Ligation Calculator: Insert Mass for an Insert-to-Vector Molar Ratio

This calculator works out how much insert DNA to add to a ligation. Enter the mass of vector, the lengths of vector and insert in base pairs and the molar ratio of insert to vector you want; you get the insert mass in ng and the femtomoles of vector and insert.

Formula

Insert ng = vector ng × (insert bp ÷ vector bp) × ratio.

• Vector ng: mass of linearised vector in the reaction
• bp: lengths in base pairs
• Ratio: insert-to-vector molar ratio; 3:1 is a common starting point, often varied from 1:1 to 10:1
• fmol = ng × 10⁶ ÷ MW, with MW = bp × 617.96 + 36.04 g/mol (a commonly used average for double-stranded DNA)

Worked Example

50 ng of a 3,000 bp vector, a 750 bp insert and a 3:1 insert-to-vector ratio.

1. Length ratio: 750 ÷ 3000 = 0.25
2. Insert mass: 50 × 0.25 × 3 = 37.50 ng
3. Vector: 50 × 10⁶ ÷ 1,853,916.04 = 26.97 fmol
4. Insert: 37.5 × 10⁶ ÷ 463,506.04 = 80.91 fmol, about 3 × 26.97

Assumptions

• Both pieces are double-stranded DNA, so the weight per base pair cancels in the mass formula.
• The masses are of the purified, cut fragments, measured accurately.
• The ratio counts molecules (moles), not masses.

How to read the result

The insert mass is the amount that gives the chosen number of insert molecules per vector molecule. The femtomole values show the ratio directly: about 81 fmol of insert to 27 fmol of vector is 3:1. A short insert needs only a small mass for a high molar ratio. To convert a stock concentration to nM first, use the DNA molarity calculator.

Limits and common mistakes

• Using a mass ratio of 3:1 instead of a molar ratio: for a short insert this adds far too many insert molecules, for a long one too few.
• Entering lengths in kb for one piece and bp for the other.
• Using the length of the uncut plasmid when part of it was removed by the digest.

Frequently Asked Questions

How do I calculate insert amount for ligation?

Insert ng = vector ng × insert length ÷ vector length × molar ratio.

How much of a 750 bp insert for 50 ng of a 3 kb vector at 3:1?

37.5 ng.

What molar ratio should I use?

A 3:1 insert-to-vector ratio is a common start; follow your lab method and test other ratios if colonies are few.

Does the formula need the molecular weight?

No; for two double-stranded DNAs the weight per base pair cancels, leaving the length ratio.

in vng | Vector mass | ng | 50 | 0
in vbp | Vector length | bp | 3000 | 1
in ibp | Insert length | bp | 750 | 1
in ratio | Insert to vector molar ratio | - | 3 | 0
out ing | Insert mass needed | ng | vng * ibp / vbp * ratio | 2
out vf | Vector amount | fmol | vng * 1000000 / (vbp * 617.96 + 36.04) | 2
out ifm | Insert amount | fmol | ing * 1000000 / (ibp * 617.96 + 36.04) | 2