The DNA ligation calculator above works out how many nanograms of insert to put into a ligation reaction to achieve a chosen insert-to-vector molar ratio, given the two fragment lengths and the mass of vector you are using. It also converts both amounts into femtomoles and, if you supply stock concentrations, into pipetting volumes.
Arb Digital publishes this as bench arithmetic for molecular cloning. It sits alongside our DNA concentration calculator, which converts absorbance readings into a concentration, and the molar ratio calculator, which handles general stoichiometry. This page does one specific job: the mass-to-molarity conversion that makes a ligation ratio mean what it says.
What This DNA Ligation Calculator Does
Ligation protocols specify a molar ratio because ligase joins molecules, not milligrams. The number of molecules in a given mass of DNA depends entirely on the length of the fragment, so two tubes containing the same mass of a 1 kb insert and a 5 kb vector hold five times as many insert molecules as vector molecules. Working in mass without converting is the single most common way a stated ratio ends up being something else.
The tool takes the vector length, the insert length, the vector mass and the target ratio, and returns the insert mass. It shows both components in femtomoles so you can see the molecule counts directly, and it computes volumes from your stock concentrations so the numbers go straight onto the bench sheet. The mass-per-base-pair constant is exposed as an input rather than hidden, because it is an approximation and you should be able to see it.
How to Use It
- Enter both fragment lengths in base pairs, using the digested sizes rather than the sizes of the parent plasmids.
- Set the vector mass. Fifty nanograms is a common starting quantity for a standard cloning reaction.
- Choose the molar ratio. Three parts insert to one part vector is the usual first attempt for a small insert.
- Add your stock concentrations to convert the masses into microlitres.
- Check the femtomole figures against the ratio you asked for. They should divide out to exactly that ratio.
The Formula and How It's Calculated
The mass calculation collapses to a single line once the molar conversion is done:
Insert mass (ng) = ratio × vector mass (ng) × (insert length ÷ vector length)
Underneath it is a conversion between mass and moles. New England Biolabs sets out the standard approach in its note on how to calculate the molarity of DNA ends, using an average of 650 g/mol per base pair of double-stranded DNA. That gives:
pmol = (mass in ng × 1,000) ÷ (length in bp × 650)
Work the default. Fifty nanograms of a 5,000 bp vector is (50 × 1,000) ÷ (5,000 × 650) = 0.0154 pmol, which is 15.4 femtomoles. A 3:1 ratio needs 46.2 fmol of insert. Converting back, 0.0462 pmol of a 1,000 bp fragment weighs 0.0462 × 1,000 × 650 ÷ 1,000 = 30 ng. The shortcut gives the same answer directly: 3 × 50 × (1,000 ÷ 5,000) = 30 ng. From a 20 ng/µL insert stock that is 1.5 µL, and 50 ng of vector from a 25 ng/µL stock is 2 µL.
It is worth noticing what the shortcut formula quietly cancels. Both the vector and the insert are converted from mass to moles using the same constant, so that constant divides out entirely and never appears in the final expression. This is why the answer is insensitive to the exact mass-per-base-pair figure you use, and why the field is exposed on this page as an input rather than presented as a critical parameter. It matters for the femtomole readouts and not at all for the ratio itself.
The Assumptions Behind the Number
Three approximations are baked in, and all three are worth knowing. First, 650 g/mol per base pair is an average across the four base pairs; a fragment with unusual base composition deviates from it slightly, though never enough to matter at the scale of a ligation. Second, the calculation assumes both preparations are pure and correctly quantified, which is a much bigger assumption than the constant.
Third, it assumes the molecules are what you think they are. Residual uncut vector, incompletely digested fragments, a partial second band on the gel, or carryover of the original template will all be counted by a spectrophotometer as DNA and will not participate in the intended ligation. The calculator can only work with the numbers you give it, and a concentration measured on an impure prep produces a ratio that is right on paper and wrong in the tube.
Why 3:1 Is the Usual Starting Point
Addgene's DNA ligation protocol recommends a 3 insert to 1 vector molar ratio for the standard case where the insert is smaller than the backbone. The reasoning is a competition between two outcomes: the vector can circularise on itself, or it can capture an insert. Providing an excess of insert molecules shifts that competition toward the product you want.
The excess is not unlimited, because too much insert promotes multiple inserts ligating into a single vector or forming concatemers of their own. Where the insert is similar in size to the vector, a 1:1 ratio is more usual, and difficult ligations are often set up as a small series across several ratios rather than as a single guess. Running the calculator two or three times and pipetting a row of tubes is usually faster than optimising one tube at a time.
