# Specific modulus

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Ratio of stiffness to mass for a material

**Specific modulus** is a [materials property](/source/Materials_property) consisting of the [elastic modulus](/source/Elastic_modulus) per mass [density](/source/Density) of a material. It is also known as the **stiffness to weight ratio** or **specific stiffness**. High specific modulus materials find wide application in [aerospace](/source/Aerospace) applications where minimum structural [weight](/source/Weight) is required. The [dimensional analysis](/source/Dimensional_analysis) yields units of distance squared per time squared. The equation can be written as:

- specific modulus = E / ρ {\displaystyle {\text{specific modulus}}=E/\rho }

where E {\displaystyle E} is the elastic modulus and ρ {\displaystyle \rho } is the density.

The utility of specific modulus is to find materials which will produce structures with minimum weight, when the primary design limitation is deflection or physical deformation, rather than load at breaking—this is also known as a "stiffness-driven" structure. Many common structures are stiffness-driven over much of their use, such as airplane wings, bridges, masts, and bicycle frames.

To emphasize the point, consider the issue of choosing a material for building an airplane. Aluminum seems obvious because it is "lighter" than steel, but steel is stronger than aluminum, so one could imagine using thinner steel components to save weight without sacrificing (tensile) strength. The problem with this idea is that there would be a significant sacrifice of stiffness, allowing, e.g., wings to flex unacceptably. Because it is stiffness, not tensile strength, that drives this kind of decision for airplanes, we say that they are stiffness-driven.

The connection details of such structures may be more sensitive to strength (rather than stiffness) issues due to effects of [stress risers](/source/Stress_risers).

Specific modulus is not to be confused with [specific strength](/source/Specific_strength), a term that compares strength to density.

## Applications

### Specific stiffness in tension

The use of specific stiffness in [tension](/source/Tension_(physics)) applications is straightforward. Both [stiffness](/source/Stiffness) in [tension](/source/Tension_(physics)) and total [mass](/source/Mass) for a given length are directly proportional to [cross-sectional area](/source/Cross_section_(geometry)). Thus performance of a beam in tension will depend on *[Young's modulus](/source/Young's_modulus) divided by [density](/source/Density)*.

### Specific stiffness in buckling and bending

Specific stiffness can be used in the design of [beams](/source/Beam_(structure)) subject to [bending](/source/Bending) or Euler [buckling](/source/Buckling), since bending and buckling are stiffness-driven. However, the role that [density](/source/Density) plays changes depending on the problem's constraints.

#### Beam with fixed dimensions; goal is weight reduction

Examining the formulas for [buckling](/source/Buckling) and [deflection](/source/Deflection_(engineering)), we see that the force required to achieve a given deflection or to achieve buckling depends directly on [Young's modulus](/source/Young's_modulus).

Examining the [density](/source/Density) formula, we see that the [mass](/source/Mass) of a beam depends directly on the density.

Thus if a beam's cross-sectional dimensions are constrained and weight reduction is the primary goal, performance of the beam will depend on *[Young's modulus](/source/Young's_modulus) divided by [density](/source/Density)*.

#### Beam with fixed weight; goal is increased stiffness

By contrast, if a beam's weight is fixed, its cross-sectional dimensions are unconstrained, and increased stiffness is the primary goal, the performance of the beam will depend on Young's modulus divided by either density squared or cubed. This is because a beam's overall [stiffness](/source/Stiffness), and thus its resistance to Euler [buckling](/source/Buckling) when subjected to an axial load and to [deflection](/source/Deflection_(engineering)) when subjected to a [bending moment](/source/Bending_moment), is directly proportional to both the Young's modulus of the beam's material and the [second moment of area](/source/Second_moment_of_area) (area moment of inertia) of the beam.

Comparing the [list of area moments of inertia](/source/List_of_area_moments_of_inertia) with formulas for [area](/source/Area) gives the appropriate relationship for beams of various configurations.

#### Beam's cross-sectional area increases in two dimensions

Consider a beam whose cross-sectional area increases in two dimensions, e.g. a solid round beam or a solid square beam.

