
1012:
973:
934:
889:
827:
779:
727:
686:
550:Derived quantities
526:
501:
481:luminous intensity
458:
433:
397:
372:
336:
311:
275:
250:
214:
189:
153:
128:
58:
47:ISO/IEC 80000
1852:
1851:
1780:
1779:
1431:978-92-822-2272-0
1103:{\displaystyle 1}
1070:
1069:
743:Derived quantity
547:
546:
498:
436:{\displaystyle n}
375:{\displaystyle T}
314:{\displaystyle I}
253:{\displaystyle t}
192:{\displaystyle m}
131:{\displaystyle l}
1882:
1834:
1833:
1789:
1788:
1763:
1733:
1711:
1706:
1684:
1679:
1675:
1673:
1665:electric current
1646:
1620:
1616:
1612:
1587:
1538:
1537:
1519:
1512:
1505:
1496:
1495:
1464:
1463:
1461:
1459:
1449:
1441:
1435:
1434:
1423:
1413:
1407:
1406:
1404:
1403:
1389:
1383:
1382:
1370:
1364:
1363:
1362:
1360:
1347:
1326:
1323:
1312:
1308:ISO 80000-1:2009
1304:
1298:
1291:
1285:
1282:
1109:
1107:
1106:
1101:
1066:
1064:
1063:
1058:
1056:
1055:
1047:
1046:
1021:
1019:
1018:
1013:
1011:
1010:
1005:
1004:
982:
980:
979:
974:
972:
971:
966:
965:
943:
941:
940:
935:
933:
932:
924:
923:
898:
896:
895:
890:
888:
887:
879:
878:
868:
867:
859:
858:
836:
834:
833:
828:
826:
825:
817:
816:
788:
786:
785:
780:
778:
777:
769:
768:
740:
739:
736:
734:
733:
728:
726:
725:
717:
716:
698:dimension symbol
695:
693:
692:
687:
685:
684:
679:
678:
671:
670:
665:
664:
657:
656:
651:
650:
643:
642:
637:
636:
629:
628:
623:
622:
615:
614:
609:
608:
601:
600:
595:
594:
566:derived quantity
535:
533:
532:
527:
525:
524:
510:
508:
507:
502:
500:
499:
496:
467:
465:
464:
459:
457:
456:
442:
440:
439:
434:
406:
404:
403:
398:
396:
395:
381:
379:
378:
373:
345:
343:
342:
337:
335:
334:
320:
318:
317:
312:
298:electric current
284:
282:
281:
276:
274:
273:
259:
257:
256:
251:
223:
221:
220:
215:
213:
212:
198:
196:
195:
190:
162:
160:
159:
154:
152:
151:
137:
135:
134:
129:
92:
91:
1890:
1889:
1885:
1884:
1883:
1881:
1880:
1879:
1855:
1854:
1853:
1848:
1821:
1790:
1786:
1781:
1762:
1756:
1731:
1704:
1683: I
1677:
1671:
1644:
1618:
1614:
1610:
1585:
1574:
1569:
1561:
1533:Base quantities
1528:
1523:
1472:
1470:Further reading
1467:
1457:
1455:
1447:
1443:
1442:
1438:
1432:
1421:
1415:
1414:
1410:
1401:
1399:
1391:
1390:
1386:
1371:
1367:
1358:
1356:
1349:
1348:
1339:
1335:
1330:
1329:
1324:
1315:
1305:
1301:
1292:
1288:
1283:
1279:
1274:
1247:
1208:
1177:
1149:
1143:
1137:
1132:
1095:
1092:
1091:
1075:
1048:
1039:
1038:
1037:
1035:
1032:
1031:
1006:
1000:
999:
998:
996:
993:
992:
967:
961:
960:
959:
957:
954:
953:
925:
916:
915:
914:
912:
909:
908:
880:
871:
870:
869:
860:
854:
853:
852:
850:
847:
846:
818:
806:
805:
804:
802:
799:
798:
770:
764:
763:
762:
760:
757:
756:
718:
709:
708:
707:
705:
702:
701:
680:
674:
673:
672:
666:
660:
659:
658:
652:
646:
645:
644:
638:
632:
631:
630:
624:
618:
617:
616:
610:
604:
603:
602:
596:
590:
589:
588:
586:
583:
582:
578:
562:
560:SI derived unit
552:
520:
519:
517:
514:
513:
495:
491:
489:
486:
485:
452:
451:
449:
446:
445:
428:
425:
424:
391:
390:
388:
385:
384:
367:
364:
363:
330:
329:
327:
324:
323:
306:
303:
