Stock to Working Solution Dilution Calculator (C₁V₁ = C₂V₂ with Unit Conversion)
Work out how much stock solution and diluent to mix for a working solution: solve C₁V₁ = C₂V₂ for any value, mix M, mM, µM, nM, mg/mL, µg/mL, % and X units, convert between molar and mass units with the molar mass, and get a pipetting table for common volumes.
How it works
C₁ × V₁ = C₂ × V₂ · V₁ = C₂ × V₂ ÷ C₁ · V₂ = C₁ × V₁ ÷ C₂ · C₂ = C₁ × V₁ ÷ V₂ · Diluent = V₂ − V₁ · Dilution factor = C₁ ÷ C₂ = V₂ ÷ V₁ · Molar to mass: g/L = mol/L × molar mass
Diluting a stock adds solvent but no solute, so the amount of solute you pipette out (C₁ × V₁) equals the amount in the finished working solution (C₂ × V₂). Give any three of the four values and the calculator solves for the fourth, then subtracts the stock volume from the final volume to get the diluent to add. Both concentrations must be in the same unit before they go into the equation. Choose “Any unit” when they already are (for example both in mg/mL), or pick real units and the calculator converts within a family: M, mM, µM, nM and pM step by 1,000; g/L equals mg/mL, 1 µg/mL is 1 mg/L, and 1% w/v is 10 g/L. To go between a molar unit and a mass unit, enter the solute’s molar mass, since g/L = mol/L × g/mol. X concentrations (10X, 50X buffers) only dilute to other X values. The dilution factor C₁ ÷ C₂ is also V₂ ÷ V₁. A 1:10 dilution means 1 part stock in 10 parts total, which is 1 part stock plus 9 parts diluent; the stock : diluent ratio is shown separately so the two notations are not confused. The equation assumes volumes add up, which holds for dilute aqueous solutions; for concentrated acids, alcohols or salt solutions, make up to the final volume in a volumetric flask instead of adding the two volumes.
Worked example
With the default inputs (stock 10, working 1, same unit, 100 mL final): V₁ = 1 × 100 ÷ 10 = 10 mL of stock, topped up with 100 − 10 = 90 mL of diluent. The dilution factor is 10× (1:10), which is 1 part stock to 9 parts diluent. With units: to make 50 mL of 100 µM from a 10 mM stock, 100 µM = 0.1 mM, so V₁ = 0.1 × 50 ÷ 10 = 0.5 mL (500 µL) of stock plus 49.5 mL of diluent, a 100-fold dilution.
Sources: Hello Bio: Dilution calculator (C₁V₁ = C₂V₂, 10 mM to 100 µM example) · Leinco: Antibody working-solution dilution calculator (10 mM to 50 µM example) · Calculate.co.nz: Dilution calculator C1V1 = C2V2 (solve for any value)
Frequently asked questions
How do I dilute a 10X stock to 1X?
Use one part of the 10X stock for every ten parts of final volume: for 1 L of 1X buffer, take 100 mL of 10X stock and add 900 mL of water. For a 50X stock (such as TAE), use 20 mL per litre plus 980 mL of water.
Can the stock and working concentrations be in different units?
Yes, as long as they can be converted. Molar units (M, mM, µM, nM) convert among themselves, and mass units (g/L, mg/mL, µg/mL, % w/v) convert among themselves. To go from molar to mass units, enter the molar mass of the solute. A 10 mM stock to a 100 µM working solution, for example, is a 100-fold dilution.
What is the difference between a 1:10 dilution and a 1:10 ratio?
In dilution notation, 1:10 usually means 1 part stock in 10 parts total (1 part stock + 9 parts diluent), a dilution factor of 10. Some recipes write mixing ratios as stock : diluent, where 1:10 means 1 part stock plus 10 parts diluent, a factor of 11. This calculator shows both: the dilution factor and the stock : diluent ratio.
The stock volume is too small to pipette. What should I do?
Make an intermediate dilution. For example, to make 1 nM from a 1 mM stock in 10 mL, the direct route needs 0.01 µL. Instead dilute the stock 1:1,000 to 1 µM first (1 µL in 1 mL), then take 10 µL of that and make it up to 10 mL.
Should I add stock to diluent or the other way round?
For most solutions it does not matter: pipette the stock and bring it up to the final volume with diluent, then mix. For concentrated acids, always add the acid slowly to water to control the heat released.
Why does C₁V₁ = C₂V₂ work?
The amount of solute does not change when you add solvent. Concentration × volume is the amount of solute, so the amount you take from the stock equals the amount in the diluted solution.
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Educational estimate. Check the units, the protocol and your lab’s safety rules before preparing any solution.