Audited —·Last updated 29 Jul 2026·6 citations·Tier 1·0 uses

PCR Annealing Temperature Calculator

Calculate PCR annealing temperature from primer sequences using nearest-neighbour Tm (SantaLucia 1998), with Taq and high-fidelity rules and a gradient window.

PCR Annealing Temperature Calculator

Unambiguous A, C, G and T only. Spaces, hyphens and 5'/3' markers are stripped automatically. Degenerate bases (N, R, Y), inosine and modified backbones are not modelled and will be rejected rather than silently approximated.
Enter the reverse primer as synthesised, 5' to 3' — not the reverse complement of the forward primer. The calculator scores each primer against its own perfectly matched template.
Polymerase rule
Used only when the rule above is set to Custom. Enter the offset your enzyme's manufacturer specifies — negative to anneal below the lower Tm, positive to anneal above it.
°C
Final concentration of each primer in the reaction. 500 nM (0.5 µM) is the usual starting point. Tm depends on this logarithmically, so a tenfold change moves Tm by only a couple of degrees.
nM
Total monovalent cation, [Na⁺] or [K⁺], in the reaction buffer. Standard Taq buffer is 50 mM KCl. Magnesium is NOT included — see the note beside the result.
mM
Strand condition
Annealing temperature
44.3685
The block temperature to programme, computed from the UNROUNDED lower primer Tm plus the selected enzyme offset. Round it to the nearest degree — the model's own residual error is larger than a tenth of a degree.
Tm, forward primer
54.9704 °C
Tm, reverse primer
49.3685 °C
Lower Tm
49.3685 °C
Tm difference
5.6019 °C
Gradient low
39.3685 °C
Gradient high
49.3685 °C
Design notes
Rule applied — Taq / standard polymerase: 5 °C below the lower primer Tm (Lorenz 2012). The two primer Tm values differ by 5.6 °C. Lorenz (2012) recommends no more than 5 °C: the hotter primer will keep priming at temperatures where the cooler one has fallen off, which costs specificity. Consider lengthening the cooler primer or trimming the hotter one. Tm is the nearest-neighbour prediction of SantaLucia (1998) at 50 mM monovalent cation and 500 nM primer, with the primer in excess over the template, as in PCR. No magnesium or dNTP correction is applied, so calculators that apply one report a higher Tm and a higher annealing temperature for these same primers. Round the result to the nearest degree and run a gradient across the window shown — the prediction assumes a perfectly matched, two-state duplex and says nothing about primer dimers, hairpins or template structure.

Background.

This calculator predicts a PCR annealing temperature from your two primer sequences, and it keeps two separate things visibly separate — because the literature does, and because conflating them is where most annealing-temperature advice goes wrong. The first is a melting temperature: the thermodynamics of the primer–template duplex. The second is an offset from that melting temperature, which depends on which polymerase you are using and which pulls in opposite directions for different enzymes.

For the melting temperature this page uses nearest-neighbour thermodynamics — the unified parameter set published by SantaLucia in PNAS in 1998, which remains the reference model for short DNA duplexes. Rather than counting bases, the model sums an enthalpy and an entropy contribution for every overlapping pair of adjacent bases, adds an initiation term for each end of the duplex determined by whether that end is a G·C or an A·T pair, corrects the entropy for salt, and then solves for the temperature at which half the strands are paired. That is a genuinely different calculation from the rules of thumb it replaced, and it gives a genuinely different answer: for a 17-mer the Wallace 2-plus-4 rule and nearest-neighbour thermodynamics routinely disagree by several degrees, and the disagreement grows with length and with GC skew.

For the offset, the page gives you named published rules rather than a single hard-coded number. Lorenz's 2012 PCR protocol in the Journal of Visualized Experiments sets the annealing step "about 5 °C below the apparent Tm of the primers", which is the classic Taq rule and the default here. New England Biolabs instructs the opposite for its Q5 high-fidelity enzyme: anneal 3 °C above the lower primer Tm. Neither is wrong. Q5's binding chemistry tolerates more stringency than Taq's, so the same primers want a hotter block. Hard-coding either one would produce confidently wrong advice for half of all users, so both ship as labelled modes, alongside a custom offset for enzymes with their own published guidance.

