What melting temperature means for a primer
The melting temperature of an oligonucleotide is the temperature at which half of it is bound to its complement and half is free in solution. It is not a property of the sequence alone. Change the salt concentration and Tm moves; change the primer concentration and it moves again. That is why two calculators can give different answers for the same sequence and both be right — they were asked different questions.
For PCR the number matters because the annealing step has to be cold enough that primers bind their intended site and warm enough that they let go of everything else. Set the annealing temperature too low and you amplify the wrong thing; set it too high and you amplify nothing. The window between those failures is narrow, and Tm is how you find it.
Base composition drives the number because a G·C pair makes three hydrogen bonds to an A·T pair's two, and because stacking between adjacent bases contributes at least as much as the pairing itself. That second point is the whole reason nearest-neighbour models exist: an oligo's stability depends not only on which bases it contains but on which bases sit next to which. GCGC and GGCC have identical composition and measurably different stability. Check composition separately with the primer GC content calculator.
Four formulas, and why they disagree
The Wallace rule, Tm = 2(A+T) + 4(G+C), assigns 2 °C to every A or T and 4 °C to every G or C. It was derived for short probes hybridising in 1 M salt and it is remarkably good in that narrow setting. It has no concentration terms at all, and it drifts badly above about 20 bases because it makes Tm grow without limit as length grows.
The GC-content formula, Tm = 64.9 + 41 × (G+C − 16.4) ÷ N, corrects the length behaviour by dividing by N. It is a reasonable rule of thumb for oligos of 14 bases or more and needs nothing but the sequence, but like Wallace it assumes a fixed salt condition.
The salt-adjusted formula, Tm = 81.5 + 16.6·log₁₀[Na⁺] + 0.41·%GC − 675/N, adds the one term the first two lack: a logarithmic dependence on monovalent cation concentration. Cations screen the electrostatic repulsion between the two negatively charged backbones, so more salt means a more stable duplex. Every tenfold rise in [Na⁺] adds about 16.6 °C.
Nearest-neighbour thermodynamics abandons the idea of a per-base contribution entirely. It sums a measured enthalpy and entropy for each of the ten unique dinucleotide steps, adds initiation terms for the two ends, applies the salt correction to the entropy, and then solves the thermodynamic definition of Tm directly: the temperature at which the free energy of duplex formation equals zero at the given strand concentration. The unified parameter set published by SantaLucia in 1998 reconciled seven earlier data sets into one, and it is what this calculator and essentially all modern design software use.
Two details in that last calculation are easy to miss. The concentration term uses CT/4 for a normal primer, because a primer and its distinct target are two different molecules; a self-complementary oligo, which pairs with a copy of itself, uses CT/1 and gains a further −1.4 cal/mol·K symmetry correction. And the salt correction, 0.368 × (N−1) × ln[Na⁺], scales with the number of phosphate linkages, not with base composition.
Worked example: a 20-base poly-A oligo
A homopolymer makes the nearest-neighbour sum easy to follow on paper, because every dinucleotide step is the same one. Take 5′-A₂₀-3′ in 50 mM monovalent salt at 250 nM strand concentration.
- Count the steps. A 20-mer has 19 nearest-neighbour steps, all of them AA/TT.
- Sum the enthalpy. 19 × (−7.9) = −150.1 kcal/mol. Both ends are A·T, so add 2.3 kcal/mol for each: ΔH° = −150.1 + 4.6 = −145.5 kcal/mol.
- Sum the entropy. 19 × (−22.2) = −421.8 cal/mol·K. Both A·T ends add +4.1: ΔS° = −421.8 + 8.2 = −413.6 cal/mol·K.
- Apply the salt correction. 0.368 × 19 × ln(0.05) = 6.992 × (−2.9957) = −20.95. ΔS°salt = −413.6 − 20.95 = −434.55 cal/mol·K.
- Add the concentration term. Not self-complementary, so x = 4 and CT/4 = 2.5 × 10⁻⁷ ÷ 4 = 6.25 × 10⁻⁸. R·ln(6.25 × 10⁻⁸) = 1.987 × (−16.588) = −32.96.
- Divide. Tm = (−145.5 × 1000) ÷ (−434.55 − 32.96) = −145,500 ÷ −467.51 = 311.23 K.
- Convert. 311.23 − 273.15 = 38.1 °C.
Now compare the other three for the same oligo. Wallace gives 2 × 20 + 4 × 0 = 40.0 °C. The GC formula gives 64.9 + 41 × (0 − 16.4)/20 = 31.3 °C. The salt-adjusted formula gives 81.5 + 16.6 × log₁₀(0.05) + 0 − 675/20 = 81.5 − 21.60 − 33.75 = 26.2 °C. A spread of 14 degrees for one sequence — which is the point of running all four rather than trusting one.
