Hardness (measurement & conversion)

This page is not a universal hardness comparison facility for its own sake.
It is provided to help you compare hardness scales with a reasonable degree of confidence.

There are a number of hardness comparison calculation methods available in many publications the accuracy of which is variable and difficult to gauge without a good deal of verification work. CalQlata has therefore developed its own formulas⁽¹⁾ that it can use internally with confidence. These formulas and their accuracy can be found in the following Tables. Our aim was to keep errors within ±0.5% throughout the range although the variable nature of the documented data has made this a little challenging (see Shore below).

The following Tables include documented values, calculated {Q} values and associated errors for each set of formulas (see Comparison Charts at the bottom of this page).

CalQlata has included all the following conversion formulas in a hardness conversion calculator

Rockwell C (HRC)

CalQlata has compared the most commonly used hardness measurement systems with Rockwell 'C'^#, which is regarded as the most ubiquitous hardness test method and its Grade C the most commonly used scale.
# except Rockwell 'B' which is compared with Brinell std.

Hugh and Stanley Rockwell together invented this hardness testing method in the USA in the mid 19th century, which involves no calculations and the hardness number is read from a dial or digital display. It is more accurate and less damaging than the Brinell method, simpler and quicker to operate than the Vickers method and more reliable than the Shore hardness test.

It has numerous measurement scales: A to G, 15, 30 & 45 and measures the depth of penetration of a diamond spherocone with tip diameter of 0.2mm and an included angle of 120° or a steel ball ranging in diameter from 1.5mm to 10mm all of which can be applied with a load ranging from 15kg to 3000kg.

The operational procedure is to apply an initial load of 10kg followed by the main test load which is held for 30 seconds. The hardness number is based upon the depth of penetration.

Vickers Hardness Number (HV)

This test, which was devised at Vickers Ltd. by Robert Smith and George Sandland is very accurate when compared with the Brinell and Rockwell methods and may be used on sheet material but the equipment is expensive and takes longer to operate accurately.

The Vickers test is based upon the indentation of a diamond pyramid, with an included peak angle of 136°, for a period of 30 seconds. The Vickers number (HV) is the ratio of the force (F) and the square of the depth of penetration (D). The applied force is 5, 10, 20, 30, 50 or 120kg; 50kg being the norm.

HV = F ÷ (0.5393 x d²)
where d is the diagonal length of the indentation.

HRC	HV	HV {Q}	Error	Formulas
68	940	927	1.4%	HV = (223xHRC+14500)÷(100-HRC) HRC = (100xHV-14500)÷(223+HV)
67	900	892	0.9%
66	865	859	0.7%
65	832	828	0.4%
64	800	799	0.1%
63	772	772	0.1%
62	746	745	0.1%
61	720	721	0.1%
60	697	697	0.0%
59	674	675	0.1%
58	653	653	0.0%
57	633	633	0.0%
56	613	613	0.1%
55	595	595	0.0%
54	577	577	0.0%
53	560	560	0.0%
52	544	544	0.1%
51	528	528	0.0%
50	513	513	0.0%
49	498	499	0.1%
48	484	485	0.1%
47	471	471	0.1%
46	458	458	0.1%
45	446	446	0.0%
44	434	434	0.0%
43	423	423	0.1%
42	412	411	0.1%
41	402	401	0.3%
40	392	390	0.4%
39	382	380	0.5%
38	372	371	0.4%
37	363	361	0.5%
36	354	352	0.6%
35	345	343	0.5%
34	336	335	0.4%
33	327	326	0.2%
32	318	318	0.1%
31	310	310	0.1%
30	302	303	0.2%
29	294	295	0.4%
28	286	288	0.7%
27	279	281	0.8%
26	272	274	0.8%
25	266	268	0.6%
24	260	261	0.5%
23	254	255	0.4%
22	248	249	0.3%
21	243	243	0.1%
20	238	237	0.4%

Brinell Hardness Number - std (BHN)

A standard ball is used for the Brinell hardness test on materials with a BHN value of less than 450.

This test, which was devised by the Swedish engineer Dr Johan August Brinell is less accurate than the Vickers method but benefits from not actually requiring any special equipment so long as you can accurately measure the applied load, making it ideal for improvisation. However, the thickness of the test specimen must be greater than 10 times the depth of the indentation, which is not insignificant and cannot be regarded as non-destructive testing due to the size of the indentation produced.

