How this instrument works
Quantitative PCR standard curves, plasmid titering and many molecular cloning steps need to know how many individual DNA molecules — copies — a given mass of DNA represents, not just the mass itself. Converting between the two requires knowing the DNA's molecular weight, which depends on how long the fragment is: longer DNA molecules weigh more per molecule, so the same mass of a long fragment contains far fewer copies than the same mass of a short one.
The average molecular weight of one base pair of double-stranded DNA is taken as approximately 650 grams per mole — a standard approximation used across molecular biology, since the four DNA bases have slightly different individual weights that average out close to this figure for typical, mixed-sequence DNA. Multiplying a fragment's length in base pairs by 650 gives its approximate molar mass in g/mol, the same way multiplying atomic weights by a formula's subscripts gives a compound's molar mass in chemistry.
From there, Avogadro's number (6.022 × 10²³ molecules per mole) converts moles to an actual molecule count: dividing the sample's mass by the fragment's molar mass gives moles present, and multiplying by Avogadro's number converts that to copies. This instrument combines both steps into one formula, taking a mass in nanograms and a length in base pairs directly and returning the copy number, without requiring a separate mass-to-moles calculation first.
- Enter the total mass of DNA in your sample, in nanograms, into DNA mass (ng).
- Enter the length of the DNA fragment, in base pairs, into DNA length (base pairs) — for a plasmid, this is its total size; for a linear fragment, its length.
- Read Copy number — the estimated number of individual DNA molecules present in that mass.
- This calculation assumes double-stranded DNA with a typical, mixed-sequence base composition; a sample with an unusually skewed GC content will deviate slightly from the 650 g/mol/bp average this formula uses.
Worked example — 100 ng of a 1,000 bp fragment
A sample contains 100 ng of a 1,000 base pair DNA fragment. Enter 100 into DNA mass (ng) and 1000 into DNA length (base pairs): Copy number reads approximately 92,646,153,846.15, roughly 9.26 × 10^10 copies (about 92.6 billion).
Working the arithmetic through: (100 × 6.022×10²³) equals 6.022×10²⁵, and the denominator (1,000 × 650 × 10⁹) equals 6.5×10¹⁴; dividing 6.022×10²⁵ by 6.5×10¹⁴ gives about 9.264615×10¹⁰ — the same figure the instrument reports, confirming that this is plain unit-canceling arithmetic once the molar mass of the fragment (650,000 g/mol for 1,000 bp) is known.
Questions
Why does fragment length change the copy number for the same mass?
Because longer DNA molecules are heavier per molecule, so a fixed mass of long DNA contains fewer individual molecules than the same mass of short DNA — doubling the fragment length roughly halves the copy number for a given mass, all else equal. This is exactly analogous to how a gram of a heavy compound contains fewer moles than a gram of a light one in general chemistry.
Where does the 650 g/mol per base pair figure come from?
It is a standard, widely used approximation for the average molecular weight of one base pair of double-stranded DNA, averaged across the four bases' individually slightly different weights and typical base composition. It is precise enough for standard-curve and titering purposes across most sequences, though DNA with an unusually extreme GC or AT content will deviate from it by a small amount.
Does this work for both linear DNA fragments and circular plasmids?
Yes — the formula only needs the total length in base pairs and total mass, regardless of whether the DNA is linear (a PCR product or restriction fragment) or circular (a plasmid). For a plasmid, use its full size in base pairs, including the vector backbone, not just an insert.
How is copy number used in qPCR?
Quantitative PCR standard curves are commonly built from a dilution series of a DNA standard with a known copy number, so that unknown samples' cycle threshold values can be converted into an estimated copy number by comparison. Converting a measured mass of standard DNA (from a spectrophotometer or fluorometer reading) into copies, as this calculator does, is the first step in preparing that standard curve.
Does the DNA need to be double-stranded for this formula to apply?
Yes — the 650 g/mol/bp constant used here specifically describes double-stranded DNA. Single-stranded DNA has a different average molecular weight per base (closer to 330 g/mol per nucleotide, and measured in bases rather than base pairs), so this formula's constant would need to be swapped to apply it correctly to single-stranded material.