--- title: "Young's Modulus of Steel and Stainless Steel" source: "https://www.laxconsteels.com/youngs-modulus-of-steel/" description: "Young's modulus of steel is 200 to 210 GPa and of austenitic stainless steel 193 to 200 GPa. Values by family, shear modulus, Poisson's ratio, temperature." --- # Young's Modulus of Steel and Stainless Steel: Elastic Modulus, Shear Modulus and Poisson's Ratio Send an enquiry 8 min read Young's modulus of steel, also called the modulus of elasticity or the elastic modulus, is the ratio of stress to strain while the steel deforms elastically, and it measures how stiff the metal is. For carbon and low-alloy steel it is about 200 to 210 GPa, or 29 to 30.5 million psi. For austenitic stainless steel such as 304 and 316 it is about 193 to 200 GPa, and ferritic, martensitic and duplex stainless steels lie between 200 and 220 GPa. The value changes little with grade, heat treatment or hardness, so a hardened alloy steel bends under a given load almost exactly as far as a mild steel bar of the same size. Two other elastic constants are used with it: the shear modulus, about 77 to 82 GPa for steels, and Poisson's ratio, close to 0.3. ## What Young's modulus measures A bar pulled in tension first stretches in proportion to the load and springs back to its original length when the load is removed. In this elastic range the stress, which is the force divided by the cross-section, and the strain, which is the extension divided by the original length, keep a constant ratio. That ratio is Young's modulus, written E. Strain has no unit, so E carries the unit of stress, and for metals it is stated in gigapascals. A modulus of 200 GPa means that a stress of 200 MPa stretches the steel by 0.1 percent, or 1 mm in every metre of length. An annealed 304 bar loaded to its specified minimum proof stress of 205 MPa is therefore about 1 mm per metre longer under load. On the stress-strain curve of the [tensile test](https://www.laxconsteels.com/yield-strength-vs-tensile-strength/), E is the slope of the straight first part of the line. Carbon steel follows that line closely up to its yield point. Austenitic stainless steel bends away from it gradually, which is why its yield strength is reported as a proof stress. The modulus is measured statically, from the slope of a load and extension record taken with an extensometer (ASTM E111), or dynamically, from the natural frequency at which a bar rings when struck (ASTM E1876). It varies so little within a family of steels that EN 10088-1 lists it as reference data, not as a tested requirement, and it does not appear on a mill test certificate. ## Young's modulus of steel and other metals *Young's modulus of steel families and other metals at room temperature, in GPa and million psi* | Material | Young's modulus, GPa | Million psi | Note | | --- | --- | --- | --- | | Carbon and low-alloy steel | 200 to 210 | 29.0 to 30.5 | EN 1993-1-1 design value 210 GPa | | Austenitic stainless steel ( [304](https://www.laxconsteels.com/grades/aisi-304/), 316, 321) | 193 to 200 | 28.0 to 29.0 | American data sheets 193, EN 10088-1 200 | | Ferritic stainless steel (430) | 200 to 220 | 29.0 to 31.9 | EN 10088-1 lists 220 | | Martensitic stainless steel (410, 420) | 200 to 215 | 29.0 to 31.2 | EN 10088-1 lists 215 | | Duplex stainless steel ( [2205](https://www.laxconsteels.com/grades/duplex-2205/), 2304) | 200 | 29.0 | same in EN and American data | | Titanium and titanium alloys | 105 to 120 | 15.2 to 17.4 | about 116 commercially pure | | Copper | 110 to 130 | 16.0 to 18.9 | 110 annealed | | Brass | 100 to 125 | 14.5 to 18.1 | depends on the alloy | | Aluminium and aluminium alloys | 68 to 70 | 9.9 to 10.2 | about one third of steel | | Magnesium | about 45 | 6.5 | under a quarter of steel | Steel is about three times as stiff as aluminium and nearly twice as stiff as titanium. Per unit of mass the three are almost equal. Dividing the modulus in GPa by the density in grams per cubic centimetre gives 25.5 for steel, 25.6 for aluminium and 25.7 for the common titanium alloy, using the densities in the [density of steel](https://www.laxconsteels.com/density-of-steel/) article. A lighter metal therefore saves weight where strength sets the size of a part, and saves little where stiffness does. ## Young's modulus of stainless steel Two sets of reference values are in use for stainless steel. American producers' data sheets and handbooks give 193 GPa for 304 and 316 and 200 GPa for the ferritic, martensitic and duplex grades. EN 10088-1 gives 200 GPa for the austenitic and duplex