Second moment of inertia

The second moment of inertia indicates the resistance to deflection of a particular section of a profile or beam. Other (more) correct names are moment of inertia of plane area, area moment of inertia, or second area moment. The unit used for the 2^nd moment is length to the fourth power (m⁴).

The second moment of inertia is independent of material and environment and is purely determined by geometric values of the element. That is, shape, length and width. The outcome of the calculation can be used to determine the response of an element to a particular load. This is usually a form of deflection. The calculators on this website assume that the element always bends around its neutral line which runs across the gravitational center of the cross section.

Closely related is the section modulus which is used to determine stress at a certain load. For this, the second moment of inertia is divided by the outer fiber distance seen from the neutral line. The polar moment of inertia is determined from the same geometric input and is used in torque calculations.

It is common for the second moment of inertia to be confused with the mass moment of inertia that indicates the resistance to acceleration of an object.

Standard universal steel beams

At the bottom of this page several tables are placed containing data of standard universal beams. The tables contain next to second moment of inertia data about section modulus, geometrics, cross sectional area and more.

Properties of standard beams

	Description	unit
Size	The designation of the size of the standard beam. E.g. HEA 100.	mm
G	The weight of the standard beam per unit length.	kg/m
h	Height of the profile.	mm
b	Width of the profile.	mm
A	Area of the cross section.	mm²
t_w	Thickness or width of the vertical element(s).	mm
t_f	Thickness of the flange.	mm
A_p	Paint area per unit length of profile.	m²/m
I_y	Second moment of inertia around y-axis.	cm⁴
W_y	Section modulus around y-axis	cm³
I_z	Second moment of inertia around z-axis.	cm⁴
W_z	Section modulus around z-axis	cm³

HEA

Size	G	A	h	b	t_w	t_f	A_p	I_y	W_y	I_z	W_z
100	17	2124	96	100	5	8	0.561	349	72.8	134	26.8
120	20.3	2534	114	120	5	8	0.677	606	106	231	38.5
140	25.1	3142	133	140	5.5	8.5	0.794	1033	155	389	55.6
160	31	3877	152	160	6	9	0.906	1673	220	616	76.9
180	36.2	4525	171	180	6	9.5	1.02	2510	294	925	103
200	43.1	5383	190	200	6.5	10	1.14	3692	389	1336	134
220	51.5	6434	210	220	7	11	1.26	5410	515	1955	178
240	61.5	7684	230	240	7.5	12	1.37	7763	675	2769	231
260	69.5	8682	250	260	7.5	12.5	1.48	10455	836	3668	282
280	77.8	9726	270	280	8	13	1.6	13673	1013	4763	340
300	90	11253	290	300	8.5	14	1.72	18263	1260	6310	421
320	99.5	12437	310	300	9	15.5	1.76	22929	1479	6985	466
340	107	13347	330	300	9.5	16.5	1.79	27693	1678	7436	496
360	114	14276	350	300	10	17.5	1.83	33090	1891	7887	526
400	127	15989	390	300	11	19	1.91	45069	2311	8564	571
450	142	17803	440	300	11.5	21	2.01	63722	2896	9465	631
500	158	19754	490	300	12	23	2.11	86975	3550	10367	691
550	169	21176	540	300	12.5	24	2.21	111932	4146	10819	721
600	181	22646	590	300	13	25	2.31	141208	4787	11271	751
650	193	24164	640	300	13.5	26	2.41	175178	5474	11724	782
700	208	26048	690	300	14.5	27	2.5	215301	6241	12179	812
800	229	28583	790	300	15	28	2.7	303443	7682	12639	843
900	256	32053	890	300	16	30	2.9	422075	9485	13547	903
1000	277	34685	990	300	16.5	31	3.1	553846	11189	14004	934