The depth of indentation (d) is generated by applying a force 'F' to a hard steel sphere of diameter 'D' for a period of at least 15 seconds (30 seconds for nonferrous metals).
The Brinell hardness number (BHN) is calculated as follows:

BHN = F ÷ A
where A is the surface area of the indentation: A = ½.π.D x ( D - √[D²-d²] )

A certain amount of intelligence is required to use this method accurately in that insufficient and/or excessive depth of impression will result in misleading or inaccurate results. The optimum depth will be between 2.5 and 4.75mm for a standard 10mm ball.

The following table is based upon a 10mm diameter ball and a force of 3000kg

HRC	BHN	BHN {Q}	Error	Formulas
52	508	497	2.2%	BHN = 122+HRC1.5 HRC = 1.5√[BHN-122]
51	494	486	1.6%
50	481	476	1.1%
49	469	465	0.9%
48	455	455	0.1%
47	443	444	0.3%
46	432	434	0.5%
45	421	424	0.7%
44	409	414	1.2%
43	400	404	1.0%
42	390	394	1.1%
41	381	385	0.9%
40	371	375	1.1%
39	362	366	1.0%
38	353	356	0.9%
37	344	347	0.9%
36	336	338	0.6%
35	327	329	0.6%
34	319	320	0.4%
33	311	312	0.2%
32	301	303	0.7%
31	294	295	0.2%
30	286	286	0.1%
29	279	278	0.3%
28	271	270	0.3%
27	264	262	0.6%
26	258	258	0.1%	BHN = 156+HRC1.42 HRC = 1.42√[BHN-156]
25	253	253	0.1%
24	247	248	0.2%
23	243	242	0.4%
22	237	237	0.2%
21	231	231	0.1%
20	226	226	0.0%

Brinell Hardness Number - Hultgren (BHN-H) ⁽⁴⁾

A spherical ball manufactured from Axel Gustaf Emanuel Hultgren's tungsten steel, which has since become known as Hultgren steel, will flatten less than a standard hardened steel ball and is used for the Brinell hardness test on materials with a BHN value of up to 500.

The following table is based upon a 10mm diameter ball and a force of 3000kg

HRC	BHN-H	BHN-H {Q}	Error	Formulas
60	613	613	0.0%	BHN = 70+HRC1.538 HRC = 1.538√[BHN-70]
59	599	599	0.0%
58	587	585	0.3%
57	575	572	0.6%
56	561	558	0.5%
55	546	545	0.2%
54	534	532	0.4%
53	519	519	0.1%
52	508	506	0.4%
51	494	493	0.2%
50	481	480	0.2%
49	469	468	0.3%
48	455	455	0.1%
47	443	443	0.0%
46	432	431	0.3%
45	421	419	0.5%
44	409	409	0.0%	BHN = 129+HRC1.489 HRC = 1.489√[BHN-129]
43	400	400	0.1%
42	390	390	0.1%
41	381	381	0.0%
40	371	372	0.2%
39	362	363	0.3%
38	353	354	0.3%
37	344	345	0.4%
36	336	337	0.2%
35	327	328	0.3%
34	319	320	0.2%
33	311	311	0.1%
32	301	303	0.7%
31	294	295	0.4%
30	286	287	0.4%
29	279	279	0.2%
28	271	272	0.3%
27	264	264	0.1%
26	258	257	0.4%
25	253	253	0.1%	BHN = 153.4+HRC1.43 HRC = 1.43√[BHN-153.4]
24	247	248	0.2%
23	243	242	0.4%
22	237	237	0.2%
21	231	231	0.1%
20	226	226	0.0%

Brinell Hardness Number - tungsten (BHN-W)

A spherical ball manufactured from tungsten carbide will flatten less than standard or Hultgren balls and is used for hard materials with a BHN value of up to 630.

Whilst tungsten carbide balls may need to be smaller than steel balls (10mm) the accuracy of this test remains maximised by using the largest ball available. Therefore, even for very hard materials it is advisable to use a 10mm tungsten carbide ball where possible along with a suitably high load.