grades, 215 GPa for the martensitic grades and 220 GPa for the ferritic grades. The difference between 193 and 200 GPa changes a calculated deflection by about 3.5 percent. A designer normally takes the value that goes with the design code in use. Both sets place the families in the same order. The austenitic grades, which have a face-centred cubic crystal structure, sit at the low end. The ferritic, martensitic and duplex grades, whose structure is wholly or partly body-centred cubic like that of carbon steel, sit at or above the carbon steel value. ## Shear modulus, Poisson's ratio and bulk modulus The shear modulus, G, also called the modulus of rigidity, is the ratio of shear stress to shear strain. It governs how far a shaft twists under a torque. For carbon steel it is about 80 GPa, with published values from 77 to 82 GPa; EN 1993-1-1 uses 81 GPa. For austenitic stainless steel it is about 77 to 79 GPa. Poisson's ratio is the lateral contraction of a bar divided by its axial extension when it is pulled. For carbon and stainless steels it is close to 0.3, with measured values from about 0.29 to 0.31. For a material that behaves the same in every direction, the constants are linked: G equals E divided by 2(1 + Poisson's ratio). With E at 210 GPa and a ratio of 0.3, G is 81 GPa, which is the Eurocode figure. The bulk modulus, K, measures resistance to a uniform pressure on all sides. It follows from the same two constants, as E divided by 3(1 minus twice Poisson's ratio), and for steel it is about 160 to 170 GPa. ## Why heat treatment barely changes the modulus Young's modulus is set by the forces between atoms in the crystal lattice. Strength is set by how easily dislocations move through that lattice. Hardening, tempering, cold drawing and grain refinement act on the dislocations. They can raise the yield strength two or three times over and leave the modulus within a few percent. Published figures show this. Kaye and Laby list a carbon steel at 210 GPa before hardening and 201 GPa after, and a tool steel at 212 GPa and 203 GPa. Annealed 2205 duplex has more than twice the minimum proof stress of annealed 304, 450 MPa against 205 MPa, and its modulus is the same or at most 4 percent higher. The practical consequence is that a stronger grade lets a part carry more load before it yields, but does not make it deflect or vibrate less. Only the shape and size of the section change that. ## How temperature changes Young's modulus The modulus falls as temperature rises. Between room temperature and 300 degrees Celsius, carbon steel and austenitic stainless steel lose about 8 to 11 percent of their stiffness. At 500 degrees Celsius austenitic grades are about 18 percent below their room-temperature value. Above about 450 degrees Celsius carbon steel loses stiffness faster than austenitic stainless steel: ASME B31.1 gives about 141 GPa for carbon steel at 538 degrees Celsius, against 157 GPa for the austenitic grades. Below room temperature the modulus rises slightly. For this reason pressure piping codes tabulate the modulus against temperature. ## Units and conversions One gigapascal is 1,000 megapascals, and one megapascal is one newton per square millimetre, so 200 GPa is written 200,000 MPa or 200,000 N/mm2 in design calculations. American sources state the modulus in pounds per square inch. One ksi (1,000 psi) is 6.895 MPa, so 200 GPa is 29,000 ksi, or 29 million psi, and 193 GPa is 28 million psi. Older European tables use kilograms-force per square millimetre, where 1 kgf/mm2 is 9.807 MPa and 200 GPa is about 20,400 kgf/mm2. ## Young's modulus and shaft deflection: a worked example A round bar of 50 mm diameter rests on two bearings 1,000 mm apart and carries a load of 2 kN at mid-span. The deflection at the centre is F L3 / (48 E I), where I, the second moment of area of a round section, is pi d4 / 64, or 306,800 mm4. With E at 200,000 N/mm2 the deflection is 2,000 x 1,0003 / (48 x 200,000 x 306,800), or 0.68 mm. The bending stress in the same shaft is the bending moment, 500,000 N mm, divided by the section modulus, 12,270 mm3, or 41 MPa. That is a fifth of the 205 MPa minimum proof stress of annealed 304, so the shaft is nowhere near yielding. Its deflection may still be too large for a gear mesh or a seal. Changing to a stronger grade leaves it unchanged. Taking the 304 figure of 193 GPa gives 0.70 mm, and an aluminium bar of the same size would deflect 1.97 mm. Increasing the diameter to 55 mm reduces the deflection to 0.46 mm, about a third less, because I rises with the fourth power of the diameter. For