Protein Folding Free Energy Estimator

Estimate a protein's folding free energy dG and melting temperature Tm from the enthalpy and entropy change of folding using the two-state model.

🧬 Protein Folding Free Energy Estimator
Enthalpy change (ΔH)
kcal/mol
Entropy change (ΔS)
cal/(mol·K)
Temperature
°C
Folding free energy (ΔG)
—
Melting temperature (Tm)
—
Step-by-step working

🧬 What is the Protein Folding Free Energy Estimator?

The protein folding free energy estimator finds the Gibbs free energy difference, dG, between a protein's folded and unfolded states using the two-state thermodynamic model dG = dH - TdS. A negative dG means the folded state is more stable (favored); a positive dG means the unfolded, denatured state is favored at that temperature. The calculator also reports the melting temperature Tm, the temperature at which the two states are equally populated.

Biochemistry and structural biology courses use this calculator to build intuition for why proteins are only marginally stable, typically by just a handful of kcal/mol, and why that marginal stability makes them sensitive to heat, pH, and chemical denaturants. Protein engineers and pharmaceutical scientists use similar dH/dS reasoning when interpreting differential scanning calorimetry (DSC) data to compare the thermal stability of engineered protein variants or antibody formulations. Students studying enzyme and receptor biology use it to connect the abstract Gibbs free energy equation to concrete, measurable folding stability numbers.

A common misconception is that protein folding is driven mainly by favorable entropy. The opposite is usually true, folding is entropically unfavorable (the compact folded chain has vastly fewer accessible conformations than the unfolded chain), and it is a strongly favorable enthalpy change, mostly from burying hydrophobic side chains away from water and forming internal hydrogen bonds, that must outweigh this entropy penalty for folding to be spontaneous overall.

This calculator removes the arithmetic of unit conversion (entropy is conventionally reported in the smaller cal/(mol·K) unit while enthalpy uses kcal/mol) and lets students and researchers immediately see both the numeric stability and the melting temperature implied by a given dH/dS pair.

📐 Formula

ΔG  =  ΔH − TΔS
ΔG = Gibbs free energy of folding (kcal/mol); negative favors the folded state
ΔH = enthalpy change of folding (kcal/mol); typically negative (favorable)
T = absolute temperature in Kelvin (°C + 273.15)
ΔS = entropy change of folding (cal/(mol·K), converted to kcal/(mol·K) by dividing by 1000); typically negative (unfavorable)
Melting temperature (where ΔG = 0): Tm = ΔH / ΔS
Example: ΔH=−80 kcal/mol, ΔS=−230 cal/(mol·K), 37°C → ΔG ≈ −8.67 kcal/mol, Tm ≈ 74.68°C.

📖 How to Use This Calculator

Steps

1
Enter the enthalpy change. Type dH, the enthalpy change of folding, in kilocalories per mole (typically negative).
2
Enter the entropy change. Type dS, the entropy change of folding, in calories per mole per Kelvin (typically negative).
3
Enter the temperature and read the result. Type the temperature in degrees Celsius and read the folding free energy dG and the melting temperature Tm.

💡 Example Calculations

Example 1 — Stable Globular Protein at Body Temperature

ΔH=−80 kcal/mol, ΔS=−230 cal/(mol·K), T=37°C

1
T = 37°C + 273.15 = 310.15 K; ΔS = −230 cal/(mol·K) = −0.230 kcal/(mol·K)
2
ΔG = −80 − (310.15 × −0.230) = −80 + 71.33 = −8.67 kcal/mol, folded state favored
3
Tm = −80 / −0.230 = 347.83 K = 74.68°C, a realistic melting temperature for a moderately stable globular protein
ΔG = −8.67 kcal/mol (Tm = 74.68°C)
Try this example →

Example 2 — Marginally Stable Small Protein

ΔH=−40 kcal/mol, ΔS=−125 cal/(mol·K), T=37°C

1
T = 310.15 K; ΔS = −0.125 kcal/(mol·K)
2
ΔG = −40 − (310.15 × −0.125) = −40 + 38.77 = −1.23 kcal/mol, only marginally stable
3
Tm = −40 / −0.125 = 320.00 K = 46.85°C, close to body temperature, this protein would denature relatively easily with even a modest fever-range heat stress
ΔG = −1.23 kcal/mol (Tm = 46.85°C)
Try this example →