The following table is based upon a 10mm diameter ball and a force of 3000kg

HRC	BHN-W	BHN-W {Q}	Error	Formulas
65	739	743	0.5%	BHN = HRC1.593-30 HRC = 1.593√[BHN+30]
64	722	724	0.2%
63	705	705	0.0%
62	688	687	0.2%
61	670	668	0.3%
60	654	650	0.6%
59	634	632	0.3%
58	615	614	0.1%
57	595	597	0.3%
56	577	579	0.4%
55	560	562	0.4%
54	543	545	0.4%
53	525	528	0.6%
52	512	511	0.1%
51	496	495	0.2%
50	481	479	0.5%
49	469	468	0.2%	BHN = 110+HRC1.511 HRC = 1.511√[BHN-110]
48	455	457	0.4%
47	443	446	0.7%
46	432	435	0.8%
45	421	425	0.9%
44	409	414	1.3%
43	400	404	1.0%
42	390	394	0.9%
41	381	383	0.6%
40	371	373	0.7%
39	362	364	0.4%
38	353	354	0.2%
37	344	344	0.1%
36	336	335	0.4%
35	327	325	0.5%
34	319	316	0.8%	BHN = 143+HRC1.462 HRC = 1.462√[BHN-143]
33	311	309	0.6%
32	301	302	0.2%
31	294	294	0.2%
30	286	287	0.5%
29	279	280	0.5%
28	271	274	0.9%
27	264	267	1.1%
26	258	260	0.8%
25	253	254	0.2%
24	247	247	0.1%
23	243	241	0.9%
22	237	235	0.9%
21	231	229	1.0%
20	226	223	1.4%

Rockwell Hardness Number - A (HRA)

The Rockwell A grade is suitable for extremely hard materials such as tungsten carbides, hardened high carbon steels and ceramics. It is also used for hard thin metal sheets.

The following table is based upon a diamond indenter and a force of 60kg

HRC	HRA	HRA {Q}	Error	Formulas
68	85.6	85	0.4%	HRA = 49.742+0.5229xHRC HRC = (HRA-49.742)÷0.5229
67	85	85	0.3%
66	84.5	84	0.3%
65	83.9	84	0.2%
64	83.4	83	0.2%
63	82.8	83	0.1%
62	82.3	82	0.2%
61	81.8	82	0.2%
60	81.2	81	0.1%
59	80.7	81	0.1%
58	80.1	80	0.0%
57	79.6	80	0.1%
56	79	79	0.0%
55	78.5	79	0.0%
54	78	78	0.0%
53	77.4	77	0.1%
52	76.8	77	0.2%
51	76.3	76	0.1%
50	75.9	76	0.0%
49	75.2	75	0.2%
48	74.7	75	0.2%
47	74.1	74	0.3%
46	73.6	74	0.3%
45	73.1	73	0.2%
44	72.5	73	0.3%
43	72	72	0.3%
42	71.5	72	0.3%
41	70.9	71	0.4%
40	70.4	71	0.4%
39	69.9	70	0.3%
38	69.4	70	0.3%
37	68.9	69	0.3%
36	68.4	69	0.2%
35	67.9	68	0.2%
34	67.4	68	0.2%
33	66.8	67	0.3%
32	66.3	66	0.3%
31	65.8	66	0.2%
30	65.3	65	0.2%
29	64.7	65	0.3%
28	64.3	64	0.1%
27	63.8	64	0.1%
26	63.3	63	0.1%
25	62.8	63	0.0%
24	62.4	62	0.2%
23	62	62	0.4%
22	61.5	61	0.4%
21	61	61	0.5%
20	60.5	60	0.5%

Rockwell Hardness Number - B (HRB)

The same operational method as for the 'A' scale (see above) but this test applies to softer materials, such as low carbon steels, or steels in annealed condition and soft metals that fall below or around the lower end of the Rockwell 'C' Scale (i.e. less than 300).

A comparison is carried out using the standard Brinell test ball of 10mm and a 3000kg applied load (see BHN above) in order to facilitate a conversion with other hardness measurement systems.