By combining the [area](/source/Area) and [density](/source/Density) formulas, we can see that the radius of this beam will vary with approximately the inverse of the square of the density for a given mass.

By examining the formulas for [area moment of inertia](/source/List_of_area_moments_of_inertia), we can see that the stiffness of this beam will vary approximately as the fourth power of the radius.

Thus the second moment of area will vary approximately as the inverse of the density squared, and performance of the beam will depend on *[Young's modulus](/source/Young's_modulus) divided by [density](/source/Density) squared*.

#### Beam's cross-sectional area increases in one dimension

Consider a beam whose cross-sectional area increases in one dimension, e.g. a thin-walled round beam or a rectangular beam whose height but not width is varied.

By combining the [area](/source/Area) and [density](/source/Density) formulas, we can see that the radius or height of this beam will vary with approximately the inverse of the density for a given mass.

By examining the formulas for [area moment of inertia](/source/List_of_area_moments_of_inertia), we can see that the stiffness of this beam will vary approximately as the third power of the radius or height.

Thus the second moment of area will vary approximately as the inverse of the cube of the density, and performance of the beam will depend on *[Young's modulus](/source/Young's_modulus) divided by [density](/source/Density) cubed*.

However, caution must be exercised in using this metric. Thin-walled beams are ultimately limited by local buckling and [lateral-torsional buckling](/source/Buckling#Lateral-torsional_buckling). These buckling modes depend on material properties other than stiffness and density, so the stiffness-over-density-cubed metric is at best a starting point for analysis. For example, most wood species score better than most metals on this metric, but many metals can be formed into useful beams with much thinner walls than could be achieved with wood, given wood's greater vulnerability to local buckling. The performance of thin-walled beams can also be greatly modified by relatively minor variations in geometry such as [flanges](/source/Flange) and stiffeners.[1][2][3]

### Stiffness versus strength in bending

Note that the ultimate strength of a beam in bending depends on the ultimate strength of its material and its [section modulus](/source/Section_modulus), not its stiffness and second moment of area. Its deflection, however, and thus its resistance to Euler buckling, will depend on these two latter values.

## Approximate specific stiffness for various materials

Specific stiffness of the full range of materials

Specific stiffness of materials within the range 0.9–5.0 g/cm3 density and 10–1300 GPa stiffness