One scope limit belongs up here rather than in an FAQ, because it changes how the number should be read. This calculator applies a monovalent salt correction only. Real PCR buffers contain 1.5 to 3 mM magnesium chloride plus dNTPs, and divalent cations stabilise the duplex further. Calculators that apply a divalent correction — New England Biolabs' and IDT's among them — will therefore report a higher Tm, and a correspondingly higher annealing temperature, for exactly the same primers. That is not a disagreement about thermodynamics; it is a difference in how much of the buffer each tool models. The reason this page does not apply a magnesium correction is simple and worth stating: the coefficients for it could not be verified from primary text, and inventing them would be worse than declaring the limit.

There is also a convention that quietly changes the answer by about a degree, and this page exposes it rather than choosing for you. The nearest-neighbour melting equation contains a strand-concentration term, and its form depends on whether the two strands are present at equal concentration or one is in vast excess. PCR is the second case — primer massively outnumbers template — so the term is the natural log of the primer concentration. Annealing two synthetic oligos in a tube is the first case, and the term picks up a factor of a half. SantaLucia's paper gives both forms. Picking one silently would be exactly the kind of undocumented choice that makes a calculator irreproducible, so it is a dropdown, it defaults to PCR, and the size of the difference is stated.

Finally, treat the output as a starting point for a gradient, not as a setting. A predicted Tm assumes a perfectly matched, two-state duplex in a clean buffer. It knows nothing about primer dimers, hairpins, template secondary structure, mispriming sites elsewhere in the genome, or the particular quirks of your thermocycler's block calibration. The page therefore reports a ±5 °C window with every result, and the honest workflow is to run it.

What is pcr annealing temperature calculator?

The annealing temperature, usually written Ta, is the temperature of the second step of each PCR cycle — the step at which primers bind their complementary sequences on the denatured template before the polymerase extends them. It is the single most powerful specificity control in the reaction. Too low, and primers tolerate mismatches, bind at unintended sites, and you amplify a smear or the wrong product. Too high, and the primers do not stay bound long enough for the polymerase to engage, and you amplify nothing. Ta is set relative to the melting temperature, Tm, of the primer–template duplex. Tm is defined as the temperature at which half of the duplexes in a population are dissociated; it is a property of a sequence under stated conditions, not an intrinsic constant, and it moves with salt concentration, strand concentration and the presence of divalent cations. Nearest-neighbour thermodynamics computes Tm from the standard enthalpy and entropy of duplex formation: Tm = ΔH° ÷ (ΔS° + R ln C), where ΔH° and ΔS° are summed over every adjacent base pair step in the sequence plus an initiation term at each end, R is the gas constant, and C is a concentration term whose exact form depends on the strand condition. The model is called 'nearest-neighbour' because the stability contributed by a base pair depends on which base pair sits next to it — a G·C flanked by G·C stacks more favourably than the same G·C flanked by A·T. That sequence-context dependence is precisely what simpler counting rules like the Wallace 2(A+T) + 4(G+C) formula throw away, and it is why the two approaches disagree. The offset from Tm to Ta is empirical and enzyme-specific rather than thermodynamic. It exists because a polymerase does not need every primer bound to work; it needs enough primers bound, for long enough, at sites specific enough to matter, and different enzymes have different tolerances.

How to use this calculator.

  1. Paste the forward primer 5' to 3'. Whitespace, hyphens and 5'/3' end markers are stripped for you. Only unambiguous A, C, G and T are accepted — degenerate bases are rejected rather than guessed at, because the nearest-neighbour parameter set does not cover them.
  2. Paste the reverse primer as it was synthesised, 5' to 3'. Do not enter the reverse complement of the forward primer: each primer is scored against its own perfectly matched template strand.
  3. Choose the polymerase rule. Taq and other standard enzymes anneal 5 °C below the lower Tm. Q5, Phusion and other high-fidelity enzymes anneal 3 °C above it. If your enzyme's manufacturer publishes something different, choose Custom and enter their offset.
  4. Set the primer concentration to your final in-reaction concentration — 500 nM is the usual default. The dependence is logarithmic, so getting this roughly right is enough.
  5. Set the monovalent cation to the total Na⁺ or K⁺ in your buffer. Standard Taq buffer is 50 mM KCl. Do not add magnesium into this field; magnesium is not modelled and adding it here would silently overstate the correction.
  6. Leave the strand condition on PCR unless you are annealing two synthetic oligos to each other at comparable concentrations, in which case switch to equimolar.
  7. Read the Tm difference. If it exceeds 5 °C, redesign before you optimise: no single block temperature suits both primers well, and the hotter one will prime at temperatures where the cooler one has released.
  8. Round the annealing temperature to the nearest degree and run the ±5 °C gradient shown. Take the highest temperature that still gives a clean single product — that is the most specific condition your primers support.