HRB	BHN	BHN {Q}	Error	Formulas
100	240	240.6	0.3%	BHN = 96+1.051HRB HRB = Log1.051(BHN-96)
99	234	233.6	0.2%
98	228	226.9	0.5%
97	222	220.6	0.6%
96	216	214.5	0.7%
95	210	208.8	0.6%
94	205	203.3	0.8%
93	200	198.1	0.9%
92	195	193.2	0.9%
91	190	188.4	0.8%
90	185	184.0	0.6%
89	180	179.7	0.2%
88	176	175.6	0.2%
87	172	171.8	0.1%
86	169	168.1	0.5%
85	165	164.6	0.3%
84	162	161.3	0.5%
83	159	158.1	0.6%
82	156	155.1	0.6%
81	153	152.2	0.5%
80	150	149.5	0.3%
79	147	146.9	0.1%
78	144	144.4	0.3%
77	141	142.1	0.8%
76	139	139.8	0.6%
75	137	137.7	0.5%
74	135	135.7	0.5%

Rockwell Hardness Number - D (HRD)

The Rockwell D grade is for case hardened materials that need a lighter load than the C-Grade test but is otherwise identical.

The following table is based upon a diamond indenter and a force of 100kg

HRC	HRD	HRD {Q}	Error	Formulas
68	76.9	77	0.0%	HRD = 24.767+0.7667xHRC HRC = (HRD-24.767)÷0.7667
67	76.1	76	0.0%
66	75.4	75	0.0%
65	74.5	75	0.1%
64	73.8	74	0.0%
63	73	73	0.1%
62	72.2	72	0.1%
61	71.5	72	0.0%
60	70.7	71	0.1%
59	69.9	70	0.1%
58	69.2	69	0.1%
57	68.5	68	0.0%
56	67.7	68	0.0%
55	66.9	67	0.1%
54	66.1	66	0.1%
53	65.4	65	0.0%
52	64.6	65	0.1%
51	63.8	64	0.1%
50	63.1	63	0.0%
49	62.1	62	0.4%
48	61.4	62	0.3%
47	60.8	61	0.0%
46	60	60	0.1%
45	59.2	59	0.1%
44	58.5	59	0.0%
43	57.7	58	0.1%
42	56.9	57	0.1%
41	56.2	56	0.0%
40	55.4	55	0.1%
39	54.6	55	0.1%
38	53.8	54	0.2%
37	53.1	53	0.1%
36	52.3	52	0.1%
35	51.5	52	0.2%
34	50.8	51	0.1%
33	50	50	0.1%
32	49.2	49	0.2%
31	48.4	49	0.3%
30	47.7	48	0.1%
29	47	47	0.0%
28	46.1	46	0.3%
27	45.2	45	0.6%
26	44.6	45	0.2%
25	43.8	44	0.3%
24	43.1	43	0.2%
23	42.1	42	0.7%
22	41.6	42	0.1%
21	40.9	41	0.1%
20	40.1	40	0.0%

Rockwell Hardness Number - 15-15N (HR15) ⁽⁵⁾⁽⁶⁾

The same operational method as for the A, B, C & D ranges applies to this hardness range but uses the '15' scale and a 15kg load.

This scale is used for materials that will result in very small indentations such as very hard materials, the harder the material the greater the load (i.e. 30kg or 45kg see below).

The following table is based upon a diamond indenter, a force of 15kg and the 'N' sub-scale

HRC	HR15	HR15 {Q}	Error	Formulas
68	93.2	93	0.1%	HR15 = 61.5+HRC0.82 HRC = 0.82√[HR15-61.5]
67	92.9	93	0.0%
66	92.5	93	0.1%
65	92.2	92	0.0%
64	91.8	92	0.0%
63	91.4	91	0.0%
62	91.1	91	0.1%
61	90.7	91	0.1%
60	90.2	90	0.0%
59	89.8	90	0.2%	HR15 = 56+HRC0.865 HRC = 0.865√[HR15-56]
58	89.3	90	0.3%
57	88.9	89	0.1%
56	88.3	89	0.3%
55	87.9	88	0.1%
54	87.4	88	0.1%
53	86.9	87	0.1%
52	86.4	87	0.1%
51	85.9	86	0.1%
50	85.5	85	0.0%
49	85	85	0.0%
48	84.5	84	0.0%
47	83.9	84	0.1%
46	83.5	83	0.1%
45	83	83	0.1%
44	82.5	82	0.1%
43	82	82	0.1%
42	81.5	81	0.2%
41	80.9	81	0.1%
40	80.4	80	0.1%
39	79.9	80	0.1%
38	79.4	79	0.2%
37	78.8	79	0.1%
36	78.3	78	0.1%
35	77.7	78	0.1%
34	77.2	77	0.1%
33	76.6	77	0.0%
32	76.1	76	0.1%
31	75.6	75	0.1%
30	75	75	0.1%
29	74.5	74	0.1%
28	73.9	74	0.1%
27	73.3	73	0.0%
26	72.8	73	0.1%
25	72.2	72	0.0%
24	71.6	72	0.0%
23	71	71	0.1%
22	70.5	70	0.0%
21	69.9	70	0.0%
20	69.4	69	0.1%

Rockwell Hardness Number - 30-30N (HR30) ⁽⁵⁾⁽⁶⁾

The same operational method as for the '15' scale (see above) but uses the '30' scale and a 30kg load.