Approximate specific stiffness for various materials. No attempt is made to correct for materials whose stiffness varies with their density. Material Young's modulus (GPa) Density (g/cm3) Young's modulus per density; specific stiffness (106 m2s−2) Young's modulus per density squared (103 m5kg−1s−2) Young's modulus per density cubed (m8kg−2s−2) Reference Latex foam, low density, 10% compression[4] 5.9×10^−7 0.06 9.83×10^−6 0.000164 0.00273 Reversible Assembled Cellular Composite Materials 0.0123 0.0072 1.71 237 32,953 [5][6] Self Reprogrammable Mechanical Metamaterials 0.0011129 0.0103 0.108 10.5 1,018 [7][8] Latex foam, low density, 40% compression[4] 1.8×10^−6 0.06 3×10^−5 0.0005 0.00833 Latex foam, high density, 10% compression[4] 1.3×10^−5 0.2 6.5×10^−5 0.000325 0.00162 Latex foam, high density, 40% compression[4] 3.8×10^−5 0.2 0.00019 0.00095 0.00475 Silica aerogel, medium density[9] 0.00035 0.09 0.00389 0.0432 0.48 Rubber (small strain) 0.055±0.045 1.055±0.145[10] 0.059±0.051 0.06345±0.05655 0.0679±0.0621 Expanded polystrene (EPS) foam, low density (1 lb/ft3)[11] 0.00137 0.016 0.086 5.35 334 Silica aerogel, high density[9] 0.024 0.25 0.096 0.384 1.54 Expanded polystrene (EPS) foam, medium density (3 lb/ft3)[11] 0.00524 0.048 0.11 2.3 47 Low-density polyethylene 0.2 0.925±0.015 0.215±0.005 0.235±0.005 0.255±0.015 PTFE (Teflon) 0.5 2.2 0.23 0.10 0.047 Duocel aluminum foam, 8% density[12] 0.102 0.216 0.472 2.19 10.1 Extruded polystrene (XPS) foam, medium density (Foamular 400)[13][14] 0.013789 0.0289 0.48 16.5 571 Extruded polystrene (XPS) foam, high density (Foamular 1000)[13][14] 0.02551 0.0481 0.53 11 229 HDPE 0.8 0.95[15] 0.84 0.89 0.93 Duocel copper foam, 8% density[16] 0.736 0.717 1.03 1.43 2 Polypropylene[17] 1.2±0.3 0.9 1.33±0.33 1.48±0.37 1.65±0.41 Polyethylene terephthalate 2.35±0.35 1.4125±0.0425 1.7±0.3 1.17±0.23 0.875±0.225 Nylon 3.0±1.0 1.15 2.6±0.9 2.25±0.75 1.95±0.65 Polystyrene 3.25±0.25 1.05 3.1±0.2 2.95±0.25 2.8±0.2 Biaxially-oriented Polypropylene[17] 3.2±1.0 0.9 3.56±1.11 3.95±1.23 4.39±1.37 Medium-density fibreboard 4 0.75[18] 5.3 7.1 9.5 Titanium foam, low density[19] 5.3 0.991 5.35 5.4 5.45 Titanium foam, high density[19] 20 3.15 6.35 2.02 0.64 Foam glass[20] 0.9 0.12 7.5 62.5 521 Copper (Cu) 117 8.94 13 1.5 0.16 Brass and bronze 112.5±12.5 8.565±0.165 13.0±2.0 1.55±0.25 0.18±0.03 Zinc (Zn) 108 7.14 15 2.1 0.29 Oak