Ligation Ratio Calculator

Q: Why does ligation use a molar ratio instead of a mass ratio?

Because ligation joins molecules, not grams. One insert end ligates to one vector end, so the outcome depends on how many of each molecule are present. Equal masses of a small insert and a large vector contain very different numbers of molecules; the molar ratio equalizes the molecules, which is what the ligase actually sees.

Q: What insert:vector ratio should I start with?

3:1 is the standard starting point for compatible sticky ends. Use 1:1 for blunt-end ligations (which are less efficient and prone to concatemers), and 6:1 to 10:1 when the insert is much smaller than the vector or when a 3:1 ligation gave too few colonies. Many people set up two or three ratios in parallel for a difficult construct.

Q: Do I need the molecular weight of my fragments?

No. Because DNA molecular weight is proportional to length, the size ratio in bp replaces the MW ratio and the masses come out directly in ng. If you want the molecular weight itself for another calculation, the plasmid molecular weight calculator gives it from the size.

Q: How much vector should I use in total?

A common range is 10–100 ng of vector per 10–20 µL ligation. Too little vector gives few colonies; too much total DNA can inhibit the ligase. Pick a vector mass in that range, compute the insert mass from the ratio, and keep the total DNA moderate.

Q: My ligation gave no colonies — how does the reverse mode help?

Enter the masses you actually added and the calculator reports the molar ratio you really set up. If it is far from your target (for example 0.3:1 or 15:1), the ratio was the problem: too little insert favours empty vector, too much favours insert concatemers. Correct the masses and re-plan the ligation.

Q: Does this work for multi-fragment or Gibson assemblies?

This tool balances a single insert against a single vector. For multi-fragment assemblies you apply the same molar principle to each fragment in turn, which is more involved; for Gibson or Golden Gate the equimolar logic is similar but the reaction chemistry and ratios differ, so follow the assembly protocol.

A ligation is set by the molar ratio of insert to vector, not their mass ratio, because ligation efficiency depends on how many molecules of each are present. Since molecular weight is proportional to length, the mass of insert to add is mass_insert = molar ratio × (insert size / vector size) × vector mass. For a 1000 bp insert into a 2686 bp vector (pUC19) at 3:1 with 50 ng of vector, the size ratio is 1000/2686 = 0.372 and you add 3 × 0.372 × 50 = 55.8 ng of insert. This calculator solves that forward, and also runs in reverse: give it both masses and it reports the molar ratio you actually set up — the first diagnostic when a ligation fails.

Ligation is the step that joins your insert to the vector, and the single number that controls it is the insert:vector molar ratio. A typical protocol says "use a 3:1 insert:vector ratio", but what you pipette is a mass in nanograms, and converting between the two is where most cloning mistakes happen. This page is part of the molecular cloning calculator set and does that conversion explicitly, in both directions, with the derivation shown rather than hidden behind a button.

The reason a molar ratio matters is that ligation is a bimolecular reaction: a ligase joins one insert end to one vector end, so what counts is how many insert molecules collide with how many vector molecules. Mass is misleading on its own — 50 ng of a small insert is far more molecules than 50 ng of a large vector. Because the molecular weight of a DNA fragment is proportional to its length in base pairs, the mole ratio simplifies to a length-corrected mass ratio, and you never need to compute a molecular weight by hand. If you do want the underlying mass-per-mole, the plasmid molecular weight calculator gives it, and the DNA molecular weight calculator does the same from a sequence.

The working equation falls straight out of that proportionality. Moles equal mass divided by molecular weight, and molecular weight is proportional to size, so the molar ratio is (mass_insert / size_insert) ÷ (mass_vector / size_vector). Rearranged to solve for the unknown insert mass: mass_insert = molar ratio × (size_insert / size_vector) × mass_vector. The term size_insert/size_vector is the key intuition — a small insert needs proportionally less mass to reach the same molar ratio, which is why a 300 bp fragment at 6:1 can still be only tens of nanograms.

Choosing the ratio is a judgement the formula cannot make for you, so this page names the conventions. A 3:1 insert:vector ratio is the standard starting point for compatible sticky ends; 1:1 is common for blunt-end ligations, which are less efficient and favour a lower ratio to limit concatemers; and 6:1 to 10:1 helps when the insert is much smaller than the vector or when ligation is stubborn. Too much insert drives vector–vector and insert–insert products; too little leaves mostly empty vector. After the ligation you typically transform and then measure the outcome with the transformation efficiency calculator, which closes the cloning loop.

Solve for

Forward mode computes the insert mass for a target molar ratio; reverse mode reports the ratio your masses actually give.

Insert size (bp)

Length of the insert fragment in base pairs.

Vector size (bp)

Length of the linearized vector in base pairs (pUC19 is 2686 bp).

