Ligation Calculator — Insert:Vector Molar Ratio

Background.

This ligation calculator answers the question every cloning bench asks at the end of a gel extraction: I have this much vector and I want a 3:1 insert-to-vector molar ratio — how many nanograms of insert do I actually pipette? Enter the vector length in base pairs, the insert length in base pairs, the mass of vector going into the tube, and your target ratio. The answer comes back in nanograms, along with the amount of each species in picomoles and the total DNA load in the reaction.

The reason a mass alone is not enough is that ligation is a reaction between molecules, not between grams. A 500 bp insert and a 3000 bp vector weigh the same per molecule only if you pretend base pairs are free, and they are not: at equal mass you would have six times as many insert molecules as vector molecules. The molar-ratio formula corrects for exactly that length difference, which is why the equation carries the ratio of the two lengths. Every source that prints it — Promega's pGEM-T technical manual, QIAGEN's ligation tool, and the Davidson College teaching protocol — prints the same algebra: insert ng equals vector ng times insert length over vector length times the molar ratio.

A point worth reading before you trust the number: the ratio you set is a ratio of whole molecules, while what T4 DNA ligase actually sees is a concentration of compatible ends. Addgene makes this explicit — the 3:1 recommendation "is really meant to refer to the molarity of DNA ends available for ligation". For a clean directional double digest with one insert and one backbone, molecules and ends track each other and the calculation is exact. For blunt-end ligations, for fragments that can circularise on themselves, and for multi-fragment assemblies, it is a starting point that you titrate around rather than a prediction.

The second thing the arithmetic will not tell you is whether the reaction works. Absolute DNA concentration, not just the ratio, decides whether you get the closed circles you want or long linear concatemers you do not. Dugaiczyk, Boyer and Goodman worked this out in 1975 and the result still governs bench practice: dilute reactions favour intramolecular circularisation, concentrated ones favour intermolecular joining. That is why protocols pin total DNA near 100 ng in a 20 µL reaction rather than letting it float. This page reports the total DNA mass alongside the ratio so you can see both numbers at once.

The calculator runs in three directions. The default mode gives you the insert mass for a target ratio. The second mode takes two masses you have already committed to and tells you what ratio they really represent — useful when your insert prep came in at an awkward concentration. The third mode fixes the insert and solves for the vector. All three use the same closed-form algebra with arbitrary-precision arithmetic, and all three report the same six outputs, so you can switch modes without losing your place.

What is ligation calculator?

An insert-to-vector molar ratio is the number of insert molecules present in a ligation reaction for every one vector molecule. Writing it as 3:1 means three inserts per backbone. Because DNA is quantified by mass on a spectrophotometer or a gel, and because molecules of different lengths have different masses, converting a target molar ratio into a pipettable mass requires the lengths of both species.

The conversion runs through amount of substance. One base pair of double-stranded DNA has an average molar mass of roughly 650 g/mol, so a fragment of L base pairs has a molar mass of about 650 × L g/mol, and a mass m expressed in nanograms corresponds to m × 1000 ÷ (L × 650) picomoles. Apply that to both species, demand that the insert amount be R times the vector amount, and the base-pair constant cancels out completely — leaving the familiar mass equation with no physical constant in it at all. That cancellation is the reason four independently written protocols agree on the formula to the digit despite disagreeing about whether a base pair weighs 650 or 660 g/mol.

What the ratio is not: it is not a probability of success, not a transformation yield, and not a measure of insert quality. It is deterministic stoichiometry — exact arithmetic on quantities you supply. Whether the ligation produces colonies depends on end compatibility, dephosphorylation, ligase activity, incubation, and competent-cell efficiency, none of which appear in this equation. Use the ratio to set up the reaction, and use a vector-only no-insert control to interpret the plate.

How to use this calculator.

1. 01Choose a mode. Leave it on 'Insert mass' for the standard question: how much insert do I add to the vector I have?
2. 02Enter the vector length in base pairs. Use the length of the linearised backbone after digestion — if you cut a 5.2 kb plasmid and dropped a 200 bp stuffer, the backbone is 5000 bp, not 5200. Enter base pairs, not kilobases.
3. 03Enter the insert length in base pairs. For a PCR product, count the amplicon including any restriction sites you engineered into the primers.
4. 04Enter the mass of vector you plan to use, in nanograms. 50–100 ng is the usual range for a 20 µL reaction.
5. 05Set the target molar ratio. 3 means 3:1 insert:vector, the standard starting point for a sticky-end clone with an insert smaller than the vector. Try 5:1 or 7:1 for very small inserts and 1:1 for inserts larger than the backbone.
6. 06Read the insert mass, then work out the volume yourself: volume in µL equals the insert mass in ng divided by your insert concentration in ng/µL.
7. 07Check the total DNA figure. If it is far above about 100 ng in a 20 µL reaction, scale both masses down together — the ratio will not change, but the circular-versus-concatemer balance will.
8. 08Leave the base-pair molar mass at 650 g/mol unless your vendor's tool uses 660. It changes the picomole readouts but never the nanograms of insert.
9. 09Watch the direction of the colon. This page writes insert:vector. Promega's manual writes the same reaction as vector:insert = 1:3. Same experiment, reciprocal notation.