The formula.

Tm = ΔH° ⁄ (ΔS° + R·ln C) − 273.15
Ta = Tm(lower) + offsetΔH° · NN enthalpy sum (cal/mol)ΔS° · entropy sum, salt-correctedR · 1.987 cal/(mol·K)C · strand-concentration term (M)offset · −5 Taq · +3 Q5 · custom

The calculation runs in four stages, and every constant in it comes from a named source.

Stage 1 — sum the nearest-neighbour steps. For an L-base primer there are L−1 overlapping adjacent-base steps. Each contributes a standard enthalpy in kcal/mol and a standard entropy in cal/(mol·K) taken from the unified parameter set of SantaLucia (1998), Table 2, referenced to 1 M NaCl. There are ten distinct steps because a step and its reverse complement are thermodynamically identical: AA/TT, AT/TA, TA/AT, CA/GT, GT/CA, CT/GA, GA/CT, CG/GC, GC/CG and GG/CC.

Stage 2 — add the initiation terms. Duplex formation costs something at each end, and the cost depends on whether that end is a G·C pair (ΔH° = 0.1 kcal/mol, ΔS° = −2.8 cal/(mol·K)) or an A·T pair (ΔH° = 2.3, ΔS° = +4.1). This is why two primers of identical length and identical GC percentage can still differ in Tm — the terminal bases matter. If the sequence happens to be its own reverse complement, a symmetry correction of −1.4 cal/(mol·K) is added to the entropy, and the concentration term changes form.

Stage 3 — correct the entropy for salt. SantaLucia's Equation 8 states ΔS°([Na⁺]) = ΔS°(1 M NaCl) + 0.368 × N × ln[Na⁺], where N is the number of phosphates divided by two, which for a primer with a free 5'-hydroxyl is L−1. Note the direction: ln of a sub-molar concentration is negative, so lowering the salt makes ΔS° more negative, which lowers Tm. Salt stabilises duplexes by screening the phosphate backbone's negative charge.

Stage 4 — solve for Tm and apply the offset. Tm in kelvin is 1000 × ΔH° divided by (ΔS° + R ln C), where R is 1.987 cal/(mol·K) and C is the strand-concentration term. Subtract 273.15 for Celsius. Then Ta is the LOWER of the two primer Tm values plus the enzyme offset — the lower one, because a reaction can only be as stringent as its weakest primer.

Rounding stage: FINAL ONLY, and here it genuinely matters. The offset is applied to the unrounded Tm, and rounding to ten decimal places happens once, at the moment each field is returned. If Tm were rounded to a whole degree first and the offset applied afterwards, the annealing temperature could be up to half a degree away from the value shown — the exact class of defect that a formula rounding at the wrong stage produces, and which passes every test that only checks the middle of a range. A shipped test asserts that the annealing temperature equals the lower Tm minus five to ten decimal places, so an intermediate rounding cannot be introduced without failing the suite.

Invalid-domain behaviour. The equation takes the natural logarithm of both the salt concentration and the strand concentration, so both must be strictly positive; zero is rejected with a message rather than returning negative infinity. A one-base sequence has no nearest-neighbour step and is rejected. If a combination of inputs drives the denominator ΔS° + R ln C to zero or above, Tm has a pole there, and the calculator refuses those conditions instead of returning an absurd or infinite temperature. Sequences above 100 bases are refused because the oligonucleotide parameter set is not a polymer model; between 36 and 100 bases the result is returned but flagged as indicative.

A worked example.