Vector mass (ng)

Amount of vector DNA you are adding to the ligation.

Insert:vector molar ratio (:1)

Target molar ratio. 3:1 for sticky ends, 1:1 for blunt, 6:1–10:1 for a small insert.

Insert mass (reverse mode) (ng)

Used only in reverse mode: the insert mass you actually added, to report the molar ratio achieved.

Insert DNA needed55.8451 ng

Insert size1000 bp

Vector size2686 bp

Size ratio (insert ÷ vector)0.372301

Total DNA105.845 ng

size ratio = insert / vector = 1000 bp / 2686 bp = 0.372301
insert mass = molar ratio × size ratio × vector mass = 3 × 0.372301 × 50 ng = 55.8451 ng
total DNA = vector + insert = 50 ng + 55.8451 ng = 105.845 ng

How to use the ligation ratio calculator

Leave Solve for on "Insert mass" to plan a ligation. Enter the insert size and vector size in bp, the vector mass in ng you will use, and the target insert:vector molar ratio (3 is the default).

Press Calculate. The primary card is the insert mass to add in ng; the cards below echo the size ratio and the total DNA in the reaction, and the derivation panel shows each algebraic step so you can check the logic against your protocol.

Switch Solve for to "Actual molar ratio" to diagnose a ligation you already ran. Enter the insert mass you actually added along with the sizes and vector mass, and the calculator reports the molar ratio achieved — compare it with what you intended.

Use the size in bp, not kb, unless you convert first; the ratio is unitless so any consistent length unit works, but bp avoids decimal slips. Get fragment sizes from your vector map or a gel, and the vector mass from the DNA concentration calculator if you measured it by absorbance.

If you are preparing the vector or insert stock itself, the dilution calculator turns your measured concentration into the volume to pipette for the mass shown here.

Ligation Ratio formula

molar ratio = (mass_insert / size_insert) ÷ (mass_vector / size_vector)

mass_insert = molar ratio × (size_insert / size_vector) × mass_vector [forward]

molar ratio = (mass_insert / mass_vector) × (size_vector / size_insert) [reverse]

total DNA = mass_vector + mass_insert

Molecular weight cancels because it is proportional to length for dsDNA, so the size ratio (bp/bp) replaces the MW ratio. This is the same relation the Addgene and NEB ligation tools use, shown here step by step.

Variables and units

Symbol	Meaning	Unit
size_insert	Insert fragment length	bp
size_vector	Linearized vector length	bp
mass_vector	Vector DNA added to the ligation	ng
mass_insert	Insert DNA to add (forward) or added (reverse)	ng
molar ratio	Insert:vector mole ratio	:1

How ligation ratio is calculated

Confirm both fragment sizes in bp and the vector mass in ng.
Compute the size ratio: size_insert / size_vector.
Forward: multiply molar ratio × size ratio × vector mass to get the insert mass in ng.
Reverse: divide the mass ratio (insert/vector) by the size ratio to get the molar ratio achieved.
Report the total DNA (vector + insert) so you can sanity-check the reaction concentration.
Carry the masses into your ligation mix and, after transformation, into the efficiency calculation.

Worked laboratory examples

Example 1 — Standard 3:1 into pUC19

Given: insert 1000 bp · vector 2686 bp (pUC19) · vector mass 50 ng · target ratio 3:1

size ratio = 1000 / 2686 = 0.3723.
insert mass = 3 × 0.3723 × 50 = 55.8 ng.
total DNA = 50 + 55.8 = 105.8 ng in the reaction.

Result: 55.8 ng insert (105.8 ng total)

Example 2 — Blunt-end 1:1 ligation

Given: insert 1000 bp · vector 2686 bp · vector mass 50 ng · target ratio 1:1

size ratio = 1000 / 2686 = 0.3723.
insert mass = 1 × 0.3723 × 50 = 18.6 ng.
A blunt ligation uses the lower 1:1 ratio to limit vector concatemers.

Result: 18.6 ng insert

Example 3 — Small insert at 6:1 into a large vector

Given: insert 300 bp · vector 5000 bp · vector mass 100 ng · target ratio 6:1

size ratio = 300 / 5000 = 0.06.
insert mass = 6 × 0.06 × 100 = 36 ng.
Even at a high 6:1 molar ratio the small insert is only 36 ng because the size ratio is small.

Result: 36 ng insert (136 ng total)

Example 4 — Reverse: what ratio did I actually set up?

Given: insert 55.8 ng added · vector 50 ng · insert 1000 bp · vector 2686 bp

mass ratio = 55.8 / 50 = 1.117.
size ratio = 1000 / 2686 = 0.3723.
molar ratio = 1.117 / 0.3723 = 3.0, confirming the intended 3:1.

