Free Dilution Calculator
This dilution calculator solves the classic dilution equation C₁V₁ = C₂V₂ for any single unknown. Enter any three of the four quantities — initial (stock) concentration C₁, initial volume V₁, final (diluted) concentration C₂ and final volume V₂ — and the calculator finds the missing value, then tells you how much stock to take and how much solvent to add. It is the everyday tool chemists, biologists and lab technicians use to dilute a concentrated stock solution down to a working concentration without re-deriving the algebra each time.
Enter any three values — leave one blank to solve it with C₁V₁ = C₂V₂.
C₁V₁ = C₂V₂ · Keep concentration units (e.g. M) the same on both sides and volume units (e.g. mL) the same on both sides.
Quick answer
To dilute a solution, use the dilution equation C₁V₁ = C₂V₂, where C₁ and V₁ are the concentration and volume of the concentrated stock and C₂ and V₂ are the concentration and volume of the final diluted solution. Rearrange to solve for the unknown — for example, the stock volume needed is V₁ = C₂V₂ / C₁. Diluting a 1 M stock to 0.1 M in a 100 mL final volume needs V₁ = (0.1 × 100) / 1 = 10 mL of stock topped up with 90 mL of solvent.
Formula & method
C₁V₁ = C₂V₂
- C₁ — Initial (stock) concentration, e.g. in molarity (M)
- V₁ — Volume of stock solution to take (e.g. mL)
- C₂ — Final (diluted) concentration, in the same unit as C₁
- V₂ — Final total volume of the diluted solution (same unit as V₁)
C₁ = initial (stock) concentration, V₁ = initial volume of stock used, C₂ = final (diluted) concentration, V₂ = final total volume. Rearrange for any unknown: V₁ = C₂V₂/C₁, C₂ = C₁V₁/V₂, V₂ = C₁V₁/C₂, C₁ = C₂V₂/V₁.
Examples
- Input
- C₁ = 1 M, C₂ = 0.1 M, V₂ = 100 mL (find V₁)
- Result
- V₁ = 10 mL
- Why
- Rearrange C₁V₁ = C₂V₂ to V₁ = C₂V₂ / C₁ = (0.1 × 100) / 1 = 10 / 1 = 10 mL. Measure 10 mL of the 1 M stock and add 90 mL of solvent to reach a 100 mL final volume at 0.1 M — a 10-fold dilution.
- Input
- C₁ = 2 M, C₂ = 0.5 M, V₂ = 250 mL (find V₁)
- Result
- V₁ = 62.5 mL
- Why
- V₁ = C₂V₂ / C₁ = (0.5 × 250) / 2 = 125 / 2 = 62.5 mL. Take 62.5 mL of the 2 M stock and add 187.5 mL of solvent to make 250 mL of 0.5 M solution.
- Input
- C₁ = 10 M, V₁ = 5 mL, V₂ = 500 mL (find C₂)
- Result
- C₂ = 0.1 M
- Why
- C₂ = C₁V₁ / V₂ = (10 × 5) / 500 = 50 / 500 = 0.1 M. Diluting 5 mL of a 10 M stock up to 500 mL gives a 0.1 M working solution — a 100-fold dilution.
- Input
- V₁ = 25 mL, C₂ = 0.2 M, V₂ = 1000 mL (find C₁)
- Result
- C₁ = 8 M
- Why
- C₁ = C₂V₂ / V₁ = (0.2 × 1000) / 25 = 200 / 25 = 8 M. If 25 mL of stock diluted to 1000 mL produced 0.2 M, the original stock must have been 8 M.
When to use this tool
- Preparing a working solution by diluting a concentrated stock to a known target molarity in the lab.
- Figuring out how many millilitres of stock to pipette to hit a specific final concentration and final volume.
- Back-calculating the concentration of a stock when you know how it was diluted and the resulting concentration.
- Planning buffer, reagent or standard preparations where you must conserve solute amount across the dilution.
Common mistakes
- Mixing concentration units between the two sides. C₁ and C₂ must be in the same unit (both M, both mg/mL, etc.). If your stock is in % and your target is in M, convert first — the equation only balances when units match.
- Confusing V₁ (the volume of stock you take) with the volume of solvent you add. The solvent to add is V₂ − V₁, not V₁ itself. For a 10 mL stock diluted to 100 mL, you add 90 mL of solvent, not 100 mL.
- Adding the stock to a fixed volume of solvent instead of topping up to the final volume. Always bring the mixture up to V₂ in a volumetric flask or graduated container, because mixing can change the total volume slightly.
- Forgetting that C₁V₁ = C₂V₂ assumes ideal mixing where total amount of solute is conserved and volumes are additive. It does not account for serial dilutions, density changes in very concentrated solutions, or temperature-dependent volume changes.
Frequently asked questions
What is the C1V1 = C2V2 formula used for?
C₁V₁ = C₂V₂ is the dilution equation. It states that the amount of solute (concentration × volume) is conserved when you dilute a solution: the moles in the stock you take (C₁V₁) equal the moles in the final diluted solution (C₂V₂). You use it to find how much concentrated stock and solvent are needed to reach a desired concentration and volume.
How do I calculate how much stock solution I need?
Rearrange the dilution equation to V₁ = C₂V₂ / C₁. Multiply the final concentration you want by the final volume, then divide by the stock concentration. For example, to make 100 mL of 0.1 M from a 1 M stock: V₁ = (0.1 × 100) / 1 = 10 mL of stock, topped up with 90 mL of solvent.
Do C1 and C2 have to be in molarity?
No. The dilution equation works with any concentration unit — molarity (M), mass/volume (mg/mL), percent, or X-fold — as long as C₁ and C₂ use the same unit. Likewise V₁ and V₂ must share a unit. This calculator labels the inputs in M and mL, but the same numbers apply to any consistent unit pair.
What is the difference between V1 and the amount of solvent to add?
V₁ is the volume of concentrated stock you measure out. The solvent (diluent) you add to reach the final volume is V₂ − V₁. So to make 100 mL of diluted solution from 10 mL of stock, you add 90 mL of solvent. The calculator shows both the stock volume and the solvent to add.
What does a 1:10 dilution mean and how does it relate to this formula?
A 1:10 (or 10-fold) dilution means the final concentration is one-tenth of the stock, i.e. C₂ = C₁ / 10. In terms of volumes, you take 1 part stock and bring it to 10 parts total — for example 10 mL of stock topped up to 100 mL. That matches C₁V₁ = C₂V₂ with V₂/V₁ = C₁/C₂ = 10.
Can I use this for serial dilutions?
Each step of a serial dilution is a single C₁V₁ = C₂V₂ calculation, so you can use this tool one stage at a time. For a serial dilution, the diluted concentration C₂ from one step becomes the stock C₁ for the next step. Run the calculator once per dilution step, carrying the output concentration forward.
Sources & references
- Dilution (equation) - Wikipedia
- Solution Dilution - Concentration and Molarity | Chemistry LibreTexts
- Molarity and dilutions | Khan Academy
External references open in a new tab. We are independent and not affiliated with these organizations.
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