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Helmholtz Free Energy Calculator

Work out helmholtz free energy instantly with clear inputs, formula shown and shareable results.

About Helmholtz Free Energy Calculator

The Helmholtz free energy A = U - TS is the portion of internal energy available as work at constant temperature and volume. With U = 5000 J, T = 300 K and S = 12 J/K, the TS term locks away 3600 J, leaving 1400 J extractable. Spontaneous processes at fixed T and V lower A.

Formulas

Helmholtz free energy

A = U - T S

Spontaneity

dA < 0 at constant T and V

Worked example

With the default values below, Helmholtz Free Energy Calculator returns Helmholtz Free Energy of 1,400.0. Change any input above and every figure here is recalculated in your browser.

Inputs used

Internal energy U
5,000 J
Temperatureminimum 0 K
300 K
Entropy Sminimum 0 J/K
12 J/K

Results

Helmholtz Free Energy
1,400.0 J
Energy Bound By Entropy
3,600.0 J
Share Of Internal Energy Available As Work
28.00%
Spontaneity Test
Not spontaneous under these conditions

Step by step

  1. 1Values used
  2. 2Helmholtz free energy
  3. 3Spontaneity
  4. 4Helmholtz Free Energy= 1,400.0 J
  5. 5Energy Bound By Entropy= 3,600.0 J
  6. 6Share Of Internal Energy Available As Work= 28.00
  7. 7Spontaneity Test= Not spontaneous under these conditions

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How does this differ from Gibbs free energy?

Gibbs uses enthalpy, G = H - TS, and applies at constant pressure. Helmholtz applies at constant volume, which suits sealed vessels and statistical mechanics.

What is the TS term?

The energy tied up in disorder, unavailable for work. It grows with temperature, which is why hot systems waste more of their energy content.

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