Dilution Calculator (C1V1 = C2V2) & Serial Dilutions
C₁V₁ = C₂V₂, mixing, serial dilutions and dilution ratios — with the volumes to pipette.
Dilution table
At the bench
How it was worked out
About the Dilution Calculator (C1V1 = C2V2) & Serial Dilutions
Work out any dilution with C₁V₁ = C₂V₂: how much stock to measure, the final volume, or the concentration you end up with. Concentrations can be molar (M to pM), mass per volume (g/L, mg/mL, µg/mL, % w/v), percent and ppm, “×” buffer strengths (10× to 1×) or counts such as cells per mL — and molar and mass units can be mixed when you give the molar mass.
Three more modes cover the rest of the bench: mix two solutions of the same solute to hit a target concentration, plan a serial dilution for tubes or a 96-well plate row (transfer and diluent volumes and the concentration in every tube), or make a set of standards directly from one stock — and dilution ratios such as 1:64 for cleaning concentrates, in gallons and fluid ounces too. Every answer comes with the working and the steps to follow at the bench.
How to use it
- Choose a mode: C₁V₁ = C₂V₂, Mix two solutions, Serial dilution or Ratio (1:X).
- For C₁V₁ = C₂V₂, pick what to solve for, then type the other three values with their units (type the molar mass only if you mix molar and mass units).
- For a serial dilution, type the stock concentration, the fold per step, the number of steps and one of the per-step volumes; tick “first tube holds the undiluted stock” for plate layouts that start at the top concentration.
- Read the answer and the steps to follow; copy them, or download the dilution table as CSV.
Examples
0.850 L of 5.00 M Cu(NO₃)₂ diluted to 1.80 L
C₂ = 2.36 M
OpenStax Chemistry 2e Example 3.19.
5.00 L of 0.100 M KOH from 1.59 M stock
V₁ = 0.314 L (314 mL), plus 4.686 L of water
OpenStax Example 3.21.
11 mL of 0.45 M HBr diluted to 0.12 M
V₂ = 41 mL
OpenStax Example 3.20.
1 mg/mL stock of a 66.5 kDa protein, 1 mL at 10 µM
V₁ = 665 µL of stock + 335 µL of buffer
500 mL of 1× from a 10× stock
50 mL of 10× + 450 mL of water
1 mM stock, 6 tubes, 900 µL left in each
100 µL into 900 µL each: 100 µM, 10 µM … 1 nM
100 µg/mL in A1, two-fold to A12, 100 µL per well
A1 gets 200 µL of stock; A12 is 48.83 ng/mL
1:64 (1 part + 64 parts water), 1 US gallon
1.969 US fl oz of concentrate + 126 US fl oz of water
Common uses
- Making working solutions and buffers from concentrated stocks in the lab.
- Standard curves: serial or direct dilutions with the concentration of every standard.
- Dose–response and MIC plates: two-fold or three-fold series across a 96-well plate row.
- Cell culture: diluting a counted cell suspension to the seeding density.
- Chemistry homework on dilution, with every step shown.
- Diluting cleaning, garden or photographic concentrates by a label ratio.
The dilution equation
Adding solvent changes the volume but not the amount of solute, so concentration × volume is the same before and after: C₁V₁ = C₂V₂, where 1 is the stock and 2 the diluted solution (OpenStax Chemistry 2e §3.3). It works in any units as long as both concentrations are in the same kind of unit and both volumes in volume units.
- Dilution factor = C₁ ÷ C₂ = V₂ ÷ V₁. A 10-fold dilution is 1 part stock in 10 parts in total.
- Diluent to add = V₂ − V₁.
- Mixing two solutions of the same solute: C = (C_A·V_A + C_B·V_B) ÷ (V_A + V_B); to reach a target C in a total volume V, use V_A = V·(C − C_B) ÷ (C_A − C_B). Use C_B = 0 for pure diluent.
Serial dilutions
In a serial dilution each tube is made from the one before: transfer a volume T into a volume D of diluent, mix, and pass T on to the next tube. Every step dilutes by F = (T + D) ÷ T, so tube n holds C₀ ÷ Fⁿ. A ten-fold series uses 100 µL into 900 µL; a two-fold series uses equal volumes, such as 100 µL into 100 µL.