Example 3 — Same Protein Above Its Melting Temperature

Same protein as Example 1, now heated to 80°C: ΔH=−80 kcal/mol, ΔS=−230 cal/(mol·K), T=80°C

1
T = 80°C + 273.15 = 353.15 K, above the 74.68°C melting temperature found in Example 1
2
ΔG = −80 − (353.15 × −0.230) = −80 + 81.22 = +1.22 kcal/mol
3
ΔG is now positive, the unfolded (denatured) state is favored at this temperature, consistent with 80°C being above the 74.68°C Tm
ΔG = +1.22 kcal/mol, unfolded state favored
Try this example →

❓ Frequently Asked Questions

What is protein folding free energy?+
Protein folding free energy, dG, is the Gibbs free energy difference between a protein's folded and unfolded states. A negative dG means the folded state is thermodynamically favored (more stable); a positive dG means the unfolded state is favored. It is calculated with the two-state model dG = dH - TdS.
What is the formula for protein folding free energy?+
dG = dH - TdS, where dH is the enthalpy change of folding (typically negative, favorable), T is absolute temperature, and dS is the entropy change of folding (typically negative, unfavorable, since folding restricts the chain's conformational freedom).
What does a negative dG of folding mean?+
A negative dG means the folded state has lower free energy than the unfolded state, so folding is thermodynamically spontaneous and the folded conformation is favored at equilibrium. Most stable, functional proteins under physiological conditions have dG of folding in the range of roughly -5 to -15 kcal/mol.
What is the melting temperature Tm of a protein?+
Tm is the temperature at which dG of folding equals exactly zero, meaning the folded and unfolded states are equally populated at equilibrium. It is calculated as Tm = dH/dS. Below Tm the folded state is favored (dG negative); above Tm the unfolded, denatured state is favored (dG positive).
Why is protein folding usually entropically unfavorable?+
The unfolded polypeptide chain can adopt an enormous number of different conformations, while the folded state is a single, specific, compact structure. This large loss of conformational freedom upon folding makes dS negative (entropically unfavorable), which is why folding needs a sufficiently negative dH to overcome it and still give a net negative dG.
Why does heat denature (unfold) proteins?+
Because dG = dH - TdS and dS is typically negative for folding, the -TdS term becomes more positive as temperature T rises, pushing dG upward. Once temperature exceeds Tm, dG becomes positive and the unfolded state becomes thermodynamically favored, this is the basic thermodynamic explanation for heat denaturation.
Can I use an equilibrium constant instead of dH and dS directly?+
Yes, an equivalent formula is dG = -RT x ln(Keq), where Keq is the folded-to-unfolded equilibrium constant measured experimentally, for example from circular dichroism or fluorescence unfolding curves. This calculator uses the dH/dS form since it directly shows the enthalpy-entropy tradeoff and yields the melting temperature Tm in the same calculation.
Is this the same as calculating the free energy of a single chemical reaction?+
The underlying thermodynamics is the same Gibbs free energy relationship used for any two-state equilibrium, but protein folding dH and dS values are typically obtained experimentally (calorimetry or fitted from thermal denaturation curves) rather than computed from a balanced chemical equation, since folding involves thousands of weak, distributed interactions rather than a single bond change.
What units does this calculator use?+
Enthalpy change dH is entered in kilocalories per mole (kcal/mol), entropy change dS in calories per mole per Kelvin (cal/(mol*K), the conventional smaller unit for entropy), and temperature in degrees Celsius. The calculator converts dS to kcal/(mol*K) internally before combining it with dH.
Why is this called a two-state model?+
The two-state model assumes a protein exists in only two populated states, fully folded or fully unfolded, with no significantly populated partially-folded intermediates. This is a good approximation for many small single-domain proteins but breaks down for larger multi-domain proteins that fold through stable intermediate states.
Tags: Protein Folding Free Energy Calculator Protein Stability Calculator Delta G Folding Calculator Melting Temperature Protein Calculator Gibbs Free Energy Protein Calculator Formula Free Online

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What is protein folding free energy?