wood (along grain) 11 0.76±0.17[21] 15.5±3.5 22.5±9.5 34.0±20.0 Concrete (under compression) 40±10 2.4 17±4 6.95±1.75 2.9±0.7 Glass-reinforced plastic[22][23][24] 31.65±14.45 1.8 18±8 9.65±4.35 5.4±2.5 Pine wood 8.963 0.505±0.155[21] 20±6 47±26 120±89 Balsa, low density (4.4 lb/ft3)[25] 1.41 0.071 20 280 3,940 Tungsten (W) 400 19.25 21 1.1 0.056 Sitka spruce green[26][27][28] 8.7±0.7 0.37 23.5±2 64±5 172±13 Osmium (Os) 550 22.59 24 1.1 0.048 Balsa, medium density (10 lb/ft3)[25] 3.86 0.163 24 145 891 Steel 200 7.9±0.15 25±0.5 3.2±0.1 0.41±0.02 Titanium alloys 112.5±7.5 4.5 25±2 5.55±0.35 1.23±0.08 Balsa, high density (16 lb/ft3)[25] 6.57 0.265 25 94 353 Wrought iron 200±10 7.7±0.2 26±2 3.35±0.35 0.445±0.055 Magnesium metal (Mg) 45 1.738 26 15 8.6 Sitka spruce dry[26][27][28] 10.4±0.8 0.4 26±2 65±5 162±12 Macor machineable glass-ceramic[29] 66.9 2.52 26.55 10.53 8.14 Cordierite[30] 70 2.6 26.9 10.4 3.98 Glass 70±20 2.6±0.2[31] 28±10 11.2±4.8 4.4±2.1 Tooth enamel (largely calcium phosphate) 83 2.8[32] 30 11 3.8 E-Glass fiber[33][34] 81 2.62 31 12 4.5 Molybdenum (Mo) 329 10.28 32 3.1 0.30 Basalt fiber 89 2.7 33 12 4.5 Zirconia[30] 207 6.04 34.3 5.67 0.939 Tungsten carbide (WC) 550±100 15.8 34.5±6.5 2.2±0.4 0.135±0.025 S-Glass fiber[33][35] 89 2.5 36 14 5.7 Flax fiber[36][37][38][39] 45±34 1.35±0.15 36.65±29.35 30±25 25±21 single-crystal Yttrium iron garnet (YIG) 200 5.17[40] 39 7.5 1.4 Kevlar 29[41] (tensile only[42]) 70.5 1.44 49 34 24 Steatite L-5[30] 138 2.71 50.9 18.8 6.93 Mullite[30] 150 2.8 53.6 19.1 6.83 Dyneema SK25 Ultra-high-molecular-weight polyethylene (tensile only)[43] 52 0.97 54 55 57 Beryllium, 30% porosity[44] 76 1.3 58.5 45 34.6 Kevlar 49[41] (tensile only[42]) 112.4 1.44 78 54 38 Silicon[45] 185 2.329 79 34 15 Alumina fiber (Al2O3)[46][47][35] 300 3.595±0.315 84±7 24±4 6.76±1.74 Syalon 501 Silicon nitride[48] 340 4.01 84.8 21.1 5.27 Sapphire[30] 400 3.97 101 25.4 6.39 Alumina[30] 393 3.8 103 27.2 7.16 Carbon fiber reinforced plastic (70:30 fibre:matrix, unidirectional, along grain)[49] 181 1.6 113 71 44 Dyneema SK78/Honeywell Spectra 2000 UHMWPE (tensile only)[43][50] 121±11 0.97 125±11 128±12 132±12 Silicon carbide (SiC) 450 3.21 140 44 14 Beryllium (Be) 287 1.85 155 84 45 Boron fiber[51] 400 2.54 157 62 24 Boron nitride[30] 675 2.28 296 130 57 Diamond (C) 1,220 3.53 347 98 28 Dupont E130 carbon fiber[52] 896 2.15 417 194 90