Example

The M13 universal primer pair — forward (−20) GTAAAACGACGGCCAGT and reverse CAGGAAACAGCTATGAC, both 17 bases — amplified with Taq in standard buffer: 50 mM KCl, 500 nM of each primer. The forward primer has sixteen nearest-neighbour steps summing to ΔH° = −136.0 kcal/mol and ΔS° = −362.0 cal/(mol·K) in 1 M NaCl. Its 5' end is a G, contributing a G·C initiation of +0.1 and −2.8; its 3' end is a T, contributing an A·T initiation of +2.3 and +4.1. Totals: ΔH° = −133.6 kcal/mol, ΔS° = −360.7 cal/(mol·K). The salt correction at 50 mM adds 0.368 × 16 × ln(0.05) = −17.64, giving ΔS° = −378.34. With the concentration term R × ln(5 × 10⁻⁷) = −28.83, the denominator is −407.17, and Tm = −133 600 ÷ −407.17 = 328.12 K, which is 55.0 °C. The reverse primer works out to ΔH° = −129.9 kcal/mol and ΔS° = −356.3 cal/(mol·K) — both ends are C, so it takes two G·C initiations — and lands at 49.4 °C. It is the weaker of the two, so it sets the ceiling. Applying the Taq rule to the unrounded lower Tm: 49.4 − 5 gives an annealing temperature of 44.4 °C. Programme the block at 44 °C, or better, run the gradient from 39.4 to 49.4 °C and keep the highest temperature that still gives one clean band. One design note the calculator raises: the two Tm values differ by 5.6 °C, just over the 5 °C maximum Lorenz recommends. That is a real, if mild, design weakness in this famous old primer pair — at 44 °C the forward primer is binding far more tightly than the reverse, which is exactly the asymmetry that produces background when the template is complex. For a plasmid insert check it does not matter. For amplification from genomic DNA it would be worth trimming the forward primer by a base or extending the reverse. If you switched the enzyme to Q5, the same primers would give 49.4 + 3 = 52.4 °C instead — eight degrees hotter than the Taq answer, from identical thermodynamics and a different published rule.

reverse PrimerCAGGAAACAGCTATGAC
sodium Concentration50
custom Offset0
polymerase Ruletaq
strand Conditionexcess
forward PrimerGTAAAACGACGGCCAGT
primer Concentration500

Frequently asked questions.

