What this calculator does
Work out how much stock solution to use, and how much liquid to add, to get the strength you need. Diluting adds solvent (the liquid, often water) but no solute (the dissolved substance). So the solute you take from the stock bottle is the same amount that ends up in the final mix. As an equation, that's C1V1 = C2V2. Stock concentration times the volume of stock used equals final concentration times final volume.
Choose which of the four values you want, and enter the other three. The usual question is how much stock to pipette. But the same equation also gives the final strength of a mix you've already made. Or it tells you how far a given volume of stock can be stretched. Units can differ on each side. The answer comes with the volume of solvent to add and the dilution factor.
Where it's used
Why this math matters outside the classroom:
- Lab stock solutions. Lab staff make 500 mL of 0.1 M solution from 2 M stock by measuring 0.1 × 500 ÷ 2 = 25 mL of stock and topping up.
- Cleaning sprays. Cleaning staff turn 50 mL of concentrate into 1 L of spray, a 20-fold dilution that leaves a twentieth of the strength.
- Serial dilutions. Microbiologists make serial tenfold dilutions so a dense culture can be counted, each step cutting the concentration by 10.
- Cold-brew coffee. Cafés dilute cold-brew concentrate 1 part to 2 parts water, so 300 mL of concentrate makes 900 mL of coffee.
Grade level and standards: Grades 10–11; Common Core State Standards for Mathematics HSA.CED.A.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Choose what to solve for. V₁ (volume of stock) is selected to start with.
- Enter the three values you know and pick a unit for each. The two concentrations must be the same kind of unit: both molar, both mass per volume, both percent, or both fold (×).
- Read the answer, the solvent to add and the dilution factor. The answer uses the unit of its partner value. For example, V₁ comes out in the unit you chose for V₂.
What the inputs mean
- Stock concentration (C₁)
- The strength (concentration) of the solution you're diluting from, usually the stock bottle.
- Volume of stock (V₁)
- The volume of stock you take. It goes into the final mix, so it counts toward V₂.
- Final concentration (C₂)
- The strength you want after diluting. It can't be higher than C₁.
- Final volume (V₂)
- The total volume after adding solvent, not the amount of solvent added.
Formula and method
C₁ × V₁ = C₂ × V₂ V₁ = C₂ × V₂ ÷ C₁ solvent to add = V₂ − V₁ dilution factor = C₁ ÷ C₂ = V₂ ÷ V₁
C₁ is the stock concentration and V₁ is the volume of stock you use. C₂ is the final concentration and V₂ is the final total volume. Both sides of the equation are the amount of solute. If both concentrations use the same unit, and both volumes do too, the units cancel out. So the equation works for molarity (moles per liter, M), mg/mL, percent, or a fold strength such as 10× buffer.
If you enter different units on each side, the calculator first converts one value so the pair matches. Then it rearranges the equation to find the unknown.
Worked example
You have a 2 M stock and need 500 mL of a 50 mM working solution.
- Rearrange for the stock volume: V₁ = C₂ × V₂ ÷ C₁.
- Convert C₁ to match C₂: 2 M = 2,000 mM.
- Put in the numbers: V₁ = 50 mM × 500 mL ÷ 2,000 mM = 12.5 mL.
- Solvent to add: 500 − 12.5 = 487.5 mL. Dilution factor: 2,000 ÷ 50 = 40.
Result: Take 12.5 mL of the 2 M stock and add 487.5 mL of solvent. That makes 500 mL of 50 mM solution (a 1 in 40 dilution).
Understanding the result
The dilution factor tells you how many times weaker the final solution is. A factor of 10 means one part stock in ten parts total. That's one part stock plus nine parts solvent, not one plus ten.
Sometimes the stock volume comes out very small, such as under a microliter. Then it's often more accurate to make an in-between dilution first, and dilute that.
Assumptions and limitations
- Volumes add up: stock plus solvent gives exactly V₂. This holds well for weak water-based solutions, but not perfectly for mixes such as ethanol and water.
- No solute is lost or gained, and nothing reacts when you mix.
- Unit conversions use exact powers of ten. Percent and fold strengths are only compared with the same kind of unit.
- The calculator doesn't convert between molar and mass units. That needs a molar mass, which the molarity calculator handles.
- A dilution can only lower the concentration. If C₂ would come out higher than C₁, the calculator stops with a message instead of giving a meaningless volume.
- For several dilutions in a row, use the calculator for each step, or multiply the individual dilution factors.
Frequently asked questions
Does C1V1 = C2V2 work with percent or mg/mL?
Yes. The equation only needs both concentrations in the same unit. Diluting 70% alcohol to 30%, or 1 mg/mL protein to 10 µg/mL, works the same way as diluting a molar solution.
Is V₂ the volume of water to add?
No. V₂ is the final total volume. The water or buffer to add is V₂ minus V₁. The calculator shows it as the solvent to add.
How do I dilute a 10× buffer to 1×?
Choose the × unit for both concentrations, then enter 10, 1 and your final volume. For 500 mL you need 50 mL of 10× buffer plus 450 mL of water.
What is the difference between a 1:10 and a 1 in 10 dilution?
People use them differently. A 1 in 10 dilution, which this calculator reports, means one part stock in ten parts total. Some people write 1:10 to mean one part stock plus ten parts solvent (eleven total). So check which way a protocol means it.
How this calculator is checked
Method: Conservation of solute on dilution, C1V1 = C2V2. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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