Approximate specific stiffness for various species of wood[53] Material Young's modulus (GPa) Density (g/cm3) Young's modulus per density; specific stiffness (106 m2s−2) Young's modulus per density squared (103 m5kg−1s−2) Young's modulus per density cubed (m8kg−2s−2) Applewood or wild apple (Pyrus malus) 8.76715 0.745 11.768 15.7959 21.2026 Ash, black (Fraxinus nigra) 11.0423 0.526 20.9929 39.9105 75.8755 Ash, blue (quadrangulata) 9.64974 0.603 16.0029 26.5388 44.0113 Ash, green (Fraxinus pennsylvanica lanceolata) 11.4738 0.610 18.8095 30.8352 50.5495 Ash, white (Fraxinus americana) 12.2485 0.638 19.1983 30.0914 47.1651 Aspen (Populus tremuloides) 8.21797 0.401 20.4937 51.1065 127.448 Aspen, large tooth (Populus grandidentata) 9.76742 0.412 23.7073 57.5421 139.665 Basswood (Tilia glabra or Tilia americanus) 10.091 0.398 25.3544 63.7045 160.061 Beech (Fagus grandifolia or Fagus americana) 11.5718 0.655 17.6669 26.9724 41.1793 Beech, blue (Carpinus caroliniana) 7.3746 0.717 10.2854 14.345 20.007 Birch, gray (Betula populifolia) 7.8159 0.552 14.1592 25.6508 46.4688 Birch, paper (Betula papyrifera) 10.9736 0.600 18.2894 30.4823 50.8039 Birch, sweet (Betula lenta) 14.9061 0.714 20.8769 29.2394 40.9515 Buckeye, yellow (Aesculus octandra) 8.12971 0.383 21.2264 55.4214 144.703 Butternut (Juglans cinerea) 8.13952 0.404 20.1473 49.8696 123.44 Cedar, eastern red (Juniperus virginiana) 6.00167 0.492 12.1985 24.7937 50.3938 Cedar, northern white (Thuja occidentalis) 5.57018 0.315 17.6831 56.1368 178.212 Cedar, southern white (Chamaecyparis thvoides) 6.42336 0.352 18.2482 51.8414 147.277 Cedar, western red (Thuja plicata) 8.03165 0.344 23.3478 67.8715 197.301 Cherry, black (Prunus serotina) 10.2578 0.534 19.2093 35.9724 67.3641 Cherry, wild red (Prunus pennsylvanica) 8.74753 0.425 20.5824 48.4292 113.951 Chestnut (Castanea dentata) 8.53179 0.454 18.7925 41.3931 91.1743 Cottonwood, eastern (Populus deltoides) 9.53206 0.433 22.014 50.8407 117.415 Cypress, southern (Taxodium distichum) 9.90472 0.482 20.5492 42.6332 88.4506 Dogwood (flowering) (Cornus Florida) 10.6402 0.796 13.3671 16.7928 21.0965 Douglas fir (coast type) (Pseudotsuga taxifolia) 13.3076 0.512 25.9915 50.7646 99.1495 Douglas fir (mountain type) (Pseudotsuga taxifolia) 9.62032 0.446 21.5702 48.3637 108.439 Ebony, Andaman marble-wood (India) (Diospyros kursii) 12.4544 0.978 12.7346 13.0211 13.314 Ebony, Ebè marbre (Mauritius, E. Africa) (Diospyros melanida) 9.8753 0.768 12.8585 16.7428 21.8005 Elm, American (Ulmus americana) 9.2967 0.554 16.7811 30.2907 54.6764 Elm, rock (Ulmus racemosa or Ulmus thomasi) 10.65 0.658 16.1854 24.5979 37.3829 Elm, slippery (Ulmus fulva or pubescens) 10.297 0.568 18.1285 31.9164 56.1908 Eucalyptus, Karri (W. Australia) (Eucalyptus diversicolor) 18.4855 0.829 22.2986 26.8982 32.4465 Eucalyptus, Mahogany (New South Wales) (Eucalyptus hemilampra) 15.7691 1.058 14.9046 14.0875 13.3153 Eucalyptus, West Australian mahogany (Eucalyptus marginata) 14.3373 0.787 18.2177 23.1483 29.4133 Fir, balsam (Abies balsamea) 8.62005 0.414 20.8214 50.2932 121.481 Fir, silver (Abies amabilis) 10.552 0.415 25.4264 61.2684 147.635 Gum, black (Nyssa sylvatica) 8.22778 0.552 14.9054 27.0025 48.9176 Gum, blue (Eucalyptus globulus) 16.5046 0.796 20.7344 26.0483 32.7239 Gum, red (Liquidambar styraciflua) 10.2479 0.530 19.3358 36.4826 68.835 Gum, tupelo (Nyssa aquatica) 8.71811 0.524 16.6376 31.7512 60.5939 Hemlock eastern (Tsuga canadensis) 8.29643 0.431 19.2492 44.6618 103.624 Hemlock, mountain (Tsuga martensiana) 7.8159 0.480 16.2831 33.9232 70.6733 Hemlock, western (Tsuga heterophylla) 9.95375 0.432 23.0411 53.3359 123.463 Hickory, bigleaf