RNA Secondary Structure Melting Temperature Calculator

Predict the melting temperature and folding free energy of an RNA helix from its sequence using published nearest-neighbor thermodynamic parameters.

🌡 RNA Secondary Structure Melting Temperature Calculator
RNA sequence (5′ to 3′)GCAUGCUAGC (10 nt)
A C G U
Total strand concentration (CT)2.00 µM
µM
0.1 µM100 µM
Monovalent salt (Na+)
mM
Melting temperature (Tm)
—
Enthalpy (ΔH°)
—
Entropy (ΔS°, salt corrected)
—
Free energy (ΔG° at 37 °C)
—
GC content
—
Helix length
—
Duplex type
—
Step-by-step working

🌡 What is the RNA Secondary Structure Melting Temperature Calculator?

The RNA melting temperature calculator predicts the temperature at which half of an RNA helix has come apart, using the nearest-neighbor thermodynamic model that has been the standard of the field since Xia and colleagues published their Watson-Crick RNA parameters in 1998. Rather than a crude base-count rule, the model sums a measured enthalpy and entropy for each stacked dinucleotide step in the helix, adds a helix initiation term, adds a penalty for every helix end closed by an A-U pair, applies a symmetry correction for self-complementary sequences, corrects the entropy for monovalent salt, and then solves the two-state melting equation for Tm.

Researchers reach for this calculation constantly. Anyone designing small interfering RNA or antisense oligonucleotides needs to know how tightly a guide strand will bind and how asymmetric the duplex ends are. Riboswitch and aptamer designers use the free energy at 37 C to check that an intended stem is stable at body temperature but not so stable it never opens. Structural biologists preparing samples for NMR or crystallography use Tm to choose annealing protocols and buffer conditions. RNA nanotechnologists building tiles and origami rely on the same parameter set that folding engines such as RNAfold and mfold use internally, so a hand check against this calculator often catches a design error early.

A common misconception is that GC content alone predicts stability. It does not, because stacking energy depends on the identity and orientation of both pairs in each step. The 5'GC3'/3'CG5' step contributes almost 4.2 kcal/mol more enthalpy than the 5'CG3'/3'GC5' step even though both are all-GC. Another mistake is transferring DNA rules to RNA. An RNA helix is A-form and stacks more strongly, so DNA nearest-neighbor tables and the familiar 2 degrees per AU plus 4 degrees per GC shortcut both give badly wrong answers. A third is forgetting that Tm for a bimolecular duplex depends on strand concentration, so a Tm reported without its concentration and buffer is not a reproducible number.

This calculator is useful because it shows the whole derivation rather than only the final temperature. The per-step table lists every stacking contribution, the initiation term, the terminal A-U penalties and the symmetry correction, with running totals at 1 M sodium and after salt correction. The melting curve chart plots the duplex fraction against temperature with the Tm crossing at 50 percent marked, and the second chart shows how Tm shifts with strand concentration across five orders of magnitude, which makes the logarithmic concentration dependence immediately obvious.

📐 Formula

Tm  =  ΔH° ÷ (ΔS° + R ln(CT ÷ 4)) − 273.15
ΔH° = summed nearest-neighbor enthalpy, in cal/mol (kcal/mol × 1000)
ΔS° = summed nearest-neighbor entropy after salt correction, in cal/(mol·K)
R = 1.987 cal/(mol·K), the gas constant
CT = total strand concentration in mol/L; use CT for self-complementary duplexes and CT÷4 otherwise
Helix initiation: ΔH = +3.61 kcal/mol, ΔS = −1.5 cal/(mol·K)
Terminal A-U penalty per helix end: ΔH = +3.72 kcal/mol, ΔS = +10.5 cal/(mol·K)
Self-complementary symmetry: ΔS = −1.4 cal/(mol·K)
Salt correction: ΔS(Na+) = ΔS(1 M) + 0.368 × (N − 1) × ln[Na+]
Free energy at 37 °C: ΔG°37 = ΔH° − 310.15 × ΔS° ÷ 1000
Example: 5′-GCAUGCUAGC-3′ at 2 µM and 100 mM Na+ gives ΔH° = −99.94 kcal/mol, ΔS° = −275.03 cal/(mol·K) and Tm = 55.76 °C.
Stacking parameters follow Xia et al. (1998), "Thermodynamic parameters for an expanded nearest-neighbor model for formation of RNA duplexes with Watson-Crick base pairs".