Result: ≈ 3:1 insert:vector

Want the reasoning behind the numbers? Read How to Calculate a Ligation Ratio (Insert:Vector).

How to interpret the result

The primary number is the insert mass to pipette. If it seems very small, that is usually correct for a small insert into a large vector — the size ratio, not an error, is driving it. Weigh it against what your stock concentration allows: if 55.8 ng means pipetting under 1 µL, dilute the insert first with the dilution calculator so the volume is measurable.

The size ratio tells you how much the length difference is skewing the masses. A ratio near 1 means insert and vector are similar in size and the mass ratio tracks the molar ratio closely; a ratio far below 1 means a small insert needs much less mass, and far above 1 means a large insert needs more.

In reverse mode, a measured molar ratio far from your target explains a failed ligation. If you intended 3:1 but the calculator reports 0.5:1, you added too little insert (vector self-ligation dominates); at 20:1 you added too much (insert concatemers). Adjust the masses and re-plan.

Total DNA matters for the ligation volume. Most ligase buffers work best in the tens-to-hundreds of ng per 10–20 µL; very high total DNA can inhibit ligation. If your total is large, concentrate or reduce the vector mass and recompute, then carry the result into the transformation efficiency calculator after you plate.

Assumptions

Both fragments are pure, fully digested and exactly the stated lengths.
Molecular weight is proportional to length, so the size ratio stands in for the MW ratio.
The vector is linearized (not recircularizing efficiently on its own) and dephosphorylated if the protocol calls for it.
Masses are accurate — the vector mass comes from a reliable quantitation, not an estimate.

Limitations

A partial digest or contaminated prep changes the effective molar ratio without changing your inputs.
The calculator gives masses to add, not ligation efficiency; ends, insert quality and ligase activity decide the outcome.
Very small fragments (< ~100 bp) ligate poorly regardless of ratio and may need optimization.
It assumes a single insert; multi-fragment assemblies need a per-fragment molar balance.

Common mistakes

Using a mass ratio instead of a molar ratio — adding equal masses of a small insert and a large vector gives far too many insert molecules.
Entering sizes in kb on one side and bp on the other, skewing the size ratio by 1000×.
Forgetting that the vector mass is the amount in the reaction, not the stock concentration.
Assuming 3:1 is universal — blunt ends and very small inserts need different ratios.
Pipetting sub-microlitre volumes of a concentrated insert instead of diluting it first.

FAQ

Why does ligation use a molar ratio instead of a mass ratio?

Because ligation joins molecules, not grams. One insert end ligates to one vector end, so the outcome depends on how many of each molecule are present. Equal masses of a small insert and a large vector contain very different numbers of molecules; the molar ratio equalizes the molecules, which is what the ligase actually sees.

What insert:vector ratio should I start with?

3:1 is the standard starting point for compatible sticky ends. Use 1:1 for blunt-end ligations (which are less efficient and prone to concatemers), and 6:1 to 10:1 when the insert is much smaller than the vector or when a 3:1 ligation gave too few colonies. Many people set up two or three ratios in parallel for a difficult construct.

Do I need the molecular weight of my fragments?

No. Because DNA molecular weight is proportional to length, the size ratio in bp replaces the MW ratio and the masses come out directly in ng. If you want the molecular weight itself for another calculation, the plasmid molecular weight calculator gives it from the size.

How much vector should I use in total?

A common range is 10–100 ng of vector per 10–20 µL ligation. Too little vector gives few colonies; too much total DNA can inhibit the ligase. Pick a vector mass in that range, compute the insert mass from the ratio, and keep the total DNA moderate.

My ligation gave no colonies — how does the reverse mode help?

Enter the masses you actually added and the calculator reports the molar ratio you really set up. If it is far from your target (for example 0.3:1 or 15:1), the ratio was the problem: too little insert favours empty vector, too much favours insert concatemers. Correct the masses and re-plan the ligation.

Does this work for multi-fragment or Gibson assemblies?

This tool balances a single insert against a single vector. For multi-fragment assemblies you apply the same molar principle to each fragment in turn, which is more involved; for Gibson or Golden Gate the equimolar logic is similar but the reaction chemistry and ratios differ, so follow the assembly protocol.

Scientific Sources

Addgene — DNA Ligation protocol (optimizing vector:insert ratio) · Tier 2 source
Wikipedia — Ligation (molecular biology) · Tier 3 source
Wikipedia — Molecular cloning · Tier 3 source

External links open in a new tab and carry rel="nofollow". We cite primary references (NIST, NIH/NCBI, peer-reviewed papers) and established manufacturer technical documentation (NEB, Thermo Fisher, Promega, IDT). Calculated results are estimates; your protocol and manufacturer guidance take precedence.

Last reviewed: 2026-09 · Method version: 1.0

Ligation Ratio Calculator