shagbark (Hicoria laciniosa) 13.0919 0.809 16.1828 20.0034 24.7261 Hickory, mockernut (Hicoria alba) 15.3964 0.820 18.7761 22.8977 27.9241 Hickory, pignut (Hicoria glabra) 15.7201 0.820 19.1708 23.379 28.511 Hickory, shagbark (Hicoria ovata) 14.9551 0.836 17.8889 21.3982 25.596 Hornbeam (Ostrya virginiana) 11.7582 0.762 15.4307 20.2502 26.5751 Ironwood, black (Rhamnidium ferreum) 20.594 1.077−1.30 17.48±1.64 14.97±2.78 12.93±3.56 Larch, western (Larix occidentalis) 11.6503 0.587 19.8472 33.8112 57.6 Locust, black or yellow (Robinia pseudacacia) 14.2 0.708 20.0565 28.3284 40.0119 Locust honey (Gleditsia triacanthos) 11.4247 0.666 17.1543 25.7572 38.6744 Magnolia, cucumber (Magnolia acuminata) 12.5133 0.516 24.2506 46.9972 91.0798 Mahogany (W. Africa) (Khaya ivorensis) 10.5814 0.668 15.8404 23.7131 35.4987 Mahogany (E. India) (Swietenia macrophylla) 8.01203 0.54 14.8371 27.4761 50.8817 Mahogany (E. India) (Swietenia mahogani) 8.72792 0.54 16.1628 29.9311 55.428 Maple, black (Acer nigrum) 11.1894 0.620 18.0474 29.1087 46.9495 Maple, red (Acer rubrum) 11.3267 0.546 20.7448 37.9942 69.5865 Maple, silver (Acer saccharinum) 7.89435 0.506 15.6015 30.833 60.9347 Maple, sugar (Acer saccharum) 12.6506 0.676 18.7139 27.6832 40.9515 Oak, black (Quercus velutina) 11.3071 0.669 16.9014 25.2637 37.7634 Oak, bur (Quercus macrocarpa) 7.09021 0.671 10.5666 15.7476 23.4688 Oak, canyon live (Quercus chrysolepis) 11.2678 0.838 13.4461 16.0455 19.1473 Oak, laurel (Quercus Montana) 10.9246 0.674 16.2086 24.0484 35.6801 Oak, live (Quercus virginiana) 13.543 0.977 13.8618 14.1881 14.5221 Oak, post (Quercus stellata or Quercus minor) 10.4245 0.738 14.1253 19.14 25.9349 Oak, red (Quercus borealis) 12.4937 0.657 19.0162 28.9441 44.0549 Oak, swamp chestnut (Quercus Montana (Quercus prinus)) 12.2289 0.756 16.1758 21.3965 28.3023 Oak swamp white (Quercus bicolor or Quercus platanoides) 14.1804 0.792 17.9046 22.6068 28.5439 Oak, white (Quercus alba) 12.2681 0.710 17.279 24.3367 34.277 Paulownia (P. tomentosa) 6.894 0.274 25.1606 91.8269 335.134 Persimmon (Diospyros virginiana) 14.151 0.776 18.2358 23.4998 30.2832 Pine, eastern white (Pinus strobus) 8.80637 0.373 23.6096 63.2964 169.696 Pine, jack (Pinus banksiana or Pinus divericata) 8.51217 0.461 18.4646 40.0533 86.8836 Pine, loblolly (Pinus taeda) 13.2782 0.593 22.3916 37.7598 63.6759 Pine, longleaf (Pinus palustris) 14.1706 0.638 22.211 34.8135 54.5665 Pine, pitch (Pinus rigida) 9.46342 0.542 17.4602 32.2144 59.4361 Pine, red (Pinus resinosa) 12.3956 0.507 24.4489 48.2227 95.1139 Pine, shortleaf (Pinus echinata) 13.1899 0.584 22.5855 38.6738 66.2223 Poplar, balsam (Populus balsamifera or Populus candicans) 7.02156 0.331 21.2132 64.0881 193.62 Poplar, yellow (Liriodendron tulipifera) 10.3754 0.427 24.2984 56.905 133.267 Redwood (Sequoia sempervirens) 9.39477 0.436 21.5476 49.4212 113.351 Sassafras (Sassafras uariafolium) 7.74725 0.473 16.379 34.6278 73.209 Satinwood (Ceylon) (Chloroxylon swietenia) 10.7971 1.031 10.4725 10.1576 9.85217 Sourwood (Oxydendrum arboreum) 10.6206 0.593 17.91 30.2023 50.9313 Spruce, black (Picea mariana) 10.4833 0.428 24.4937 57.2283 133.711 Spruce, red (Picea rubra or Picea rubens) 10.5029 0.413 25.4308 61.5758 149.094 Spruce, white (Picea glauca) 9.81646 0.431 22.776 52.8446 122.609 Sycamore (Platanus occidentalis) 9.82626 0.539 18.2305 33.8229 62.7512 Tamarack (Larix laricina or Larix americana) 11.3169 0.558 20.2811 36.3461 65.1364 Teak (India) (Tectona grandis) 11.7189 0.5892 19.8896 33.7569 57.2928 Walnut, black (Juglans nigra) 11.6209 0.562 20.6777 36.7931 65.4682 Willow, black (Salix nigra) 5.03081 0.408 12.3304 30.2216 74.0726

