Dilution Calculator
C₁V₁ = C₂V₂ solved for stock volume, final concentration, stock concentration or final volume, with the solvent to add and the dilution factor.
Dilution Calculator: with the default inputs, stock volume v₁ is 10 mL.
Any unit — M, mM, %, mg/mL, ×. Both concentrations must use the same unit.
Not used when solving for V₁.
Same unit as the stock concentration.
Total volume after dilution. Not used when solving for V₂.
- Solved for
- V₁ = 10 mL
- Solvent to add (V₂ − V₁)
- 90 mL
- Final concentration C₂
- 1
- Stock concentration C₁
- 10
- Final volume V₂
- 100 mL
- Dilution factor (C₁ ÷ C₂)
- 10A factor of 10 is a 1:10 dilution — 1 part stock in 10 parts total.
Assumptions
- Volumes are additive (a good approximation for dilute aqueous solutions).
- The solute does not react with or precipitate from the solvent.
- Both concentrations are in the same unit.
| Final volume | Stock to take(mL) | Solvent to add(mL) |
|---|---|---|
| 10 mL | 1 mL | 9 mL |
| 25 mL | 2.5 mL | 22.5 mL |
| 50 mL | 5 mL | 45 mL |
| 100 mL | 10 mL | 90 mL |
| 250 mL | 25 mL | 225 mL |
| 500 mL | 50 mL | 450 mL |
| 1 L | 100 mL | 900 mL |
Add the stock to the flask first, then make up to the final volume with solvent — do not add the listed solvent volume to the listed stock volume, because mixing changes the total slightly. For concentrated acids, always add acid to water.
How this is worked out
The formula
C₁ × V₁ = C₂ × V₂ C₁ = stock (starting) concentration V₁ = volume of stock to use C₂ = final (target) concentration V₂ = final total volume Solvent to add = V₂ − V₁ Dilution factor = C₁ ÷ C₂ = V₂ ÷ V₁
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Solve for
- Choose one of 4 options.Stock volume needed (V₁) · Final concentration (C₂) · Stock concentration (C₁) · Final volume (V₂)
- Stock concentration (C₁)
- Any unit — M, mM, %, mg/mL, ×. Both concentrations must use the same unit.0 or more · defaults to 10
- Stock volume (V₁)
- Not used when solving for V₁.in mL, L, fl oz, cup, gal · 0 or more · defaults to 10
- Final concentration (C₂)
- Same unit as the stock concentration.0 or more · defaults to 1
- Final volume (V₂)
- Total volume after dilution. Not used when solving for V₂.in mL, L, fl oz, cup, gal · 0 or more · defaults to 100
What you get back
- Stock volume V₁main answer
- Solved for
- Solvent to add (V₂ − V₁)
- Final concentration C₂
- Stock concentration C₁
- Final volume V₂
- Dilution factor (C₁ ÷ C₂)
- A factor of 10 is a 1:10 dilution — 1 part stock in 10 parts total.
What this assumes
- Volumes are additive (a good approximation for dilute aqueous solutions).
- The solute does not react with or precipitate from the solvent.
- Both concentrations are in the same unit.
About this calculator
Diluting a solution doesn't change the amount of solute in it — only the volume it is spread through. That single fact is the whole dilution equation: C₁V₁ = C₂V₂. Concentration times volume is the amount of solute, and it is the same before and after. Enter any three of the four quantities and the calculator gives the fourth, plus the two numbers you actually need at the bench: how much stock to measure out and how much solvent to add.
How to use it
Concentrations can be in any unit — molar, millimolar, percent, mg/mL, or "×" for buffer stocks — as long as both use the same one. Volumes take mL by default and convert from L or other units. The usual question is "how much stock do I need?", so Stock volume (V₁) is the default; switch Solve for to check what concentration you made, what a stock must be, or how far a stock stretches.
Reading the results
- Stock volume V₁ is what you pipette. Solvent to add is V₂ − V₁, which is not the same as V₂ — a common slip that makes solutions too weak.
- Dilution factor is C₁ ÷ C₂. A factor of 10 is a "1:10" or "10×" dilution: one part stock brought to ten parts total (nine parts solvent). Note that some fields write 1:10 to mean one part stock plus ten parts solvent — check which convention your protocol uses.
Serial dilutions
When the factor is large — a 10,000× dilution of a stock into a 1 mL final volume needs 0.1 µL of stock, far below what a pipette can deliver accurately — do it in steps. Two successive 1:100 dilutions (10 µL into 1 mL, twice) reach the same 1:10,000 with volumes you can measure. The factors multiply: three 1:10 steps make 1:1,000. Serial dilutions also produce a concentration series for standard curves and for counting bacteria by plating. The calculator warns when V₁ falls under 1 µL.
Common mistakes
- Adding V₂ of solvent instead of V₂ − V₁.
- Mixing units between C₁ and C₂ (mM stock, M target).
- Trying to reach a concentration higher than the stock; the calculator refuses, because dilution only goes down.
- Assuming volumes add perfectly. Mixing ethanol and water, for example, gives slightly less than the sum; for exact work, dilute to the mark in a volumetric flask rather than adding a computed volume of solvent.
Frequently asked questions
▸What is the dilution formula?
C₁V₁ = C₂V₂: stock concentration times stock volume equals final concentration times final volume. It works because the amount of solute (concentration × volume) is unchanged by adding solvent.
▸How do I make a 1:10 dilution?
Combine one part stock with nine parts solvent, so the stock is one-tenth of the total. For 100 mL, that is 10 mL stock plus 90 mL solvent. (Some protocols write 1:10 to mean 1 part in 10 parts solvent — check.)
▸How much water do I add?
The final volume minus the stock volume, V₂ − V₁. To make 100 mL of 1 M from 10 M you take 10 mL of stock and add 90 mL of water, not 100.
▸What is a serial dilution?
A chain of dilutions where each step starts from the previous one. Factors multiply, so three 1:10 steps give 1:1,000. It is used when the overall factor is too large to pipette accurately in one step, and to make a concentration series.
▸Can I use this for percent or mg/mL concentrations?
Yes. Any concentration unit works as long as the stock and target use the same one, because the units cancel in the ratio. The volumes must also share a unit, which the calculator handles.
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