Turning Tm into an annealing temperature
The common starting rule is to set the annealing temperature about 5 °C below the lower of the two primers' nearest-neighbour Tm values, and that is what the suggested figure here does. It is a starting point for an optimisation, not a specification. Treat the first run as an experiment: a gradient across roughly ±5 °C of the suggestion will usually show you a clean window, and it costs one plate.
Several chemistries move the target. Proofreading polymerase manufacturers frequently publish their own Tm algorithm and recommend annealing above the calculated Tm, sometimes by 3 °C, because their buffers differ substantially from standard Taq buffer. When a supplier gives an annealing rule for their enzyme, follow it rather than the generic minus-five.
Match your pair, not just each primer. A pair whose Tm values differ by more than about 5 °C has no annealing temperature that suits both: the cooler primer binds poorly at a temperature that suits the warmer one, and the warmer one primes non-specifically at a temperature that suits the cooler. Redesign to bring them within a couple of degrees, adjusting length rather than pushing GC content outside 40–60%.
Finally, watch the 3′ end separately from the whole-primer Tm. Extension starts there, so a mismatch in the last two or three bases is far more damaging than one in the middle, and a run of Gs and Cs at that end can hold a primer down at an unintended site even when the overall Tm says it should have released. One or two G or C bases in the final five is the usual compromise.
Unified nearest-neighbour parameters (SantaLucia 1998)
| Step (5′→3′) | ΔH° (kcal/mol) | ΔS° (cal/mol·K) | ΔG°₃₇ (kcal/mol) |
|---|---|---|---|
| AA / TT | −7.9 | −22.2 | −1.01 |
| AT | −7.2 | −20.4 | −0.87 |
| TA | −7.2 | −21.3 | −0.59 |
| CA / TG | −8.5 | −22.7 | −1.46 |
| GT / AC | −8.4 | −22.4 | −1.45 |
| CT / AG | −7.8 | −21.0 | −1.29 |
| GA / TC | −8.2 | −22.2 | −1.31 |
| CG | −10.6 | −27.2 | −2.16 |
| GC | −9.8 | −24.4 | −2.23 |
| GG / CC | −8.0 | −19.9 | −1.83 |
| Initiation, terminal G·C | +0.1 | −2.8 | +0.97 |
| Initiation, terminal A·T | +2.3 | +4.1 | +1.03 |
Each step is listed with its equivalent read on the complementary strand, which is why AA and TT share a row. A GC step is more stable than a CG step despite identical composition — the clearest evidence that stacking, not just hydrogen bonding, sets duplex stability.
Magnesium is not included here
This calculator applies the monovalent salt correction only. PCR buffers also contain magnesium, typically 1.5–2 mM, and divalent cations stabilise duplexes far more effectively per mole than monovalent ones — so the true Tm in a PCR tube is higher than the value shown. Commercial design tools apply a divalent correction that also accounts for magnesium chelated by dNTPs.
The practical consequence is that you should treat these numbers as a consistent basis for comparing primers and for matching a pair, and treat the annealing temperature as something you confirm on a gradient rather than something you calculate exactly. Comparisons are unaffected by the missing term because it shifts every primer in the same direction.
Design rules worth applying alongside the Tm
- Length 18–25 bases. Long enough to be unique in a complex genome, short enough to anneal efficiently.
- GC content 40–60%. Outside this band it becomes hard to match Tm across a pair without changing length awkwardly.
- Pair Tm within about 2 °C. A mismatched pair has no annealing temperature that suits both primers.
- One or two G/C in the last five bases. Enough to anchor the 3′ end, not so many that it primes non-specifically.
- Avoid runs of four or more identical bases, particularly G, which can form quadruplex structures.
- Check for self-dimers and hairpins. Tm says nothing about whether the primer prefers to bind itself; a 3′-end self-dimer will out-compete the template.
- Check specificity against the genome, not just the intended target. A perfect Tm on a primer with three genomic sites is still a failed primer.
When each method is the right one to quote
Use the nearest-neighbour value for anything that matters: PCR primer design, probe design, matching a pair, or deciding an annealing temperature. It is the only one of the four grounded in measured thermodynamics and the only one that responds to your buffer and primer concentration.
Use the Wallace rule when someone quotes it to you, and for very short probes in high salt. Its persistence is a matter of convenience: it can be done in your head, and for a 17-mer in 1 M salt it is not far wrong.
Use the salt-adjusted formula for long hybridisation probes — Southern and northern blots, in situ hybridisation — where oligos run to 30 bases and beyond and where the salt in the hybridisation buffer varies over a wide range.
None of the four addresses secondary structure, mismatches, modified bases, LNA or locked chemistries, or the divalent cation contribution. For those, use a design tool built for the chemistry and validate empirically. Once the primers exist, set the reaction up with the PCR master mix calculator, quantify the template with the A260 concentration calculator, and check how many template molecules you are actually putting in each well with the DNA copy number calculator.