Strain Energy Calculator: U = sigma^2 V / (2E)

The energy stored in a material when it is stretched or compressed within its elastic limit.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • U = \frac{\sigma^2V}{2E}
  • \sigma = \sqrt{\frac{2EU}{V}}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the strain energy: strain energy = (1/2 x stress^2 x volume of the bar) / (young's modulus)
  2. Put the values in (every value in its SI unit): strain energy = (1/2 x 2.0e+8^2 x 0.0001) / (2.0e+11)
  3. The answer: strain energy: 10 J
  4. The same answer in other units: 0.01 kJ

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is strain energy?

The energy stored in an elastic material when it is loaded. It equals the area under the stress-strain line, times the volume.

Why do springs store energy?

They deform elastically, so the strain energy is released when the load is removed.

What is the modulus of resilience?

The strain energy per unit volume at the yield stress. It is yield stress squared divided by twice Young's modulus.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any strength of materials text (strain energy).

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