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How do I dilute a stock when the concentration units differ?
Turn a stock label and target concentration into a measurable transfer
To prepare 100 mL at 50 µM from a 10 mM stock, first convert the stock to 10,000 µM. Then V₁ = (50 × 100) ÷ 10,000 = 0.5 mL, or 500 µL. Transfer that stock and make up to 100 mL final volume; do not add it to 100 mL of diluent.
The numbers below assume the inputs in the assumptions section. Change any of them in the calculator to fit your own project.
Your stock bottle is labeled 10 mM, while the protocol asks for 100 mL of a 50 µM working solution. The immediate task is to find a stock volume you can measure and a final volume you can prepare. Entering the bare numbers 10 and 50 into the dilution equation would compare different units and reverse the apparent concentration relationship.
Convert both concentrations to the same unit before calculating. Here, 1 mM = 1,000 µM, so the stock is 10,000 µM. The embedded C₁V₁ = C₂V₂ solver has one shared concentration-unit selector, not separate units for each input. It is prefilled with 10,000 and 50 in µM, with volumes in mL, so the calculation is already normalized.
This example is a planning calculation for a compatible, nonreacting solution and a protocol-approved diluent. It does not specify chemical handling, sterility, stability, mixing order, or suitability for clinical use. Follow the material's safety data sheet and your laboratory procedure. If the required transfer falls outside your equipment's reliable range, plan a validated intermediate dilution rather than rounding away the needed precision.
Prefer the full version with the explanation and examples? Open the calculator page directly.
Calculate the normalized stock volumeThe prefix conversion is performed before the numbers enter the shared-unit solver.
Both concentrations describe the same solute on a molar basis.
This includes the transferred stock, not just the diluent.
Assumes no solute is lost, consumed, precipitated, or created during preparation.
Use appropriate calibrated equipment and a compatible diluent according to the protocol.
Prepare a 50 µM working solution from a stock labeled in mM
- 1Normalize concentration units: 10 mM × 1,000 = 10,000 µM. Both C₁ and C₂ now use µM.
- 2Rearrange the dilution equation for the transferred stock: V₁ = C₂ × V₂ ÷ C₁.
- 3Substitute the same-unit values: V₁ = 50 µM × 100 mL ÷ 10,000 µM = 0.5 mL. The concentration units cancel.
- 4Convert the transfer to a convenient pipetting unit: 0.5 mL × 1,000 = 500 µL. Check that this is within the equipment's specified operating range.
- 5Transfer the stock and use the compatible diluent to make up to 100 mL final volume, following the protocol. The nominal diluent difference is 100 − 0.5 = 99.5 mL; the final-volume mark is the preparation target.
- 6Check the dilution factor: 10,000 ÷ 50 = 200, and 100 ÷ 0.5 = 200. Independently, 10 mM × 0.0005 L = 0.005 mmol = 5 µmol, which in 0.1 L gives 50 µM.
Label the working solution with its actual concentration and units. Keep the original stock units in your notes alongside the normalized values so another person can check the prefix conversion and transfer.
- Entering C₁ = 10 and C₂ = 50 without converting mM to µM. The solver uses one common concentration unit and does not silently convert mismatched input labels.
- Adding 500 µL of stock to 100 mL of diluent. That makes about 100.5 mL total and gives about 49.75 µM under an additive-volume assumption, not the intended 50 µM.
- Changing the shared concentration-unit label without changing the numbers. Recalculate both numerical concentrations whenever you change their unit.
- Treating a 200-fold dilution as one part stock plus 200 parts diluent. It is one part stock in 200 parts final solution, nominally one plus 199.
- Mixing molar concentration with mg/mL or percent by mass as though only a prefix changed. Those conversions require the correct molar mass and, for some concentration definitions, density or other information.
- Rounding a very small transfer to whatever the pipette can measure. Choose a suitable method or a validated intermediate dilution instead.
Does the embedded solver convert mM and µM automatically?
No. This C₁V₁ = C₂V₂ solver uses one shared concentration unit. The example converts 10 mM to 10,000 µM first, then enters C₁ = 10,000 and C₂ = 50 with µM selected. Changing the label alone is not a numerical conversion.
Could I do the same calculation entirely in mM?
Yes. Convert 50 µM to 0.05 mM, keep the stock at 10 mM, and use V₁ = 0.05 × 100 ÷ 10 = 0.5 mL. Set the shared concentration unit to mM and change both numbers accordingly. The required stock volume is unchanged.
Should I add 99.5 mL or 100 mL of diluent?
The target is 100 mL of final solution including the 0.5 mL stock transfer. The nominal difference is 99.5 mL, but make up to the final volume with suitable equipment and the protocol's mixing procedure. Do not add the stock to an already measured 100 mL of diluent.
What does a 200-fold dilution mean here?
The stock is 200 times the target concentration: 10,000 µM ÷ 50 µM = 200. Stock therefore occupies 1/200 of the final volume, or 0.5%. For this 100 mL preparation, that is 0.5 mL stock and a nominal 99.5 mL diluent.
Can I use the same prefix conversion for a stock labeled mg/mL?
Not directly. mg/mL is mass per volume, whereas mM and µM are amount of substance per volume. Converting between them requires the solute's correct molar mass. Check the chemical form, hydration, purity, and protocol before treating the resulting molar concentration as a usable stock value.