This scale is used for materials that will result in very small indentations such as very hard materials, the harder the material the greater the load (i.e. 15kg see above or 45kg see below).

The following table is based upon a diamond indenter, a force of 30kg and the 'N' sub-scale

HRC	HR30	HR30 {Q}	Error	Formulas
68	84.4	85	0.2%	HR30 = 22.6+HRC0.978 HRC = 0.978√[HR30-22.6]
67	83.6	84	0.1%
66	82.8	83	0.0%
65	81.9	82	0.0%
64	81.1	81	0.1%
63	80.1	80	0.0%
62	79.3	79	0.1%
61	78.4	78	0.1%
60	77.5	77	0.1%
59	76.6	77	0.1%
58	75.7	76	0.1%
57	74.8	75	0.1%
56	73.9	74	0.1%
55	73	73	0.1%
54	72	72	0.1%
53	71.2	71	0.0%
52	70.2	70	0.1%
51	69.4	69	0.0%
50	68.5	68	0.0%
49	67.6	68	0.0%
48	66.7	67	0.0%
47	65.8	66	0.0%
46	64.8	65	0.1%
45	64	64	0.0%
44	63.1	63	0.0%
43	62.2	62	0.0%
42	61.3	61	0.0%
41	60.4	60	0.0%
40	59.5	59	0.0%
39	58.6	59	0.0%
38	57.7	58	0.0%
37	56.8	57	0.0%
36	55.9	56	0.1%
35	55	55	0.1%
34	54.2	54	0.3%
33	53.3	53	0.3%
32	52.1	52	0.3%
31	51.3	51	0.1%
30	50.4	50	0.1%
29	49.5	50	0.1%
28	48.6	49	0.0%
27	47.7	48	0.0%
26	46.8	47	0.0%
25	45.9	46	0.0%
24	45	45	0.0%
23	44	44	0.2%
22	43.2	43	0.1%
21	42.3	42	0.1%
20	41.5	41	0.4%

Rockwell Hardness Number - 45-45N (HR45) ⁽⁵⁾⁽⁶⁾

The same operational method as for the '15' scale (see above) but uses the '45' scale and a 45kg load.

This scale is used for materials that will result in very small indentations such as very hard materials, the harder the material the greater the load (i.e. 30kg or 45kg see above).

The following table is based upon a diamond indenter, a force of 45kg and the 'N' sub-scale

HRC	HR45	HR45 {Q}	Error	Formulas
68	75.4	75	0.1%	HR45 = 0.86+HRC1.022 HRC = 1.022√[HR45-0.86]
67	74.2	74	0.2%
66	73.3	73	0.1%
65	72	72	0.2%
64	71	71	0.0%
63	69.9	70	0.0%
62	68.8	69	0.1%
61	67.7	68	0.1%
60	66.6	67	0.1%
59	65.5	65	0.2%
58	64.3	64	0.0%
57	63.2	63	0.1%
56	62	62	0.1%
55	60.9	61	0.0%
54	59.8	60	0.3%	HR45 = HRC1.038-2.85 HRC = 1.038√[HR45+2.85]
53	58.6	59	0.3%
52	57.4	58	0.3%
51	56.1	56	0.5%
50	55	55	0.3%
49	53.8	54	0.3%
48	52.5	53	0.5%
47	51.4	52	0.3%
46	50.3	50	0.1%
45	49	49	0.3%
44	47.8	48	0.3%
43	46.7	47	0.1%
42	45.5	46	0.1%
41	44.3	44	0.1%
40	43.1	43	0.2%
39	41.9	42	0.2%
38	40.8	41	0.0%
37	39.6	40	0.0%
36	38.4	38	0.0%
35	37.2	37	0.0%
34	36.1	36	0.2%
33	34.9	35	0.2%
32	33.7	34	0.1%
31	32.5	32	0.1%
30	31.3	31	0.0%
29	30.1	30	0.0%
28	28.9	29	0.1%
27	27.8	28	0.2%
26	26.7	27	0.5%
25	25.5	25	0.4%
24	24.3	24	0.3%
23	23.1	23	0.2%
22	22	22	0.5%
21	20.7	21	0.1%
20	19.6	20	0.2%