HEB

Size	G	A	h	b	t_w	t_f	A_p	I_y	W_y	I_z	W_z
100	20.8	2604	100	100	6	10	0.567	450	89.9	167	33.5
120	27.2	3401	120	120	6.5	11	0.686	864	144	318	52.9
140	34.4	4296	140	140	7	12	0.805	1509	216	550	78.5
160	43.4	5425	160	160	8	13	0.918	2492	312	889	111
180	52.2	6525	180	180	8.5	14	1.04	3831	426	1363	151
200	62.5	7808	200	200	9	15	1.15	5696	570	2003	200
220	72.8	9104	220	220	9.5	16	1.27	8091	736	2843	258
240	84.8	10599	240	240	10	17	1.38	11259	938	3923	327
260	94.8	11844	260	260	10	17.5	1.5	14919	1148	5135	395
280	105	13136	280	280	10.5	18	1.62	19270	1376	6595	471
300	119	14908	300	300	11	19	1.73	25166	1678	8563	571
320	129	16134	320	300	11.5	20.5	1.77	30824	1926	9239	616
340	137	17090	340	300	12	21.5	1.81	36656	2156	9690	646
360	145	18063	360	300	12.5	22.5	1.85	43193	2400	10141	676
400	158	19778	400	300	13.5	24	1.93	57681	2884	10819	721
450	174	21798	450	300	14	26	2.03	79888	3551	11721	781
500	191	23864	500	300	14.5	28	2.12	107176	4287	12624	842
550	203	25406	550	300	15	29	2.22	136691	4971	13077	872
600	216	26996	600	300	15.5	30	2.32	171041	5701	13530	902
650	229	28634	650	300	16	31	2.42	210616	6480	13984	932
700	245	30638	700	300	17	32	2.52	256888	7340	14441	963
800	267	33418	800	300	17.5	33	2.71	359084	8977	14904	994
900	297	37128	900	300	18.5	35	2.91	494065	10979	15816	1054
1000	320	40005	1000	300	19	36	3.11	644748	12895	16276	1085

HEM

Size	G	A	h	b	t_w	t_f	A_p	I_y	W_y	I_z	W_z
100	42.6	5324	120	106	12	20	0.619	1143	190	399	75.3
120	53.1	6641	140	126	12.5	21	0.738	2018	288	703	112
140	64.4	8056	160	146	13	22	0.857	3291	411	1144	157
160	77.6	9705	180	166	14	23	0.97	5098	566	1759	212
180	90.6	11325	200	186	14.5	24	1.09	7483	748	2580	277
200	105	13128	220	206	15	25	1.2	10642	967	3651	354
220	120	14944	240	226	15.5	26	1.32	14605	1217	5012	444
240	160	19959	270	248	18	32	1.46	24290	1799	8153	657
260	176	21964	290	268	18	32.5	1.57	31307	2159	10449	780
280	192	24016	310	288	18.5	33	1.69	39547	2551	13163	914
300	242	30308	340	310	21	39	1.83	59201	3482	19403	1252
320	250	31205	359	309	21	40	1.87	68135	3796	19709	1276
340	253	31583	377	309	21	40	1.9	76372	4052	19711	1276
360	255	31881	395	308	21	40	1.93	84867	4297	19522	1268
400	261	32578	432	307	21	40	2	104119	4820	19335	1260
450	268	33544	478	307	21	40	2.1	131484	5501	19339	1260
500	275	34430	524	306	21	40	2.18	161929	6180	19155	1252
550	284	35438	572	306	21	40	2.28	197984	6923	19158	1252
600	291	36366	620	305	21	40	2.37	237448	7660	18975	1244
650	299	37374	668	305	21	40	2.47	281668	8433	18979	1245
700	306	38302	716	304	21	40	2.56	329278	9198	18797	1237
800	323	40427	814	303	21	40	2.75	442598	10875	18627	1230
900	339	42363	910	302	21	40	2.93	570434	12537	18452	1222
1000	355	44421	1008	302	21	40	3.13	722299	14331	18459	1222

INP

Size	G	A	h	b	t_w	t_f	A_p	I_y	W_y	I_z	W_z
80	6.06	757	80	42	3.9	5.9	0.303	77.7	19.4	6.28	2.99
100	8.5	1062	100	50	4.5	6.8	0.37	170	34.1	12.1	4.86
120	11.3	1418	120	58	5.1	7.7	0.438	327	54.5	21.4	7.38
140	14.6	1824	140	66	5.7	8.6	0.506	572	81.8	35.1	10.6
160	18.2	2280	160	74	6.3	9.5	0.573	934	117	54.6	14.7
180	22.3	2787	180	82	6.9	10.4	0.641	1444	160	81.2	19.8
200	26.7	3343	200	90	7.5	11.3	0.709	2138	214	116	25.9
220	31.6	3950	220	98	8.1	12.2	0.776	3055	278	162	33.1
240	36.9	4608	240	106	8.7	13.1	0.844	4239	353	220	41.5
260	42.7	5332	260	113	9.4	14.1	0.908	5734	441	287	50.9
280	48.8	6101	280	119	10.1	15.2	0.967	7575	541	363	61
300	55.2	6899	300	125	10.8	16.2	1.03	9785	652	449	71.9
320	62.2	7771	320	131	11.5	17.3	1.09	12494	781	554	84.6
340	69.3	8668	340	137	12.2	18.3	1.15	15669	922	672	98.1
360	77.6	9698	360	143	13	19.5	1.21	19575	1087	817	114
380	85.6	10698	380	149	13.7	20.5	1.27	23978	1262	973	131
400	94.2	11774	400	155	14.4	21.6	1.33	29173	1459	1156	149

