# Converting signal area ratio to molar and weight ratio

Assuming you are dealing with two peaks, each from a different molecule (A and B), and you want to figure out their molar ratio and weight ratio.

First, measure the signal area of the two peaks, area(A) and area(B).

Second, count number of protons (or other nuclei in question) contributing to the peak, N(A) and N(B).

Third, find out the molecular weight of the molecules, MW(A) and MW(B).

The molar ratio is:

mol(A)/mol(B) = [area(A)/N(A)]/[area(B)/N(B)]

The weight ratio is:

wt(A)/wt(B) = [mol(A) * mw(A)]/[mol(B) * mw(B)]

You can also calculate the concentration of one sample using another sample as a reference with known structure and concentration.  First, run NMR for the two samples.  They will have to be run with the same NMR techniques, same parameters, and with the same rg (receiver gain).  Second, integrate the peaks in the reference sample.  Third, integrate the peaks in the sample in which you want to find the concentration, then right click on the integration and select “Use last scale for calibration”.  Then you will be able to find the area ratio between the two samples.  This ratio, normalized by number of scans, can be used to further determine mole ratio, weight ratio, or concentration ratio.

Same principles can be applied when calculating moles and weights of interested molecules in solid-state NMR. For two samples A and B, the weight ratio for the molecules contributing to the peaks of interest is:

wt(A)/wt(B) ={ [area(A)*mw(A)]/[N(A)*NS(A)] } / { [area(B)*mw(B)]/[(N(B)*NS(B)] }