Millimolar to molar
Millimolar (mM) and molar (M) are molarity units based on moles per liter. The SI prefix milli means \(10^{-3}\), so millimolar is a thousandth of a molar.
\[ 1\ \mathrm{mM}=10^{-3}\ \mathrm{M} \qquad\text{and}\qquad 1\ \mathrm{M}=10^{3}\ \mathrm{mM} \]
\[ M=(\text{mM})\times 10^{-3} \qquad\text{and}\qquad \text{mM}=M\times 10^{3} \]
Meaning of the units in lab concentration
Molarity is defined as \[ M=\frac{n}{V} \] where \(n\) is the amount of solute in moles and \(V\) is solution volume in liters. Millimolar uses the same definition but with a milli-prefix applied to the molar unit.
- Millimolar (mM): \(1\ \mathrm{mM}=1\times 10^{-3}\ \mathrm{mol\cdot L^{-1}}=1\ \mathrm{mmol\cdot L^{-1}}\).
- Molar (M): \(1\ \mathrm{M}=1\ \mathrm{mol\cdot L^{-1}}\).
Dimensional analysis form
The conversion factor can be written as a unit ratio equal to 1:
\[ (\text{mM})\times\frac{10^{-3}\ \mathrm{M}}{1\ \mathrm{mM}}=(\text{mM})\times 10^{-3}\ \mathrm{M} \]
The inverse ratio maps molar to millimolar:
\[ (M)\times\frac{10^{3}\ \mathrm{mM}}{1\ \mathrm{M}}=(M)\times 10^{3}\ \mathrm{mM} \]
Worked examples
Example A: \(250\ \mathrm{mM}\) as molar
\[ 250\ \mathrm{mM}=250\times 10^{-3}\ \mathrm{M}=0.250\ \mathrm{M} \]
Example B: \(0.015\ \mathrm{M}\) as millimolar
\[ 0.015\ \mathrm{M}=0.015\times 10^{3}\ \mathrm{mM}=15\ \mathrm{mM} \]
Quick-reference values
| Millimolar (mM) | Molar (M) | Equivalent in molarity units |
|---|---|---|
| 1 | \(0.001\) | \(1\ \mathrm{mmol\cdot L^{-1}}=0.001\ \mathrm{mol\cdot L^{-1}}\) |
| 10 | \(0.010\) | \(10\ \mathrm{mmol\cdot L^{-1}}=0.010\ \mathrm{mol\cdot L^{-1}}\) |
| 100 | \(0.100\) | \(100\ \mathrm{mmol\cdot L^{-1}}=0.100\ \mathrm{mol\cdot L^{-1}}\) |
| 500 | \(0.500\) | \(500\ \mathrm{mmol\cdot L^{-1}}=0.500\ \mathrm{mol\cdot L^{-1}}\) |
| 1000 | \(1.000\) | \(1000\ \mathrm{mmol\cdot L^{-1}}=1.000\ \mathrm{mol\cdot L^{-1}}\) |
Visual scale for millimolar and molar
Common pitfalls in biology lab work
- Milli prefix: \(1\ \mathrm{mM}\) equals \(0.001\ \mathrm{M}\), not \(0.01\ \mathrm{M}\).
- Liter basis: molarity assumes liters; mixing milliliters into the definition without conversion changes numerical values.
- Molality vs molarity: \(m\) (molality) uses \(\mathrm{mol\cdot kg^{-1}}\), while \(M\) uses \(\mathrm{mol\cdot L^{-1}}\); the symbols are similar but the quantities differ.
- “mmol/L” equivalence: \(\mathrm{mmol\cdot L^{-1}}\) is numerically identical to mM by definition.