- Mix each tube or well thoroughly before the next transfer, and change tips between steps — carry-over is the commonest source of error.
- The last tube ends up with T more than the others; remove T from it if every tube must hold the same volume.
- Small errors multiply along a series. For the best accuracy, make each standard directly from the stock (the Direct from stock scheme) where the volumes allow it.
What “1:10” means
Dilution ratios are written two ways. In most lab protocols a “1:10 dilution” means 1 part in 10 parts in total (1 part sample + 9 parts diluent, a dilution factor of 10). Many product labels and some textbooks instead mean 1 part concentrate + 10 parts water (11 parts in total). For large ratios the difference is small (1:64 is 1.97 or 2.00 fluid ounces per gallon), but for small ones it matters (1:1 is a half-strength mix or a full-strength one). The serial mode reads “1:10” as a factor of 10; the ratio mode lets you choose either reading.
Units that can be mixed
- Units of the same kind always convert: M, mM, µM, nM, pM; g/L, mg/mL, µg/mL, % w/v (1 % w/v = 10 g/L); %, ppm, ppb.
- Molar and mass units convert when you give the molar mass: g/L = mol/L × g/mol (for proteins, 1 kDa = 1,000 g/mol).
- Percent and ppm convert to mass per volume only for dilute aqueous solutions, assuming a density of 1 g/mL (1 ppm ≈ 1 mg/L); the result says when this was used.
- “×” strengths and counts per volume (cells, copies, units per mL) cannot be converted into other kinds.
Sources
- OpenStax, Chemistry 2e, §3.3 Molarity: the dilution equation C₁V₁ = C₂V₂ and worked Examples 3.19–3.21.
- NIST Special Publication 811 (2008), Appendix B.8: US gallon = 3.785 411 784 L and imperial gallon = 4.546 09 L (exact); fluid ounces are 1/128 and 1/160 of them.
Limitations
- Mixing assumes volumes add. That is true for dilute aqueous solutions, but not exactly for some mixtures (ethanol and water shrink slightly) — for exact work, make up to the mark in a volumetric flask.
- Percent by mass (w/w) strictly needs the solution densities; treating it like a volume ratio is a good approximation only for dilute solutions.
- The calculator does not check solubility, stability or pipette ranges beyond warning about volumes below 1 µL.
- A serial dilution multiplies pipetting errors along the series; the concentrations shown are the nominal ones.
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Frequently asked questions
How do I use C1V1 = C2V2?
Put in the three values you know and solve for the fourth. To make 100 mL of 0.1 M from a 1 M stock: V₁ = C₂V₂ ÷ C₁ = 0.1 × 100 ÷ 1 = 10 mL of stock, made up to 100 mL with 90 mL of diluent.
What is the difference between C1V1 = C2V2 and M1V1 = M2V2?
None — M₁V₁ = M₂V₂ is the same equation written for molarity. C₁V₁ = C₂V₂ works for any concentration unit, provided C₁ and C₂ use the same one.
How do I calculate a dilution factor?
Divide the final volume by the volume of stock (or the stock concentration by the final concentration). 1 mL of stock made up to 50 mL is a dilution factor of 50 (1:50). In a serial dilution the factors multiply: three 1:10 steps make 1:1,000.
How do I make a 1:10 serial dilution?
Put 900 µL of diluent into each tube, add 100 µL of the stock to the first tube and mix, then move 100 µL from that tube to the next, and so on. Each tube is ten times weaker than the one before.
How do I dilute a 10× buffer to 1×?
Use one part of the 10× stock in ten parts in total: for 500 mL, 50 mL of 10× buffer plus 450 mL of water. Choose the “×” unit for both concentrations to have it calculated.
Can I mix mg/mL and µM?
Yes, if you type the molar mass of the solute: the calculator converts with g/L = mol/L × molar mass. Without the molar mass, molar and mass units cannot be compared.
Why is my final volume not exactly V₁ + diluent?
Volumes of different liquids do not always add exactly, so careful lab work adds the stock to a volumetric flask and fills to the mark rather than measuring the diluent separately. For dilute aqueous solutions the difference is negligible.