The vector mass itself is the other lever, and it is often set too high. A larger absolute amount of DNA raises the total number of ends in the tube and pushes the reaction toward intermolecular joining, which favours concatemers over the neat circular product. Fifty nanograms of vector is a common figure precisely because it keeps the reaction dilute enough for a molecule to find its own two ends. Scaling everything up to be safe usually makes a ligation worse, not better.
Where Ratio Is Not the Limiting Factor
A ligation that fails is rarely fixed by adjusting the ratio, and it is worth naming the more likely causes so a ratio calculation does not become a distraction. Incomplete digestion leaves uncut vector that transforms efficiently and produces a lawn of empty colonies. Vector that has been dephosphorylated too aggressively, or not at all, changes the background dramatically in either direction.
Blunt-end ligations are inherently far less efficient than sticky-end ones and usually need more DNA and longer incubation. Carryover of the enzymes or buffers from the previous step can inhibit ligase. None of that appears in a molar ratio, which is precisely why getting the ratio right is a necessary first step rather than a sufficient one, and why an appropriate no-insert control tells you more than any recalculation.
Reading the Femtomole Figures
The two femtomole values are the honest description of what is in the tube. They should divide out to exactly the ratio you asked for, which makes them a useful check on your own arithmetic if you are transferring numbers to a protocol by hand. They also make the scale of a ligation visible: a typical reaction contains tens of femtomoles of each component, which is a vanishingly small quantity of material and a very large number of molecules.
If you need the actual molecule count rather than a molar amount, the DNA copy number calculator converts mass and length into copies, which is the same conversion pointed at a different question. For the general case of moles from mass and molecular weight, the molarity calculator covers it, and the protein molecular weight calculator handles the equivalent problem on the protein side.
Arb Digital publishes hundreds of free, no-signup tools covering laboratory science, maths, finance, and everyday conversions — no accounts, no stored data.
Browse All Free Tools Contact Arb DigitalCommon Mistakes to Avoid
- Treating the ratio as a mass ratio. Equal masses of a 1 kb insert and a 5 kb vector are already a 5:1 molar excess.
- Using the uncut plasmid length instead of the length of the digested fragment you are actually ligating.
- Trusting a concentration from an impure prep, where absorbance counts material that will never ligate.
- Pushing the insert excess far higher to force a difficult ligation, which promotes multiple inserts and concatemers.
- Skipping the no-insert control, which is the only way to tell a ratio problem from an uncut-vector problem.
Related Free Tools From Arb Digital
Upstream of a ligation, the DNA concentration calculator turns absorbance into a concentration and the serial dilution calculator plans the dilution series. For the molecule count there is the DNA copy number calculator, and for general stoichiometry the molarity calculator and molar ratio calculator. Downstream, the primer melting temperature calculator covers screening PCR. Browse the full free online tools hub for more.
Frequently Asked Questions
Multiply the desired molar ratio by the vector mass and by the insert length divided by the vector length. For a 3:1 ratio with 50 ng of a 5,000 bp vector and a 1,000 bp insert, that is 3 times 50 times 0.2, which is 30 ng.
Multiply the mass in nanograms by 1,000 and divide by the length in base pairs multiplied by 650, the standard average mass per base pair of double-stranded DNA. Fifty nanograms of a 5,000 bp fragment is 0.0154 pmol, or 15.4 fmol.
Addgene's ligation protocol recommends 3 insert to 1 vector when the insert is smaller than the backbone. For inserts of similar size to the vector, a 1:1 ratio is more usual, and difficult ligations are often set up across several ratios at once.
It is the standard average molecular weight of a base pair in double-stranded DNA, covering both strands. It is an approximation across the four base pairs, and a fragment with unusual base composition deviates from it slightly.
By moles. Ligase joins molecules, and the number of molecules in a given mass depends on fragment length, so a ratio stated in mass terms means something different for every pair of fragment sizes.
No. Use the length of the linearised, digested fragment you are actually ligating. If digestion removes a stuffer fragment, the vector length is what remains, not the size of the parent plasmid.
Possibly, but incomplete digestion, dephosphorylation problems, blunt ends and enzyme carryover are more common causes and none of them appear in a molar ratio. A no-insert control distinguishes a ratio problem from an uncut-vector problem.
This calculator performs the published mass-to-molarity arithmetic for cloning reactions. It is a bench aid, not a protocol. Follow the manufacturer's instructions for your ligase and buffer, and the safety and biosafety rules that apply in your laboratory.