IPE

Size	G	A	h	b	t_w	t_f	A_p	I_y	W_y	I_z	W_z
80	6.11	764	80	46	3.8	5.2	0.328	80.1	20	8.49	3.69
100	8.26	1032	100	55	4.1	5.7	0.4	171	34.2	15.9	5.79
120	10.6	1321	120	64	4.4	6.3	0.475	318	53	27.7	8.65
140	13.1	1643	140	73	4.7	6.9	0.551	541	77.3	44.9	12.3
160	16.1	2009	160	82	5	7.4	0.623	869	109	68.3	16.7
180	19.2	2395	180	91	5.3	8	0.698	1317	146	101	22.2
200	22.8	2848	200	100	5.6	8.5	0.768	1943	194	142	28.5
220	26.7	3337	220	110	5.9	9.2	0.848	2772	252	205	37.3
240	31.3	3912	240	120	6.2	9.8	0.922	3892	324	284	47.3
270	36.8	4595	270	135	6.6	10.2	1.04	5790	429	420	62.2
300	43	5381	300	150	7.1	10.7	1.16	8356	557	604	80.5
330	50.1	6261	330	160	7.5	11.5	1.25	11767	713	788	98.5
360	58.2	7273	360	170	8	12.7	1.35	16266	904	1043	123
400	67.6	8446	400	180	8.6	13.5	1.47	23128	1156	1318	146
450	79.1	9882	450	190	9.4	14.6	1.61	33743	1500	1676	176
500	92.4	11552	500	200	10.2	16	1.74	48199	1928	2142	214
550	108	13442	550	210	11.1	17.2	1.88	67117	2441	2668	254
600	125	15598	600	220	12	19	2.01	92083	3069	3387	308

UNP

Size	G	A	h	b	t_w	t_f	A_p	I_y	W_y	I_z	W_z
80	8.82	1102	80	45	6	8	0.313	106	26.5	19.4	6.35
100	10.8	1345	100	50	6	8.5	0.372	205	41.1	29.1	8.45
120	13.6	1699	120	55	7	9	0.429	364	60.7	43.1	11.1
140	16.3	2037	140	60	7	10	0.487	605	86.4	62.5	14.7
160	19.2	2401	160	65	7.5	10.5	0.545	925	116	85	18.2
180	22.4	2797	180	70	8	11	0.603	1354	150	113	22.4
200	25.7	3218	200	75	8.5	11.5	0.66	1911	191	148	26.9
220	30	3744	220	80	9	12.5	0.718	2691	245	196	33.5
240	33.8	4231	240	85	9.5	13	0.776	3599	300	247	39.5
260	38.6	4828	260	90	10	14	0.833	4824	371	317	47.8
280	42.7	5342	280	95	10	15	0.891	6276	448	398	57.1
300	47	5876	300	100	10	16	0.949	8028	535	493	67.6
320	60.6	7578	320	100	14	17.5	0.984	10869	679	597	80.6
350	61.8	7725	350	100	14	16	1.05	12845	734	571	75.1
380	64.3	8035	380	102	13.5	16	1.11	15755	829	615	78.7
400	73.2	9149	400	110	14	18	1.18	20353	1018	851	102

UPE

Size	G	A	h	b	t_w	t_f	A_p	I_y	W_y	I_z	W_z
80	9.05	1131	80	50	4.5	8	0.342	118	29.4	28.3	8.99
100	11.1	1393	100	55	5	8.5	0.401	227	45.3	42.3	11.9
120	13.5	1684	120	60	5.5	9	0.46	392	65.4	60.7	15.3
140	16	2004	140	65	6	9.5	0.519	630	90	84.3	19.3
160	19	2372	160	70	6.5	10	0.577	965	121	114	23.9
180	22	2750	180	75	7	10.5	0.636	1404	156	151	29.1
200	25.3	3157	200	80	7.5	11	0.695	1972	197	196	35
220	29.4	3670	220	85	8	12	0.754	2767	252	256	43.1
240	34	4256	240	90	8.5	13	0.81	3816	318	331	52.4
270	39.5	4935	270	95	9	14	0.889	5559	412	425	63.3
300	45.3	5662	300	100	9.5	15	0.968	7823	522	538	75.6
330	54.2	6777	330	105	11	16	1.04	11008	667	681	89.7
360	62.3	7791	360	110	12	17	1.12	14825	824	844	105
400	73.5	9193	400	115	13.5	18	1.22	20981	1049	1045	123