The formula.

Start from amount of substance. A double-stranded fragment of L base pairs has a molar mass of approximately L × MW_bp grams per mole, where MW_bp is the average molar mass of one base pair. A mass m in nanograms therefore corresponds to

n (pmol) = m (ng) × 1000 ÷ [ L (bp) × MW_bp (g/mol) ]

The factor of 1000 is a pure unit conversion: 1 ng ÷ 1 g/mol = 1 nmol = 1000 pmol.

Now impose the ratio. We want n_insert = R × n_vector, so

m_i × 1000 ÷ (L_i × MW_bp) = R × m_v × 1000 ÷ (L_v × MW_bp)

The 1000 and the MW_bp appear on both sides and cancel, leaving

m_i = m_v × (L_i ⁄ L_v) × R

This is the equation Promega prints as [(ng vector × kb insert) ÷ kb vector] × (molar insert ÷ molar vector), the one QIAGEN prints as vector mass × {insert length ÷ vector length} × desired ratio, and the one Davidson College prints in its fixed 3:1 form. The cancellation is the reason they agree exactly even though the literature does not agree on MW_bp: 650 g/mol is NEB's convention, 660 g/mol is Thermo Fisher's and IDT's, and the exact free-acid residue sum is 617.96 g/mol. Change the field on this page from 650 to 660 and the picomole outputs move by about 1.5 percent while the nanograms of insert do not move at all.

The two inverse forms follow by rearrangement. Solving for the realised ratio gives R = (m_i × L_v) ÷ (m_v × L_i), which is undefined when m_v = 0 — the calculator raises a field error there rather than returning infinity, because a reaction with no vector has no ratio, not an infinite one. Solving for the vector gives m_v = (m_i × L_v) ÷ (L_i × R).

Rounding: every step runs in arbitrary-precision decimal arithmetic and the only rounding happens once, at the final result, to ten decimal places. Nothing is rounded in between — in particular the realised ratio is computed from the closed form above rather than by dividing two already-rounded picomole figures, so a 3:1 setup reports exactly 3 rather than 2.9999999998. Report your own pipetting to two or three significant figures; a P2 pipette and a spectrophotometer reading do not support more.

Working with the page example: a 5000 bp vector at 50 ng, a 2000 bp insert, target 3:1. m_i = 50 × (2000 ÷ 5000) × 3 = 50 × 0.4 × 3 = 60 ng. In picomoles, the vector is 50 × 1000 ÷ (5000 × 650) = 0.0153846154 pmol and the insert is 60 × 1000 ÷ (2000 × 650) = 0.0461538462 pmol. Dividing gives 3.0000000 exactly — the ratio you asked for. Total DNA in the tube is 110 ng.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Promega Corporation — 'Successful Ligation and Cloning of Your Insert' (Promega Connections), reproducing the equation from Technical Manual TM042, pGEM-T and pGEM-T Easy Vector Systems (rev. 10/21). Prints the ligation equation as [(ng of vector × kb size of insert) ÷ kb size of vector] × (molar amount of insert ÷ molar amount of vector) = ng of insert, with the worked example [(100 ng vector × 0.5 kb insert) ÷ 3.0 kb vector] × (3 ÷ 1) = 50 ng insert, and the ratio guidance 1:1, 1:3, 1:5, 5:1 and 10:1. Free, independent. Retrieved 2026-07-29.
2. [2]QIAGEN — Ligation Calculator tool documentation (Enzymes → Tools and Calculators). Independent second authority consulted as a cross-check on the equation above; states 'Required insert DNA mass [g] = vector DNA mass [g] × {insert DNA length / vector DNA length} × desired insert to vector molar ratio' and offers ratios from the set {1, 2, 3, 5, 7}. Agrees exactly with Promega. Free, independent. Retrieved 2026-07-29.
3. [3]Addgene — 'Protocol: How to Ligate Plasmid DNA'. Source for the 3 insert : 1 vector recommendation for standard cloning, the roughly 100 ng total-DNA guideline for a standard reaction, and the explicit caveat that the molar ratio 'is really meant to refer to the molarity of DNA ends available for ligation'. Non-profit plasmid repository, free, independent. Retrieved 2026-07-29.
4. [4]Davidson College, Department of Biology — 'How to do a Ligation' teaching protocol. Third independent statement of the same relationship in its fixed-ratio form: X ng of insert = (3)(bp insert)(50 ng linearized plasmid) ÷ (size of plasmid in bp). Academic source, free. Retrieved 2026-07-29.
5. [5]Dugaiczyk, A., Boyer, H. W. & Goodman, H. M. (1975). 'Ligation of EcoRI endonuclease-generated DNA fragments into linear and circular structures.' Journal of Molecular Biology 96(1): 171–184. The primary peer-reviewed treatment of why the balance between circular products and linear concatemers is set by absolute end concentration (the j/i ratio) rather than by the insert:vector ratio alone. Paywalled — cited bibliographically for the physical argument, not as an open link.