Dilution Calculator
Solve C₁V₁ = C₂V₂ for any one value and get plain preparation instructions, or plan a serial dilution tube by tube. Works in molar, mass-per-volume, percent and × units.
How to Use
- Choose what to solve for. Most often it is the stock volume: how much of the concentrated stock to measure out.
- Enter the other three values. Concentrations can be in M, mM, µM, nM, g/L, mg/mL, µg/mL, % w/v or × (as in a 10× buffer); C₁ and C₂ must be the same kind.
- Read the answer, the dilution factor and the water to add, and follow the preparation instructions under the buttons.
- For a series of tubes, choose Serial dilution and enter the stock, the dilution factor per step, the number of steps and the volume in each tube.
- The picture shows the stock and the flask (or the row of tubes); Show Work has every step.
Worked Example
100 mL of 0.500 M from a 2.00 M stock. V₁ = C₂V₂ ÷ C₁ = 0.500 × 100 ÷ 2.00 = 25.0 mL. Measure 25.0 mL of the stock into a 100 mL volumetric flask and add water to the mark, about 75.0 mL. The dilution factor is 2.00 ÷ 0.500 = 4.
A serial dilution. To go from a 1 mg/mL standard to 1 ng/mL is a factor of 1,000,000. In one step that would mean 1 µL in 1 L. Instead, six ×10 steps with 1 mL tubes: 900 µL of diluent in each, 100 µL moved along each time, giving 100 µg/mL, 10 µg/mL, 1 µg/mL, 100 ng/mL, 10 ng/mL and 1 ng/mL.
The common mistake: adding V₂ of water. Adding 100 mL of water to the 25.0 mL of 2.00 M stock gives 125 mL, so the concentration is 2.00 × 25.0 ÷ 125 = 0.400 M instead of 0.500 M, 20% too weak. V₂ is the total volume: fill up to 100 mL, not by 100 mL.
Show Work
Formulas
Volumetric Glassware and Mass per Volume
Measuring solutions by volume grew up with titration. Joseph Louis Gay-Lussac gave the burette and the pipette their names in 1824, and Karl Friedrich Mohr’s 1855 textbook on titration made volumetric analysis a standard laboratory method. The volumetric flask, filled to a single etched mark, is the reason dilution recipes speak of making up to a final volume rather than adding a volume of water.
Percent concentrations come in three kinds that are easy to mix up: % w/v is grams of solute per 100 mL of solution (1% w/v = 10 g/L), % w/w is grams per 100 g of solution, and % v/v is millilitres per 100 mL. C₁V₁ = C₂V₂ holds for each, as long as both concentrations are the same kind.
About This Calculator
This calculator solves C₁V₁ = C₂V₂ for whichever value you choose, refuses impossible requests such as diluting to a higher concentration, and writes out the preparation: how much stock to take and what total volume to make it up to. Serial mode lists every tube with its concentration and total dilution, and the transfer and diluent volumes for each step.
Concentrations can be molar (M, mM, µM, nM), mass per volume (g/L, mg/mL, µg/mL, mg/L, ng/mL), % w/v or fold strength (×); volumes can be in litres, millilitres or microlitres. Everything runs in your browser; nothing is sent anywhere.
Related tools: Molarity Calculator, pH Calculator, and Molar Mass Calculator.
Frequently Asked Questions
What does C₁V₁ = C₂V₂ mean?
Diluting adds solvent but not solute, so concentration × volume is the same before and after. To make 250 mL of 150 mM saline from a 1 M stock, V₁ = 150 mM × 250 mL ÷ 1,000 mM = 37.5 mL. Any units work as long as both concentrations use the same kind and both volumes the same unit.
Do I add V₂ of water to the stock?
No. V₂ is the final total volume. For 0.500 M from 2.00 M, take 25.0 mL of stock and add water up to 100.0 mL, about 75.0 mL. Adding a full 100 mL of water gives 125 mL at 0.400 M, 20% too weak. A volumetric flask filled to the mark avoids the problem.
What is a dilution factor, and what does 1:10 mean?
The dilution factor is C₁ ÷ C₂, which equals V₂ ÷ V₁. Going from 2.00 M to 0.500 M is a factor of 4. In chemistry and biology 1:10 usually means 1 part in 10 parts total (1 mL of sample plus 9 mL of diluent), which is a dilution factor of 10; this calculator uses that meaning. Some fields write 1:9 for the same thing, so check which is meant.
How do I do a serial dilution?
Repeat the same small dilution in a row of tubes. For ×10 steps with 1 mL in each tube, put 900 µL of diluent in each tube, move 100 µL of stock into the first and mix, then 100 µL of that into the next. Six steps take 1 mg/mL down to 1 ng/mL, a total dilution of 1,000,000, with far less error than one huge dilution.
Can I use percentages or mass per volume?
Yes, C₁V₁ = C₂V₂ works for any concentration unit. 1% w/v is 1 g per 100 mL, or 10 g/L: making 100 mL of 1% from a 5% w/v stock takes 20.0 mL. You cannot mix a molar unit with a mass unit without the molar mass, and % w/w needs the solution’s density. For % v/v, such as ethanol, the answer is close but not exact, because ethanol and water shrink slightly on mixing.
How do I use the Dilution Calculator?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Working solutions
100 mL of 0.500 M from a 2.00 M stock: 25.0 mL of stock made up to 100.0 mL.
Buffers
500 mL of 1× from a 10× buffer: 50.0 mL of the concentrate and 450.0 mL of water.
Saline
250 mL of 150 mM NaCl from a 1 M stock takes 37.5 mL.
Concentrated acid
5.0 mL of 12 M HCl made up to 250 mL gives 0.24 M. Always add the acid to the water.
Standard curves
Six ×10 steps take a 1 mg/mL standard to 1 ng/mL, with 100 µL moved into 900 µL each time.
Doubling dilutions
Eight ×2 steps from 100 µM end at 390.625 nM, a total dilution of 1 : 256.
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