Shore Hardness Number (SHN)

The Shore Scleroscope (or durometer) was developed by Albert F. Shore (USA) and uses a small diamond tipped hammer weighing 1/12th of an ounce (2.36246g) in a graduated glass tube to measure the hardness of a material. The hammer is dropped from a predefined height and the measured rebound height defines the hardness of the impacted material.

This is a simple system that requires no calculation and no complicated equipment. Whilst it is not considered as accurate as the other hardness testing methods, this is only because its operation is prone to misuse. However, if correctly used and read, this method should be at least as accurate as any other.

This equipment has the added advantage of being practical to transport and use in any environment, but works best on hard materials, i.e. the results for materials such as lead will be unreliable as the rebound height will be virtually non-existent.

The greater than expected errors in the calculated results are due to the erratic nature of the documented values (see image) which, if measured accurately should follow a much smoother curve. The curve generated by the formulas (SHN {Q}) is considered (by CalQlata) to be more representative of the actual Shore values than the documented values (SHN).

HRC	SHN	SHN {Q}	Error	Formulas
68	97	97	0.5%	SHN = 201.5 - 1½.√[ 125² - (36+HRC)² ] HRC = √[ 125² - ((201.5-SHN) / 1½)²] - 36
67	95	95	0.3%
66	92	93	1.2%
65	91	91	0.0%
64	88	89	1.1%
63	87	87	0.0%
62	85	85	0.1%
61	83	83	0.3%
60	81	81	0.5%
59	80	80	0.5%
58	78	78	0.1%
57	76	76	0.3%
56	75	75	0.6%
55	74	73	1.4%
54	72	71	0.9%
53	71	70	1.6%
52	69	68	1.0%
51	68	67	1.7%
50	67	65	2.3%
49	66	64	3.0%
48	64	63	2.1%
47	63	61	2.7%
46	62	60	3.3%
45	60	59	2.2%
44	58	57	1.0%
43	57	56	1.4%
42	56	55	1.8%
41	55	54	2.2%
40	54	53	2.5%
39	52	52	1.0%
38	51	50	1.2%
37	50	49	1.4%
36	49	48	1.6%
35	48	47	1.7%
34	47	46	1.8%
33	46	45	1.8%
32	44	44	0.4%
31	43	43	0.5%
30	42	42	0.6%
29	41	41	0.8%
28	41	40	1.4%
27	40	40	1.1%
26	38	39	1.8%
25	38	38	0.4%
24	37	37	0.0%
23	36	36	0.6%
22	35	35	1.2%
21	35	35	1.1%
20	34	34	0.4%

Comparison Charts

HRC: The common comparison hardness range of values (Rockwell C). Values below 20 are ignored as their reliability varies too much between test methods.

e.g. SHN: The comparable hardness range from a documented source⁽²⁾; Brinell, Vickers, Shore, etc.

e.g. SHN {Q}: The comparable range of values calculated using the formulas in the right-hand column. The graph immediately above each Table is a plot of the documented values compared with the calculated values.

Error: The percentage difference between documented and calculated values using the formulas in the right-hand column.

Formulas: The formulas used to calculate the Q values⁽³⁾.

Notes

1. Except for the 'Vickers' formula which can be found in numerous sources; e.g. https://link.springer.com/article/10.1007%2FBF02833189#page-2
2. Reference publication 2 (see Further Reading below)
3. These formulas have been devised by CalQlata
4. The same operating conditions and calculation methods are used for this test as for the Brinell standard test (see above).
5. Two sub-scales are provided: N & T
   N is for very hard materials that will result in a small indentation
   T is for softer materials to minimise the indentation
6. The hardness values are comparable with both the above sub-scales in that any given material would show the same hardness value irrespective of the sub-scale used. Each scale, however, is better suited, and therefore more accurate and reliable if used with the appropriate materials.

Further Reading

You will find further reading on this subject in reference publications^{(2, 3 & 44)}