BioDeviceHub

Concentration Unit Converter

Convert a concentration between molar units (M to pM) and mass per volume (g/L, mg/mL, µg/mL, ng/µL, mg/dL, % w/v) using the molecular weight.

Formula

cmol (mol/L)=cmass (g/L)MWc_{\mathrm{mol}}\,(\mathrm{mol/L}) = \dfrac{c_{\mathrm{mass}}\,(\mathrm{g/L})}{\mathrm{MW}}
cmass (g/L)=cmol (mol/L)×MWc_{\mathrm{mass}}\,(\mathrm{g/L}) = c_{\mathrm{mol}}\,(\mathrm{mol/L}) \times \mathrm{MW}
1 % w/v=10 g/L1\,\%\ \mathrm{w/v} = 10\ \mathrm{g/L}
1 mg/dL=0.01 g/L1\ \mathrm{mg/dL} = 0.01\ \mathrm{g/L}
MW\mathrm{MW}
molecular weight of the solute, in g/mol
% w/v\%\ \mathrm{w/v}
grams of solute per 100 mL of solution
mg/dL\text{mg/dL}
milligrams per decilitre (100 mL), the unit used on many clinical reports

How it works

A mass concentration says how many grams are in each litre; a molar concentration says how many moles. The molecular weight is the bridge between the two: dividing g/L by g/mol leaves mol/L.

Conversions inside one family are only a change of prefix and need no molecular weight. 1 g/L is the same as 1 mg/mL, and 1 µg/mL is the same as 1 ng/µL. The results table lists the entered concentration in every unit at once.

Worked example

A fasting blood glucose of 100 mg/dL, with glucose at 180.156 g/mol.

  1. 100 mg/dL = 1,000 mg/L = 1 g/L.
  2. 1 g/L / 180.156 g/mol = 0.005551 mol/L.

100 mg/dL of glucose is 5.551 mM (5.55 mmol/L).

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • The molecular weight is that of the species the concentration refers to.
  • % w/v means grams per 100 mL of solution.

Common mistakes

  • Missing the factor of ten between mg/dL and mg/L.
  • Using the molecular weight of a salt for a concentration that is reported as the free acid or free base, or the reverse.
  • Using a single molecular weight for a nucleic acid or protein preparation of mixed lengths. The molar concentration then refers only to a molecule of that exact weight.

Related tools

Molarity CalculatorMass, concentration or volume for a molar solutionOpen calculatorPercent Solution Calculator% w/v, % v/v and % w/w solutionsOpen calculatorppm and ppb CalculatorParts per million and per billion, by mass or in dilute solutionOpen calculatorMolecular Weight CalculatorMolar mass and composition from a chemical formulaOpen calculator

Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.