How to Prepare a Working Solution from a Stock

A working solution is the dilute, ready-to-use concentration you actually run an experiment with, made by diluting a concentrated stock. Preparing one is a single equation — C1V1 = C2V2 — solved for the volume of stock to withdraw, then topped up with diluent to the final volume. This guide gives the full workflow from stock to bench, a dilution-factor ready-reckoner so you can read off the volumes, per-compound worked examples with real numbers, and the ratio↔factor↔percent crosswalk that ties the different ways of describing a dilution together. The dilution calculator solves any direction and reports the stock and diluent volumes; the C1V1 calculator does the same with mixed units.

What is the difference between a stock and a working solution?

The stock is concentrated and stored — 1 M Tris, 10x buffer, 1000 ppm standard. The working solution is the dilute concentration you use at the bench — 1x buffer, 10 mM Tris, 50 ppm standard. You keep a concentrated stock because it is stable, takes little space, and lets you make many different working strengths from one preparation. The act of going from stock to working solution is a dilution, and every dilution is governed by the same relationship: the amount of solute you take from the stock equals the amount in the final solution.

The C1V1 = C2V2 workflow, step by step

Identify what you know. Stock concentration C1, target working concentration C2, and target final volume V2.
Solve for the stock volume: V1 = (C2 × V2) / C1.
Calculate the diluent: V_diluent = V2 − V1.
Pipette V1 of stock into a clean vessel.
Add diluent to bring the total to V2 (or add V_diluent if volumes are additive).
Mix thoroughly — an unmixed dilution has a concentration gradient.
Label with the working concentration, date, and contents.

For the everyday case — make 50 mL of 1.0 M from a 2.0 M stock:

V1 = (1.0 × 50) / 2.0 = 25 mL of stock
V_diluent = 50 − 25 = 25 mL
This is a 1:2 dilution (DF = 2)

How much stock do I need? A dilution-factor ready-reckoner

The dilution factor (DF) is C1 / C2, and the stock volume is always final volume ÷ DF. For a 10 mL working solution:

Stock → working	DF (1:n)	Stock for 10 mL	Diluent for 10 mL
10x → 1x	10	1.0 mL	9.0 mL
5x → 1x	5	2.0 mL	8.0 mL
1 M → 100 mM	10	1.0 mL	9.0 mL
1 M → 10 mM	100	0.1 mL (100 µL)	9.9 mL
1000 ppm → 50 ppm	20	0.5 mL	9.5 mL
10% → 5%	2	5.0 mL	5.0 mL

Scale linearly for other final volumes. If a single step would need you to pipette under ~2 µL, the measurement is unreliable — split it into a serial dilution where the factors multiply.

The ratio ↔ dilution factor ↔ percent crosswalk

The same dilution is described three interchangeable ways. “How much stock” questions usually come in one of these forms:

Ratio (1:n)	Dilution factor	Stock as % of final	Stock for 10 mL
1:2	2	50%	5.0 mL
1:10	10	10%	1.0 mL
1:20	20	5%	0.5 mL
1:100	100	1%	0.1 mL

The rule: fold-concentration = dilution factor = n in 1:n, and the stock fraction of the final volume is 1/DF. A “10x stock used at 1x” is a 1:10 dilution, DF 10, 10% stock. The C1V1 guide derives all of this from the equation.

Worked example 1: 1 M NaOH in 100 mL from a 5 M stock

C1 = 5 M, C2 = 1 M, V2 = 100 mL
V1 = (1 × 100) / 5 = 20 mL of the 5 M stock
V_diluent = 100 − 20 = 80 mL of water
DF = 5 / 1 = 5 (a 1:5 dilution)

Pipette 20 mL of the 5 M NaOH and bring to 100 mL. If you need to make the 5 M stock itself first, weigh the solid using how to make a stock solution.

Worked example 2: 1 M acetic acid in 100 mL from glacial acetic acid

Glacial acetic acid is ~17.4 M. To make 100 mL of 1 M:

C1 = 17.4 M, C2 = 1 M, V2 = 100 mL
V1 = (1 × 100) / 17.4 = 5.75 mL of glacial acetic acid
V_diluent = 100 − 5.75 = 94.25 mL of water
DF ≈ 17.4 (about a 1:17 dilution)

Add the acid to the water, not water to the acid, and expect a slight volume change on mixing — bring to the final volume rather than summing the two.

When to use a serial dilution instead

If the dilution factor is large (1:1000 or more) or you need a range of concentrations, a single step forces an impractically small transfer. A serial dilution chains smaller steps whose factors multiply: three 1:10 steps give an overall 1:1000. This is the standard route for a dose-response series, an MIC assay, or a standard curve, and it is covered in full in how to make a serial dilution. The rule for combining steps is simply DF_total = DF1 × DF2 × …

Common mistakes and troubleshooting

Adding stock to the full diluent volume. V2 is the total; pipette V1 of stock then bring up to V2, or add V2 − V1 of diluent.
Mixing concentration units. C1 and C2 must both be molar, or both %, or both ppm — convert first.
Not mixing after dilution. The result is a gradient, not a uniform working solution.
Pipetting too small a volume. Below ~2 µL, use a serial dilution.
Contaminating the stock. Never pipette back into the stock bottle; withdraw an aliquot and discard the surplus. Working solutions are often less stable than stocks, so make them fresh and store the stock instead.
Using % when the protocol needs M. They are not interchangeable without the molecular weight; convert via the ppm guide or the molarity calculator.

If the working concentration comes out higher than the stock, or the stock volume exceeds the final volume, a term has been swapped between the two sides of the equation.

Where does this fit in the wider workflow?

Preparing a working solution is the second half of the stock workflow: you make and store the concentrated stock with the stock solution calculator, then dilute it to working strength here with the dilution calculator or the C1V1 calculator. Large factors go through the serial dilution calculator. The underlying single-step math is in how to calculate a dilution, and all of these tools live in the laboratory calculators collection.