302:
269:
268:
266:
263:
262:
245:
242:
241:
208:
207:
205:
202:
201:
184:
181:
180:
147:
146:
144:
141:
140:
123:
120:
119:
109:SI unit symbol
67:base quantities
63:
61:Base quantities
17:
12:
11:
5:
1888:
1878:
1877:
1872:
1867:
1850:
1849:
1847:
1846:
1839:
1826:
1823:
1822:
1820:
1819:
1814:
1809:
1804:
1798:
1796:
1792:
1791:
1784:
1782:
1778:
1777:
1774:
1769:
1767:
1764:
1760:
1754:
1748:
1747:
1744:
1739:
1737:
1734:
1729:
1723:
1722:
1719:
1714:
1712:
1707:
1702:
1696:
1695:
1692:
1687:
1685:
1680:
1667:
1661:
1660:
1657:
1652:
1650:
1647:
1642:
1636:
1635:
1632:
1627:
1625:
1622:
1608:
1602:
1601:
1598:
1593:
1591:
1588:
1583:
1581:time, duration
1577:
1576:
1571:
1566:
1564:
1557:
1554:
1550:
1549:
1544:
1542:
1536:
1534:
1530:
1529:
1522:
1521:
1514:
1507:
1499:
1493:
1492:
1483:2008 edition,
1471:
1468:
1466:
1465:
1436:
1430:
1408:
1384:
1365:
1336:
1334:
1331:
1328:
1327:
1313:
1299:
1286:
1276:
1275:
1273:
1270:
1269:
1268:
1263:
1258:
1253:
1246:
1243:
1207:
1204:
1202:(symbol nat).
1176:
1173:
1161:field quantity
1139:Main article:
1136:
1133:
1131:
1128:
1099:
1074:
1071:
1068:
1067:
1054:
1051:
1045:
1042:
1029:
1023:
1022:
1009:
1003:
990:
984:
983:
970:
964:
951:
945:
944:
931:
928:
922:
919:
906:
900:
899:
886:
883:
877:
874:
866:
863:
857:
844:
838:
837:
824:
821:
815:
812:
809:
796:
790:
789:
776:
773:
767:
754:
748:
747:
744:
724:
721:
715:
712:
683:
677:
669:
663:
655:
649:
641:
635:
627:
621:
613:
607:
599:
593:
577:
574:
551:
548:
545:
544:
541:
536:
523:
511:
494:
483:
477:
476:
473:
468:
455:
443:
432:
422:
416:
415:
412:
407:
394:
382:
371:
361:
355:
354:
351:
346:
333:
321:
310:
300:
294:
293:
290:
285:
272:
260:
249:
239:
233:
232:
229:
224:
211:
199:
188:
178:
172:
171:
168:
163:
150:
138:
127:
117:
111:
110:
107:
102:
99:
96:
95:Base quantity
62:
59:
15:
9:
6:
4:
3:
2:
1887:
1876:
1873:
1871:
1868:
1866:
1863:
1862:
1860:
1845:
1844:
1840:
1838:
1837:
1828:
1827:
1824:
1818:
1815:
1813:
1812:2019 revision
1810:
1808:
1805:
1803:
1800:
1799:
1797:
1793:
1775:
1773:
1770:
1768:
1765:
1759:
1755:
1753:
1750:
1749:
1745:
1743:
1740:
1738:
1735:
1730:
1728:
1725:
1724:
1720:
1718:
1715:
1713:
1708:
1703:
1701:
1698:
1697:
1693:
1691:
1688:
1686:
1681:
1668:
1666:
1663:
1662:
1658:
1656:
1653:
1651:
1648:
1643:
1641:
1638:
1637:
1633:
1631:
1628:
1626:
1623:
1609:
1607:
1604:
1603:
1599:
1597:
1594:
1592:
1589:
1584:
1582:
1579:
1578:
1572:
1567:
1565:
1563:
1558:
1555:
1552:
1551:
1548:
1543:
1539:
1535:
1531:
1527:
1520:
1515:
1513:
1508:
1506:
1501:
1500:
1497:
1490:
1489:1-4379-1558-2
1486:
1482:
1478:
1474:
1473:
1453:
1446:
1440:
1433:
1427:
1420:
1419:
1412:
1398:
1394:
1388:
1380:
1376:
1369:
1354:
1353:
1346:
1344:
1342:
1337:
1322:
1320:
1318:
1309:
1303:
1296:
1290:
1281:
1277:
1267:
1264:
1262:
1259:
1257:
1254:
1252:
1249:
1248:
1242:
1240:
1236:
1232:
1228:
1224:
1223:ISO 1000
1220:
1216:
1213:
1206:Documentation
1203:
1201:
1197:
1192:
1190:
1186:
1182:
1172:
1170:
1166:
1162:
1158:
1154:
1148:
1142:
1127:
1125:
1121:
1117:
1114:" (rad) and "
1113:
1097:
1089:
1088:
1083:
1082:
1081:dimension one
1052:
1049:
1030:
1028:
1025:
1024:
1007:
991:
989:
986:
985:
968:
952:
950:
947:
946:
929:
926:
907:
905:
902:
901:
884:
881:
864:
861:
845:
843:
840:
839:
822:
819:
797:
795:
792:
791:
774:
771:
755:
753:
750:
749:
745:
742:
741:
738:
722:
719:
699:
681:
667:
653:
639:
625:
611:
597:
573:
571:
570:derived units
567:
561:
557:
542:
540:
537:
492:
482:
479:
478:
474:
472:
469:
430:
421:
418:
417:
413:
411:
408:
369:
360:
357:
356:
352:
350:
347:
308:
299:
296:
295:
291:
289:
286:
247:
238:
235:
234:
230:
228:
225:
186:
177:
174:
173:
169:
167:
164:
125:
116:
113:
112:
108:
106:
103:
100:
97:
94:
93:
90:
88:
84:
79:
77:
72:
68:
54:
50:
48:
45:
40:
38:
34:
30:
26:
22:
1841:
1829:
1806:
1757:
1476:
1456:. Retrieved
1451:
1439:
1417:
1411:
1400:. Retrieved
1387:
1381:, p. 10
1378:
1368:
1357:, retrieved
1351:
1302:
1294:
1289:
1280:
1266:SI base unit
1212:ISO standard
1209:
1193:
1183:include the
1178:
1160:
1152:
1150:
1085:
1079:quantity of
1078:
1076:
1027:acceleration
579:
565:
563:
105:SI base unit
80:
75:
66:
64:
44:ISO standard
41:
24:
20:
18:
1870:Measurement
1219:ISO 31
1124:solid angle
1120:plane angle
1859:Categories
1402:2019-10-23
1333:References
1227:quantities
554:See also:
87:sans-serif
85:(upright)
29:quantities
1560:Dimension
1541:Quantity
1179:Units of
1157:logarithm
1116:steradian
1050:−
927:−
882:−
862:−
820:−
772:−
752:frequency
720:−
648:Θ
393:Θ
1836:Category
1795:See also
1655:kilogram
1458:28 March
1245:See also
1231:SI units
904:velocity
842:pressure
227:kilogram
31:used in
1843:Outline
1772:candela
1674:
1670:
1621:, etc.
1575:symbol
1556:Symbol
1547:SI unit
1169:decibel
539:candela
33:physics
1717:kelvin
1710:Θ
1690:ampere
1606:length
1596:second
1562:symbol
1487:
1445:"1.16"
1428:
1359:23 May
1189:decade
1185:octave
1112:radian
988:volume
410:kelvin
349:ampere
288:second
115:length
89:type.
1630:metre
1570:name
1553:Name
1448:(PDF)
1422:(PDF)
1272:Notes
1153:level
1135:Level
794:force
166:metre
83:roman
1746:mol
1742:mole
1640:mass
1573:Unit
1568:Unit
1485:ISBN
1460:2015
1426:ISBN
1379:NIST
1361:2015
1221:and
1151:The
1122:and
949:area
558:and
475:mol
471:mole
237:time
176:mass
65:The
19:The
1776:cd
1659:kg
543:cd
231:kg
25:ISQ
1861::
1766:J
1736:N
1721:K
1694:A
1676:,
1649:M
1634:m
1624:L
1617:,
1613:,
1600:s
1590:T
1479:,
1450:.
1395:.
1377:,
1340:^
1316:^
1241:.
1171:.
1126:.
1077:A
572:.
564:A
414:K
353:A
292:s
170:m
1761:v
1758:I
1732:n
1705:T
1678:i
1672:I
1645:m
1619:r
1615:x
1611:l
1586:t
1518:e
1511:t
1504:v
1491:.
1462:.
1405:.
1098:1
1053:2
1044:T
1041:L
1008:3
1002:L
969:2
963:L
930:1
921:T
918:L
885:2
876:T
873:M
865:1
856:L
823:2
814:T
811:M
808:L
775:1
766:T
723:1
714:T
711:L
682:g
676:J
668:f
662:N
654:e
640:d
634:I
626:c
620:T
612:b
606:M
598:a
592:L
522:J
497:v
493:I
454:N
431:n
370:T
332:I
309:I
271:T
248:t
210:M
187:m
149:L
126:l
23:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
