There are two common methods of expressing the hardness of rubber and plastics; the durometer reading (or Shore hardness) and Young's modulus of elasticity. A durometer measures the penetration of a metal foot into the surface of a material. There are different durometer scales but Shore A and Shore D are the most common. Values are from zero for the softest materials to 100 for the hardest and they don't have units. Young's modulus is the ratio of the stress applied to a material to how much it is deformed and it is in units of pressure. As with Shore hardness, larger values indicate a harder material.
If the durometer hardness is on the Shore D scale, add 50 to its value.
Multiply the Shore A value or the modified Shore D value from the previous step by the constant 0.0235.
Subtract 0.6403 from the result of the previous step.
Find the inverse base e logarithm of the result from the previous step by raising it to the power of the constant e (2.72). The result is the Young's modulus of elasticity expressed in the metric system pressure units of megapascals.
To convert the result in megapascals to English pressure units of poundspersquare inch, multiply the result by 145.
Example: Convert a Shore D value of 60 to a Young's modulus value.
Here are the necessary keystrokes on a reverse Polish notation scientific calculator such as the ones made by Hewlett Packard:
60
ENTER
50
+
Displayed result: 110
.0235
x [multiply]
Displayed result: 2.59
.6403

Displayed result: 1.94
e(x) [power of e]
Displayed result 6.99
145
x [multiply]
Displayed result 1013.77
The Young's modulus value is 6.99 megapascals or approximately 1014 psi.
If you prefer to use Microsoft Excel to convert durometer readings to their Young's modulus values, use the following formula for the result cell:
\=EXP((A1+50)*0.02350.6403)
where A1 is the cell with the Shore D durometer value. For Shore A values omit the "+50."
Tip
While there is no direct theoretical relationship between the scales of Shore and Young's modulus, there are empirically derived mathematical formulas that are useful for converting between them. The one employed in these steps is fairly simple and is usable over a convenient range of hardness values. The results are valid for a Shore A hardness of 20 to 80 or a Shore D value of between 30 and 85.
Tips and warnings
 While there is no direct theoretical relationship between the scales of Shore and Young's modulus, there are empirically derived mathematical formulas that are useful for converting between them. The one employed in these steps is fairly simple and is usable over a convenient range of hardness values. The results are valid for a Shore A hardness of 20 to 80 or a Shore D value of between 30 and 85.
References
 Mat Web Material Property Data: Shore Hardness Testing of Plastics
 "Marks' Standard Handbook for Mechanical Engineers;" Eugene A. Avallone, Theodore Baumeister, Ali Sadegh, 2006
 Tutor Gig Tutorial Website: Shore Durometer
 Online Conversion: Pascals to PSI
 Microsoft Excel Help: EXP worksheet function