Specific stiffness of the elements[54][55] Material Young's modulus (GPa) Density (g/cm3) Young's modulus per density; specific stiffness (106 m2s−2) Young's modulus per density squared (103 m5kg−1s−2) Young's modulus per density cubed (m8kg−2s−2) Thallium 8 11.8 0.675 0.057 0.00481 Cesium 1.7 1.88 0.905 0.481 0.256 Arsenic 8 5.73 1.4 0.244 0.0426 Lead 16 11.3 1.41 0.124 0.011 Indium 11 7.31 1.5 0.206 0.0282 Rubidium 2.4 1.53 1.57 1.02 0.667 Selenium 10 4.82 2.08 0.431 0.0894 Bismuth 32 9.78 3.27 0.335 0.0342 Europium 18 5.24 3.43 0.655 0.125 Ytterbium 24 6.57 3.65 0.556 0.0846 Barium 13 3.51 3.7 1.06 0.301 Gold 78 19.3 4.04 0.209 0.0108 Plutonium 96 19.8 4.84 0.244 0.0123 Cerium 34 6.69 5.08 0.76 0.114 Praseodymium 37 6.64 5.57 0.839 0.126 Cadmium 50 8.65 5.78 0.668 0.0773 Neodymium 41 7.01 5.85 0.834 0.119 Hafnium 78 13.3 5.86 0.44 0.0331 Lanthanum 37 6.15 6.02 0.98 0.159 Promethium 46 7.26 6.33 0.872 0.12 Thorium 79 11.7 6.74 0.575 0.049 Samarium 50 7.35 6.8 0.925 0.126 Lutetium 67 9.84 6.81 0.692 0.0703 Terbium 56 8.22 6.81 0.829 0.101 Tin 50 7.31 6.84 0.936 0.128 Tellurium 43 6.24 6.89 1.1 0.177 Gadolinium 55 7.9 6.96 0.881 0.112 Dysprosium 61 8.55 7.13 0.834 0.0976 Holmium 64 8.79 7.28 0.827 0.0941 Erbium 70 9.07 7.72 0.852 0.0939 Platinum 168 21.4 7.83 0.365 0.017 Thulium 74 9.32 7.94 0.852 0.0914 Silver 85 10.5 8.1 0.772 0.0736 Antimony 55 6.7 8.21 1.23 0.183 Lithium 4.9 0.535 9.16 17.1 32 Palladium 121 12 10.1 0.837 0.0696 Zirconium 67 6.51 10.3 1.58 0.243 Sodium 10 0.968 10.3 10.7 11 Uranium 208 19.1 10.9 0.573 0.0301 Tantalum 186 16.6 11.2 0.671 0.0403 Niobium 105 8.57 12.3 1.43 0.167 Calcium 20 1.55 12.9 8.32 5.37 Yttrium 64 4.47 14.3 3.2 0.716 Copper 130 8.96 14.5 1.62 0.181 Zinc 108 7.14 15.1 2.12 0.297 Silicon 47 2.33 20.2 8.66 3.72 Vanadium 128 6.11 20.9 3.43 0.561 Tungsten 411 19.2 21.4 1.11 0.0576 Rhenium 463 21 22 1.05 0.0499 Rhodium 275 12.4 22.1 1.77 0.143 Nickel 200 8.91 22.5 2.52 0.283 Iridium 528 22.6 23.4 1.04 0.046 Cobalt 209 8.9 23.5 2.64 0.296 Scandium 74 2.98 24.8 8.31 2.78 Titanium 116 4.51 25.7 5.71 1.27 Magnesium 45 1.74 25.9 14.9 8.54 Aluminum 70 2.7 25.9 9.6 3.56 Manganese 198 7.47 26.5 3.55 0.475 Iron 211 7.87 26.8 3.4 0.432 Molybdenum 329 10.3 32 3.11 0.303 Ruthenium 447 12.4 36.1 2.92 0.236 Chromium 279 7.19 38.8 5.4 0.751 Beryllium 287 1.85 155 84 45.5

## See also

- [Specific strength](/source/Specific_strength)

## References

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Wikimedia Commons has media related to [Specific stiffness](https://commons.wikimedia.org/wiki/Category:Specific_stiffness).

---
Adapted from the Wikipedia article [Specific modulus](https://en.wikipedia.org/wiki/Specific_modulus) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Specific_modulus?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.