Why does your Tm come out lower than the NEB or IDT calculator for the same primers?
Almost certainly because of magnesium. This page applies a monovalent salt correction only — the Na⁺ or K⁺ in your buffer — and no correction for the divalent magnesium and the dNTPs that a real PCR mix contains. Divalent cations screen the phosphate backbone far more effectively than monovalent ones, so they stabilise the duplex and raise Tm. Calculators that model magnesium therefore report a higher Tm and a higher annealing temperature. The gap is systematic, not random: if you cross-check several primer pairs you will see the same offset each time. This calculator does not apply a divalent correction because the coefficients could not be verified against primary published text, and shipping unverified constants is worse than declaring the limit. Practically: use the gradient window, and if you routinely work from one calculator, stay with it so your empirical corrections transfer.
Should I use the higher primer Tm, the lower one, or the average?
The lower one, and the calculator does this for you. A PCR is only as stringent as its weakest primer: at any temperature above the lower Tm, more than half of that primer is off the template, and whatever the other primer is doing cannot rescue it. Averaging is a common shortcut and it is a bad one, because it sets a temperature at which the weak primer is under-bound and the strong primer is over-tolerant of mismatches — the worst of both. If the two Tm values are close, as they should be, the distinction hardly matters; if they are far apart, averaging actively hides the design problem that the difference is telling you about. The correct response to a large Tm gap is to redesign the primers, not to choose a cleverer average.
Why do Taq and Q5 want annealing temperatures eight degrees apart?
Because the offset from Tm to Ta is empirical enzyme guidance, not thermodynamics. The Tm is a property of your primer and template; it does not change when you change polymerase. What changes is how much primer occupancy the enzyme needs in order to initiate efficiently, and how tolerant it is of extending from a partially mismatched 3' end. Lorenz's 2012 protocol sets the classic Taq annealing step about 5 °C below the apparent Tm. New England Biolabs instructs annealing 3 °C above the lower primer Tm for Q5, its high-fidelity enzyme. The eight-degree spread between those two rules for identical primers is real and intended — Q5 achieves its specificity partly by working at higher stringency. Always use the rule your enzyme's manufacturer publishes; if they publish none, the Taq rule is the conservative starting point because it errs toward more binding rather than less.
What is the Wallace rule, and why does this page not use it?
The Wallace rule estimates a dissociation temperature as 2 °C for every A or T plus 4 °C for every G or C in the oligonucleotide, which for a 17-mer with nine G/C bases gives 2×8 + 4×9 = 52 °C. It comes from Wallace and colleagues' 1979 filter-hybridisation work in Nucleic Acids Research, carried out at around 0.9 M sodium with the oligo bound to a membrane. It is fast, memorable and adequate for choosing hybridisation conditions for a 14 to 20 base probe. It is not a solution melting temperature, it takes no account of which base sits next to which, it has no concentration term, and it embeds a salt concentration eighteen times higher than a PCR buffer. For those reasons this page uses nearest-neighbour thermodynamics instead. Our GC content calculator reports the Wallace value explicitly, labelled as such, so you can see how far apart the two approaches land for your own sequence.
How much does primer concentration actually change the answer?
Less than people expect, because the dependence is logarithmic. The concentration enters as R × ln C in the denominator of the melting equation, so a tenfold change in primer concentration shifts the denominator by R × ln 10 ≈ 4.6 cal/(mol·K). Against a typical denominator of roughly 400 for a 17-mer, that is about one percent, which works out to two or three degrees of Tm. So going from 100 nM to 1 µM primer raises Tm by a couple of degrees, and getting the field roughly right is enough — you do not need to model pipetting error. The same logic explains why the strand-condition dropdown only moves the answer by about 1.1 °C: the factor of a half inside the logarithm is R × ln 2, a smaller change still.
My primers have a 5' tail for cloning. What Tm should I use?
Two of them, at two stages, and this calculator gives you the one you need for the first stage. In the first few cycles the tail has nothing to anneal to, so only the template-complementary portion binds — enter just that portion here, and use the resulting annealing temperature for those early cycles. Once the tail has been copied into the product, the whole primer is complementary and the effective Tm jumps, so later cycles can run considerably hotter. The standard protocol is a two-phase programme: five or so cycles at the annealing temperature for the binding region alone, then the remaining cycles at the annealing temperature for the full-length primer. Run this calculator twice, once with the annealing region and once with the complete sequence, and use both numbers. The same reasoning applies to primers carrying barcodes, adapters or restriction sites.
Why does the calculator reject degenerate bases like N, R and Y?
Because the nearest-neighbour parameter set has no entries for them, and any value it produced would be an invention rather than a measurement. A degenerate position is not one duplex; it is a pool of duplexes with different stabilities, and the pool's effective Tm depends on which variants are actually present and in what proportion — which the sequence string does not tell you. Guessing an average would produce a confident-looking number with no thermodynamic basis. The practical workaround is to compute the Tm of the most stable variant and the least stable variant by substituting the extreme bases at each degenerate position, then anneal toward the lower of the two and widen your gradient. That gives you a defensible range instead of a fabricated point value.
What does it mean if my annealing temperature comes out above 72 °C?
It means a separate annealing step is buying you nothing, and the calculator says so in the design notes. Standard extension runs at 72 °C, the temperature at which Taq-family polymerases work fastest. If your primers are stable enough that the recommended annealing temperature is at or above that, the primers will be bound during the extension step anyway, and you should run a two-step protocol: denature, then a combined anneal-and-extend at 72 °C. This is normal for long, GC-rich primers and for high-fidelity enzymes with the +3 °C rule. It is also a hint that the primers may be longer than they need to be — a 20 to 25 base primer with 40 to 60 percent GC and a Tm in the high fifties is easier to optimise than a 35-mer that anneals above the extension temperature.
Does a predicted Tm guarantee my PCR will work?
No, and nothing on this page should be read that way. The nearest-neighbour model predicts the melting temperature of one perfectly matched, two-state duplex in a clean monovalent buffer. It does not model primer dimers, where the two primers anneal to each other; hairpins, where a primer folds back on itself; template secondary structure that occludes the binding site; mispriming at partially matched sites elsewhere in a complex genome; polymerase processivity; or the calibration of your particular thermal block. Any of those can defeat a perfectly reasonable annealing temperature. Treat the number as the centre of a search, run the ±5 °C gradient, and check the product on a gel. If a gradient produces nothing clean at any temperature, the problem is not the annealing temperature and no calculator will fix it.
Why did you not implement the Rychlik optimal annealing temperature equation?
Because it could not be verified against the original text, and shipping a formula from memory is how calculators end up confidently wrong. Rychlik, Spencer and Rhoads published an optimum-annealing equation in Nucleic Acids Research in 1990 that blends the primer Tm with the Tm of the amplification product — a genuinely different and often better approach, since the product's own stability affects how efficiently the reaction proceeds. The paper is real and widely cited. But the PubMed Central record for it exposes only the abstract, the 1991 record is the corrigendum rather than the paper, and the publisher's full text is subscriber-only, so the coefficients could not be confirmed first-hand. Under the rule that no constant gets guessed, the equation is named here and not implemented. If you have library access to the original, it is worth reading; it will give a different number from this page, and knowing why is more useful than a third opinion.

