Meant to be used in both the teaching and research laboratory, this calculator can be utilized to perform mass/mass concentration calculations expressed in parts per trillion (ppt), parts per billion (ppb), parts per million (ppm), parts per thousand (ppth), or parts per hundred (pph, %). The parts-per notation is very common in science and engineering, and is useful when referring to extremely small concentrations. This calculator uses the mass of solute in the numerator and the final mass of solution in the denominator to calculate the concentration (mass/mass fraction).

When using the parts-per concentration notation, it is essential to explicitly state the units used for the numerator and denominator, even if both the numerator and denominator have the same units, and the result of the fraction is unitless. Simply reporting a concentration as parts per million (ppm) does not provide sufficient information to know how the concentration was calculated. Moreover, it does not allow for comparison with other numbers reported in ppm.

Note that although mass/mass fraction is unitless, for easy reference and intuitive understanding, we have chosen convenient mass/mass fraction units. For example, we have used mg/kg for parts per million (ppm). We could have also chosen μg/g, ng/mg, or pg/μg for ppm. In all cases, ppm is still one part per one million parts. For parts per billion (ppb), we have chosen μg/kg, however, we could have chosen ng/g or pg/mg. The same is true for the units chosen for ppt and ppth.

An important note is in order. Here, we have appropriately used "mass", however, it is important to know that the scientific literature is replete with references to "weight" (which is the force of gravity acting on mass) of solutes and solutions. Therefore, "mass" and "weight" have been used interchangeably, but keep in mind that mass is correct.

If you wish you to calculate other concentration fractions, see our other parts-per concentration calculators: solute mass over solution mass (mass/mass fraction), solute mass over solution volume (mass/volume fraction), solute volume over solution mass (volume/mass fraction), or solute volume over solution volume (volume/volume fraction).

Our other parts-per (ppb, ppm, etc.) calculators allow you to perform dilution calculations, dilution factor or fold dilution calculations, and solution mixtures calculations.

When examining the above equation, it is very important to note that the denominator refers to the solution mass and not just the solvent mass. Thus, solution mass is the combined mass of solute and solvent.

Each calculator cell shown below corresponds to a term in the formula presented above. Enter appropriate values in all cells except the one you wish to calculate. Therefore, at least two cells must have values, and no more than one cell may be blank. The value of the blank cell will be calculated based on the other values entered. After a calculation is performed, the calculated cell will be highlighted and subsequent calculations will calculate the value of the highlighted cell (with no requirement to have a blank cell). However, a blank cell has priority over a highlighted cell.