📖 How to Use This Calculator

Steps

1
Enter the RNA sequence. Type the top strand of the helix using A, C, G and U. A T is automatically read as U, and the complementary strand is generated for you.
2
Set the strand concentration. Type or drag the total strand concentration in micromolar, typically 1 to 10 micromolar for an optical melting experiment.
3
Set the monovalent salt concentration. Enter the sodium or potassium concentration of your buffer in millimolar, commonly 100 mM or 1000 mM.
4
Read Tm and the thermodynamics. See the melting temperature, enthalpy, entropy, free energy at 37 C and GC content, with a per-step table and a full melting curve.

💡 Example Calculations

Example 1 — A Mixed-Sequence 10-mer at Standard Conditions

5′-GCAUGCUAGC-3′, CT = 2 µM, 100 mM Na+

1
Sum the nine stacking steps plus initiation: ΔH° = −99.94 kcal/mol. Both ends are closed by G-C pairs, so no terminal A-U penalty applies
2
ΔS° at 1 M Na+ is −267.40 cal/(mol·K); the salt correction 0.368 × 9 × ln(0.1) = −7.63 gives −275.03 cal/(mol·K)
3
Tm = −99940 ÷ (−275.03 + 1.987 × ln(5×10−7)) − 273.15 = 55.76 °C
4
ΔG°37 = −99.94 − 310.15 × (−0.27503) = −14.64 kcal/mol, a comfortably stable helix at body temperature
Tm = 55.76 °C, ΔG°37 = −14.64 kcal/mol (60.0% GC)
Try this example →

Example 2 — A GC-Rich Stem in Higher Salt

5′-GGCCAAGGCC-3′, CT = 2 µM, 150 mM Na+

1
Eight of the nine stacks involve at least one G-C pair, giving ΔH° = −107.45 kcal/mol for an 80.0% GC sequence
2
Salt-corrected ΔS° = −285.38 cal/(mol·K) at 150 mM sodium
3
Tm = 68.82 °C, about 13 degrees above the mixed-sequence 10-mer in Example 1
4
ΔG°37 = −18.94 kcal/mol, so this stem is essentially fully formed at 37 °C
Tm = 68.82 °C, ΔG°37 = −18.94 kcal/mol
Try this example →

Example 3 — A Self-Complementary All-AU Duplex

5′-AUAUAUAUAU-3′, CT = 5 µM, 100 mM Na+

1
The sequence equals its own reverse complement, so the symmetry correction of −1.4 cal/(mol·K) applies and the concentration term uses ln(CT) rather than ln(CT÷4)
2
Both ends are A-U, so two terminal penalties are added, giving ΔH° = −66.61 kcal/mol and salt-corrected ΔS° = −205.03 cal/(mol·K)
3
Tm = 17.37 °C, well below room temperature, so this duplex is mostly single stranded in a normal laboratory
4
ΔG°37 = −3.02 kcal/mol, five times weaker than the GC-rich stem of Example 2 at the same length
Tm = 17.37 °C, ΔG°37 = −3.02 kcal/mol (0.0% GC, self-complementary)
Try this example →

Example 4 — A 19-mer siRNA Guide Strand

5′-CGCAAGGAUGACACGCAAA-3′, CT = 1 µM, 100 mM Na+

1
Eighteen stacking steps give ΔH° = −186.86 kcal/mol at 52.6% GC
2
The 3′ end is an A, so one terminal A-U penalty applies; the salt correction over 18 steps gives ΔS° = −508.55 cal/(mol·K)
3
Tm = 73.68 °C even at only 1 µM, because the helix is nearly twice as long as the earlier examples
4
ΔG°37 = −29.13 kcal/mol, typical of a full-length siRNA duplex
Tm = 73.68 °C, ΔG°37 = −29.13 kcal/mol (19 nt)
Try this example →