Protein folding free energy, dG, is the Gibbs free energy difference between a protein's folded and unfolded states. A negative dG means the folded state is thermodynamically favored (more stable); a positive dG means the unfolded state is favored. It is calculated with the two-state model dG = dH - TdS.

What is the formula for protein folding free energy?

dG = dH - TdS, where dH is the enthalpy change of folding (typically negative, favorable), T is absolute temperature, and dS is the entropy change of folding (typically negative, unfavorable, since folding restricts the chain's conformational freedom).

What does a negative dG of folding mean?

A negative dG means the folded state has lower free energy than the unfolded state, so folding is thermodynamically spontaneous and the folded conformation is favored at equilibrium. Most stable, functional proteins under physiological conditions have dG of folding in the range of roughly -5 to -15 kcal/mol.

What is the melting temperature Tm of a protein?

Tm is the temperature at which dG of folding equals exactly zero, meaning the folded and unfolded states are equally populated at equilibrium. It is calculated as Tm = dH/dS. Below Tm the folded state is favored (dG negative); above Tm the unfolded, denatured state is favored (dG positive).

Why is protein folding usually entropically unfavorable?

The unfolded polypeptide chain can adopt an enormous number of different conformations, while the folded state is a single, specific, compact structure. This large loss of conformational freedom upon folding makes dS negative (entropically unfavorable), which is why folding needs a sufficiently negative dH to overcome it and still give a net negative dG.

Why does heat denature (unfold) proteins?

Because dG = dH - TdS and dS is typically negative for folding, the -TdS term becomes more positive as temperature T rises, pushing dG upward. Once temperature exceeds Tm, dG becomes positive and the unfolded state becomes thermodynamically favored, this is the basic thermodynamic explanation for heat denaturation.

Can I use an equilibrium constant instead of dH and dS directly?

Yes, an equivalent formula is dG = -RT x ln(Keq), where Keq is the folded-to-unfolded equilibrium constant measured experimentally, for example from circular dichroism or fluorescence unfolding curves. This calculator uses the dH/dS form since it directly shows the enthalpy-entropy tradeoff and yields the melting temperature Tm in the same calculation.

Is this the same as calculating the free energy of a single chemical reaction?

The underlying thermodynamics is the same Gibbs free energy relationship used for any two-state equilibrium, but protein folding dH and dS values are typically obtained experimentally (calorimetry or fitted from thermal denaturation curves) rather than computed from a balanced chemical equation, since folding involves thousands of weak, distributed interactions rather than a single bond change.

What units does this calculator use?

Enthalpy change dH is entered in kilocalories per mole (kcal/mol), entropy change dS in calories per mole per Kelvin (cal/(mol*K), the conventional smaller unit for entropy), and temperature in degrees Celsius. The calculator converts dS to kcal/(mol*K) internally before combining it with dH.

Why is this called a two-state model?

The two-state model assumes a protein exists in only two populated states, fully folded or fully unfolded, with no significantly populated partially-folded intermediates. This is a good approximation for many small single-domain proteins but breaks down for larger multi-domain proteins that fold through stable intermediate states.

📌 Quick Tips

💡This calculator uses the simple two-state model (folded vs unfolded only), real proteins can have intermediate partially-folded states, but the two-state approximation works well for many small, single-domain globular proteins.
💡A typical folded globular protein has a surprisingly modest stability, dG of folding around -5 to -15 kcal/mol, roughly the energy of just a few hydrogen bonds, this is why proteins can be denatured relatively easily by heat, pH, or chemical denaturants.
💡Protein folding is usually enthalpically favorable (dH negative, driven mainly by burying hydrophobic side chains and forming hydrogen bonds) but entropically unfavorable (dS negative, since the folded chain has far fewer accessible conformations than the unfolded chain), the two effects partially cancel, leaving a small net dG.
💡The melting temperature Tm, where dG=0 and dH=TdS exactly, is the temperature at which folded and unfolded states are equally populated, above Tm the unfolded state is favored (dG becomes positive) and below Tm the folded state is favored.
💡Because dG = dH - TdS is linear in temperature within this simplified model, dG becomes less negative (or more positive) as temperature rises whenever dS is negative, which is the usual case for folding, this is exactly why heat denatures most proteins.