this reason the diameter of a shaft is often set by deflection rather than by strength, and straightness and diameter tolerance are specified closely in [precision shaft quality bar](https://www.laxconsteels.com/everything-about-psq-bars-types-uses-and-selecting-the-right-manufacturer/). ## Bar for shafts and machined parts Laxcon Steels supplies [bright bar](https://www.laxconsteels.com/products/bright-bars/) from 5 to 115 mm and [precision shaft quality bar](https://www.laxconsteels.com/products/precision-shaft-quality-psq-bars/) from 8 to 81 mm in stainless, carbon and alloy steel grades. The certificate for each heat reports proof stress, tensile strength, elongation and hardness, and the physical properties of each grade are listed in the [grade reference](https://www.laxconsteels.com/grades/). ## Frequently asked questions ### What is the Young's modulus of steel? Carbon and low-alloy steel has a Young's modulus of about 200 to 210 GPa, or 29 to 30.5 million psi. Eurocode 3 uses 210 GPa for structural steel. The value is almost the same for every carbon and alloy steel grade, whatever its strength. ### What is the modulus of elasticity of 304 stainless steel? American data sheets give 193 GPa (28 million psi) for 304 and 316, and EN 10088-1 gives 200 GPa. The shear modulus is about 77 to 79 GPa and Poisson's ratio about 0.3. The modulus falls to about 179 GPa at 300 degrees Celsius on the EN figures. ### Does heat treatment change Young's modulus? Only by a few percent. Hardening a carbon steel lowers its modulus from about 210 to about 201 GPa, while its strength rises by a far larger proportion. Stiffness depends on the bonds between atoms, which heat treatment does not change, so a hardened part deflects almost exactly as far as an annealed one of the same size. ### Is Young's modulus the same as stiffness? No. Young's modulus is a property of the material. The stiffness of a part is the modulus multiplied by a factor that depends on its shape and length, such as the second moment of area for a beam. A larger section of a low-modulus metal can be stiffer than a small steel section. ## Sources - EN 10088-1, Stainless steels, Part 1: List of stainless steels, reference data for modulus of elasticity from 20 to 500 degrees Celsius. - EN 1993-1-1, Eurocode 3: Design of steel structures, material properties of structural steel. - ASME B31.1, Power Piping, tables of modulus of elasticity against temperature. - ASTM E111, Standard Test Method for Young's Modulus, Tangent Modulus, and Chord Modulus; ASTM E1876, Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Impulse Excitation of Vibration. - Kaye and Laby, Tables of Physical and Chemical Constants, National Physical Laboratory, section 2.2.2, elasticities of metals and alloys. - International Molybdenum Association, Practical Guidelines for the Fabrication of Duplex Stainless Steels, physical property tables. - INCO publication 2980, Austenitic chromium-nickel stainless steels: engineering properties at elevated temperatures. - ASTM A276/A276M, Standard Specification for Stainless Steel Bars and Shapes, for the proof stresses quoted. ![Stainless steel bright bars produced by Laxcon Steels](https://www.laxconsteels.com/images/products/stainless-steel-bright-bars.webp) Enquire about **Bright Bars** First name Last name Email Phone Company Location Product - Bright Bars - Precision Shaft Quality (PSQ) Bars - Pipes and Tubes - Hexagonal Bright Bars - Square Bright Bars - Cold-Drawn Flat Bars - Forged & Proof Machined Bars - HRAP Flat Bars - HRAP Equal Angles - HRAP Unequal Angles - Threaded Bars - Hot Rolled Round Cornered Squares (RCS) Bars - Hot Rolled Round Bars - Continuous Cast Billets / Blooms - Channels - Forging Quality Ingots - Precipitation Hardening Steels - Duplex Steel - T-Profile - Others Message \* Required ## From the Mill - [![Stainless steel bright bars produced by Laxcon Steels](https://www.laxconsteels.com/images/products/stainless-steel-bright-bars.webp) Bright Bars 5 mm to 115 mm](https://www.laxconsteels.com/products/bright-bars/) - [![Stainless steel precision shaft quality bars produced by Laxcon Steels](https://www.laxconsteels.com/images/products/stainless-steel-precision-shaft-quality-psq-bars.webp) Precision Shaft Quality (PSQ) Bars 8 mm to 81 mm](https://www.laxconsteels.com/products/precision-shaft-quality-psq-bars/) - [![Optical emission spectrometer used to certify grade composition](https://www.laxconsteels.com/images/quality/laxcon-steels-optical-emission-spectrometer.webp) Grade reference](https://www.laxconsteels.com/grades/)