References& sources.

  1. [1]SantaLucia, J. Jr. (1998). 'A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics.' Proceedings of the National Academy of Sciences 95(4):1460–1465, doi:10.1073/pnas.95.4.1460. PRIMARY SOURCE, peer-reviewed, open access. Table 2 supplies every ΔH° and ΔS° value, the two initiation terms and the −1.4 symmetry correction used here; Equation 8 supplies the salt correction ΔS°([Na⁺]) = ΔS°(1 M NaCl) + 0.368 × N × ln[Na⁺]; the paper states R = 1.987 cal/(mol·K) and that CT is replaced by CT/4 for non-self-complementary duplexes at equal strand concentration, or by (CA − CB/2) when the strands are unequal. Full text fetched and every value transcribed verbatim on 2026-07-29.
  2. [2]Lorenz, T. C. (2012). 'Polymerase Chain Reaction: Basic Protocol Plus Troubleshooting and Optimization Strategies.' Journal of Visualized Experiments 63:e3998, doi:10.3791/3998. INDEPENDENT SECOND AUTHORITY, peer-reviewed, open access — consulted specifically to check the offset direction of the primary calculation. States verbatim that the annealing step runs 'at a temperature set about 5 °C below the apparent Tm of the primers' and that 'the final Tm for both primers should differ by no more than 5 °C'. Both statements are implemented here. Fetched and verified 2026-07-29.
  3. [3]New England Biolabs, Q5 High-Fidelity DNA Polymerase protocol and PCR optimisation guidelines — MANUFACTURER GUIDANCE, and the source of the +3 °C rule offered as the high-fidelity mode: a 10–30 second annealing step at 3 °C above the Tm of the lower-Tm primer, with NEB's own Tm Calculator recommended for the Tm itself. Note that this points in the OPPOSITE direction from the Taq rule above; the difference is enzyme-specific and intended. NEB's servers returned HTTP 403 to automated retrieval on 2026-07-29, so this is cited as manufacturer guidance corroborated by independently hosted verbatim copies of the same protocol, not as a fetched primary document.
  4. [4]Wallace, R. B., Shaffer, J., Murphy, R. F., Bonner, J., Hirose, T. & Itakura, K. (1979). 'Hybridization of synthetic oligodeoxyribonucleotides to Phi chi 174 DNA: the effect of single base pair mismatch.' Nucleic Acids Research 6(11):3543–3557. PEER-REVIEWED, the origin of the 2(A+T) + 4(G+C) dissociation-temperature rule this page deliberately does NOT use. Cited so that readers comparing a Wallace value against this page's nearest-neighbour value can see why the two differ: Wallace's conditions were roughly 0.9 M sodium with the oligonucleotide membrane-bound, not a solution melting temperature in a PCR buffer.
  5. [5]Rychlik, W., Spencer, W. J. & Rhoads, R. E. (1990). 'Optimization of the annealing temperature for DNA amplification in vitro.' Nucleic Acids Research 18(21):6409–6412 (corrigendum: NAR 1991;19(3):698). PEER-REVIEWED. NAMED BUT NOT IMPLEMENTED: this paper's optimum-annealing equation blends the primer Tm with the product Tm, which is a different and arguably better approach, but its coefficients could not be verified from the primary text — PMC exposes the abstract only and the publisher PDF is subscriber-only — so it is disclosed rather than reproduced from memory. Checked 2026-07-29.
  6. [6]Owczarzy, R., You, Y., Moreira, B. G., Manthey, J. A., Huang, L., Behlke, M. A. & Walder, J. A. (2004). 'Effects of sodium ions on DNA duplex oligomers: improved predictions of melting temperatures.' Biochemistry 43(12):3537–3554, doi:10.1021/bi034621r. PEER-REVIEWED, BIBLIOGRAPHIC POINTER. Cited to identify the salt-correction literature that supersedes the simple linear entropy correction used here, and — with its 2008 divalent-cation successor — to name precisely what this page does not model. Not implemented; listed so a reader can find the better treatment.
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