Dilution calculator for C1V1 = C2V2, serial dilutions and stock solutions
This dilution calculator handles the four solution problems that come up every day in a chemistry, biology or clinical lab. The first mode solves the dilution equation C1V1 = C2V2 for whichever value you leave blank, and it is unit-aware: molar (M, mM, µM, nM), percent w/v, mg/mL, µg/mL, g/L, ppm, ppb and X-fold concentrations are accepted, with volumes in L, mL or µL. If the stock is molar and the target is in mg/mL, type the molar mass and the conversion is done for you.
The other modes plan a serial dilution (any factor and number of steps, with transfer and diluent volumes per tube), work out the mass to weigh for a stock made from a solid with a purity correction, and convert molarity to ppm and back. Each answer shows the formula with your numbers.
Nothing is uploaded; the arithmetic runs in your browser. The molar mass calculator supplies the g/mol figure when you do not know it.
How to use the Dilution Calculator
- Pick the mode: C1V1 = C2V2, Serial dilution, Stock from solid or Molarity ↔ ppm.
- For a simple dilution, enter three of stock concentration, stock volume, final concentration and final volume, choose the units, and leave the unknown blank.
- If the two concentrations use different unit families (molar vs mass), a molar mass box appears — fill it in.
- For a series, set the starting concentration, the factor (10 for 1:10), the number of steps and the volume in each tube to get a tube-by-tube table.
- Read the result and the working, then copy the table or the figures into your protocol.
Dilution Calculator features
Solve for any of the four values
Leave C1, V1, C2 or V2 blank; the calculator reports the answer, the diluent to add and the dilution factor, and refuses to "dilute up" a weak stock.
Eleven concentration units
M, mM, µM, nM, % w/v, mg/mL, µg/mL, g/L, ppm, ppb and X-fold, converted exactly within a family and via molar mass across families.
Serial dilution planner
Concentration, transfer volume, diluent volume and cumulative dilution for each tube, plus the total diluent you need.
Stock from solid
Mass to weigh for a target molarity or mass concentration and volume, with a purity correction.
Molarity ↔ ppm
Convert any concentration to ppm, mg/L, µg/mL, g/L or molar units and see the value in every other unit.
The dilution equation and a worked example
Diluting a solution changes its volume but not the amount of solute, so C1 × V1 = C2 × V2: the concentration and volume of the stock multiplied together equal the concentration and volume of the final solution. Any one of the four can be found from the other three. To make 250 mL of 1 M hydrochloric acid from a 10 M stock, V1 = C2 × V2 ÷ C1 = 1 × 250 ÷ 10 = 25 mL of stock made up to 250 mL with 225 mL of water (add acid to water, never the reverse).
The dilution factor is C1 ÷ C2 (or V2 ÷ V1), here 10, written 1:10. When both concentrations are in the same unit family the units cancel and no molar mass is needed; when one is molar and the other is a mass concentration the calculator uses mg/mL = mol/L × g/mol to put them on the same footing.
| Problem | Calculation | Answer |
|---|---|---|
| 250 mL of 1 M from 10 M | V1 = 1 × 250 ÷ 10 | 25 mL stock + 225 mL diluent |
| Final conc. of 5 mL of 2 M in 100 mL | C2 = 2 × 5 ÷ 100 | 0.1 M |
| 20 µL of 100 µM into 980 µL | C2 = 100 × 20 ÷ 1000 | 2 µM (1:50) |
Serial dilutions and stock solutions
A serial dilution repeats the same step so that each tube is a fixed factor weaker than the previous one. With 1 mL tubes and a 1:10 series you transfer 100 µL into 900 µL of diluent; after three steps the concentration is 1/1000 of the stock. The planner lists every tube and the total diluent to prepare. Mix each tube completely before transferring; the last tube keeps its full volume while the others lose the transferred amount.
Making a stock from a solid uses mass = C × V × M: 0.1 M sodium chloride in 250 mL needs 0.1 × 0.25 × 58.44 = 1.461 g. If the reagent is 95 % pure, divide by 0.95 and weigh 1.538 g. Dissolve in less than the final volume, then make up to the mark.
ppm, mg/L, percent and molarity
For dilute aqueous solutions 1 ppm equals 1 mg/L, which is 1 µg/mL, and 1 % w/v equals 10 g/L or 10,000 ppm. Converting between ppm and molarity needs the molar mass: ppm = M × g/mol × 1000, so 1 M NaCl is 58,440 ppm and 10 ppm is 1.71 × 10⁻⁴ M. These relationships assume a density of 1 g/mL, fine for most lab solutions but not for concentrated acids or syrups. See also the pH calculator for acid and base concentrations and the ratio calculator for mixing ratios.
Dilution Calculator FAQ
How do I use C1V1 = C2V2 to dilute a solution?
Multiply the final concentration by the final volume and divide by the stock concentration to get the stock volume you need. Then add diluent up to the final volume. The dilution calculator does this and tells you the diluent volume as well.
What does a 1:10 dilution mean?
One part stock in ten parts total (1 part stock plus 9 parts diluent), giving one tenth of the stock concentration. Some protocols write 1:10 to mean 1 plus 10; check which convention your lab uses.
Can I mix molar and mg/mL units?
Yes. When the stock and target are in different unit families the calculator asks for the molar mass and converts with mg/mL = mol/L × g/mol.
Why does the calculator say my stock is weaker than the target?
Dilution can only lower a concentration. If C2 is greater than C1 you need a stronger stock; the message stops you from getting a negative diluent volume.
How much powder do I weigh for a stock solution?
Use Stock from solid: grams = molarity × litres × molar mass, divided by purity. For 500 mL of 0.5 M glucose (180.16 g/mol) that is 45.04 g.
Is ppm the same as mg/L?
For water-based solutions, yes: 1 ppm by mass is 1 mg of solute per litre, because a litre weighs about 1 kg. It is also 1 µg/mL.