❓ Frequently Asked Questions

How do you calculate the melting temperature of an RNA duplex?+
Tm = dH / (dS + R ln(CT/4)) - 273.15 for a non-self-complementary duplex, where dH and dS are the summed nearest-neighbor enthalpy and entropy, R is 1.987 cal per mol per kelvin, and CT is the total strand concentration. Self-complementary duplexes use ln(CT) instead of ln(CT/4).
What are nearest-neighbor parameters for RNA?+
They are experimentally measured enthalpy and entropy values for each of the ten unique Watson-Crick base-pair stacks in an A-form RNA helix, published by Xia and colleagues in 1998. The strongest stack is 5'GC3'/3'CG5' at -14.88 kcal/mol enthalpy, and the weakest is 5'AA3'/3'UU5' at -6.82 kcal/mol.
Why does RNA melt at a higher temperature than DNA?+
A-form RNA helices stack more favourably than B-form DNA helices, and the 2'-hydroxyl group adds hydrogen bonding within the minor groove. For the same sequence and conditions, an RNA/RNA duplex typically melts 10 to 20 degrees above the DNA/DNA equivalent, and RNA/DNA hybrids fall in between.
What is the terminal A-U penalty in RNA thermodynamics?+
A penalty of 3.72 kcal/mol enthalpy and 10.5 cal per mol per kelvin entropy, about 0.45 kcal/mol of free energy at 37 C, applied at each helix end closed by an A-U pair. It reflects the weaker two-hydrogen-bond pair fraying at the ends of the helix.
How does salt concentration change RNA melting temperature?+
Higher monovalent salt screens phosphate repulsion and stabilises the duplex, raising Tm. This calculator applies the entropy correction dS(salt) = dS(1 M) + 0.368 x (N - 1) x ln[Na+], so the shift scales with helix length. Going from 100 mM to 1 M sodium typically raises Tm by several degrees.
What is a self-complementary RNA sequence?+
A sequence identical to its own reverse complement, such as AUAUAUAUAU or GCGCGC. Two copies of the same strand pair with each other, so the concentration term becomes ln(CT) rather than ln(CT/4), and a symmetry entropy correction of -1.4 cal per mol per kelvin is applied.
Why does Tm depend on strand concentration?+
Duplex formation is bimolecular, so by Le Chatelier's principle raising the total strand concentration pushes the equilibrium toward the duplex and raises Tm. The dependence is logarithmic, so each tenfold increase in concentration shifts Tm by only a few degrees. Unimolecular hairpins show no concentration dependence at all.
What does the folding free energy dG37 tell me?+
dG37 = dH - 310.15 x dS / 1000, the free energy of duplex formation at 37 C in kcal/mol. More negative values mean a more stable helix. A 10-mer RNA duplex with 60 percent GC typically falls near -14 to -16 kcal/mol, while an all-AU 10-mer may reach only -3 kcal/mol.
Can I use this for a hairpin stem or only for a duplex?+
The stacking, initiation and terminal A-U terms apply to the stem of a hairpin as well, so the enthalpy and free energy outputs are useful estimates. The Tm value assumes a bimolecular duplex, however, so for a true unimolecular hairpin the concentration term should be dropped and the loop penalty added separately.
How accurate is a nearest-neighbor Tm prediction?+
For short, fully Watson-Crick, two-state duplexes under 30 nucleotides the prediction is typically within 1 to 3 degrees of the measured optical Tm. Accuracy degrades for longer helices, for sequences containing mismatches, bulges or internal loops, and for structures that can adopt competing folds.
Why is GC content alone a poor predictor of RNA stability?+
Because stacking energy depends on the order of the pairs, not just their identity. The 5'GC3'/3'CG5' step contributes -14.88 kcal/mol of enthalpy while the 5'CG3'/3'GC5' step contributes only -10.64 kcal/mol, even though both are made entirely of G-C pairs. Two sequences with identical GC content can therefore differ by many degrees in Tm.
What does the melting curve shape tell me?+
The sigmoid width reflects the enthalpy of the transition. A large negative dH gives a steep, narrow melt because the duplex falls apart over a small temperature range, while a small dH produces a broad, gradual transition. Comparing a measured curve width against this predicted shape is a standard test of whether melting really is two-state.
Tags: Rna Melting Temperature Calculator Rna Tm Calculator Nearest Neighbor Thermodynamics Rna Duplex Free Energy Rna Secondary Structure Calculator Formula Free Online

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How do you calculate the melting temperature of an RNA duplex?

Tm = dH / (dS + R ln(CT/4)) - 273.15 for a non-self-complementary duplex, where dH and dS are the summed nearest-neighbor enthalpy and entropy, R is 1.987 cal per mol per kelvin, and CT is the total strand concentration. Self-complementary duplexes use ln(CT) instead of ln(CT/4).

What are nearest-neighbor parameters for RNA?

They are experimentally measured enthalpy and entropy values for each of the ten unique Watson-Crick base-pair stacks in an A-form RNA helix, published by Xia and colleagues in 1998. The strongest stack is 5'GC3'/3'CG5' at -14.88 kcal/mol enthalpy, and the weakest is 5'AA3'/3'UU5' at -6.82 kcal/mol.

Why does RNA melt at a higher temperature than DNA?

A-form RNA helices stack more favourably than B-form DNA helices, and the 2'-hydroxyl group adds hydrogen bonding within the minor groove. For the same sequence and conditions, an RNA/RNA duplex typically melts 10 to 20 degrees above the DNA/DNA equivalent, and RNA/DNA hybrids fall in between.

What is the terminal A-U penalty in RNA thermodynamics?

A penalty of 3.72 kcal/mol enthalpy and 10.5 cal per mol per kelvin entropy, about 0.45 kcal/mol of free energy at 37 C, applied at each helix end closed by an A-U pair. It reflects the weaker two-hydrogen-bond pair fraying at the ends of the helix.

How does salt concentration change RNA melting temperature?

Higher monovalent salt screens phosphate repulsion and stabilises the duplex, raising Tm. This calculator applies the entropy correction dS(salt) = dS(1 M) + 0.368 x (N - 1) x ln[Na+], so the shift scales with helix length. Going from 100 mM to 1 M sodium typically raises Tm by several degrees.

What is a self-complementary RNA sequence?

A sequence identical to its own reverse complement, such as AUAUAUAUAU or GCGCGC. Two copies of the same strand pair with each other, so the concentration term becomes ln(CT) rather than ln(CT/4), and a symmetry entropy correction of -1.4 cal per mol per kelvin is applied.

Why does Tm depend on strand concentration?

Duplex formation is bimolecular, so by Le Chatelier's principle raising the total strand concentration pushes the equilibrium toward the duplex and raises Tm. The dependence is logarithmic, so each tenfold increase in concentration shifts Tm by only a few degrees. Unimolecular hairpins show no concentration dependence at all.

What does the folding free energy dG37 tell me?

dG37 = dH - 310.15 x dS / 1000, the free energy of duplex formation at 37 C in kcal/mol. More negative values mean a more stable helix. A 10-mer RNA duplex with 60 percent GC typically falls near -14 to -16 kcal/mol, while an all-AU 10-mer may reach only -3 kcal/mol.

Can I use this for a hairpin stem or only for a duplex?

The stacking, initiation and terminal A-U terms apply to the stem of a hairpin as well, so the enthalpy and free energy outputs are useful estimates. The Tm value assumes a bimolecular duplex, however, so for a true unimolecular hairpin the concentration term should be dropped and the loop penalty added separately.

How accurate is a nearest-neighbor Tm prediction?

For short, fully Watson-Crick, two-state duplexes under 30 nucleotides the prediction is typically within 1 to 3 degrees of the measured optical Tm. Accuracy degrades for longer helices, for sequences containing mismatches, bulges or internal loops, and for structures that can adopt competing folds.

📌 Quick Tips

💡RNA duplexes melt considerably higher than the equivalent DNA duplexes. An A-form RNA helix stacks more tightly, so a GC-rich RNA stem can sit 10 to 20 degrees above its DNA counterpart at the same concentration and salt.
💡Terminal A-U pairs cost you. Each helix end closed by A-U adds about 0.45 kcal/mol to the folding free energy at 37 C, which is why designed stems almost always end in a G-C pair.
💡Tm depends on strand concentration for a bimolecular duplex, but not for a unimolecular hairpin. If your structure is an intramolecular stem loop, the concentration term drops out and the measured Tm stays flat as you dilute.
💡The salt correction scales with helix length, so long helices shift far more between 50 mM and 1 M sodium than short ones. Always report the buffer conditions alongside any predicted Tm.
💡Two-state melting is an approximation. Long helices, sequences with internal loops or bulges, and structures with competing folds all melt over a broader transition than this calculator's sigmoid curve suggests.