Dilution Calculator — C1V1 = C2V2 Made Simple

Dilutions are one of those lab tasks where a small arithmetic error means either a wasted experiment or worse, a faulty result. The relationship is elegantly simple — C₁V₁ = C₂V₂ — but when you're working quickly with multiple samples the CalcHub Dilution Calculator prevents the kind of brain-fart mistakes that happen at 11pm before a deadline.

The Formula

C₁V₁ = C₂V₂

Where:

• C₁ = initial (stock) concentration


• V₁ = volume of stock solution to use


• C₂ = desired final concentration


• V₂ = total final volume

Know any three values and you can solve for the fourth.

How to Use the Calculator

1. Open the Dilution Calculator.
2. Enter the three values you know — concentration can be in M, mM, μM, %, or ng/μL depending on context.
3. Specify which variable you want to find.
4. The result appears with the amount of diluent (water, buffer) to add alongside the stock volume.

That last part — "add X mL of diluent" — is what makes it practical at the bench rather than just mathematically correct.

Worked Examples

Example 1: How much stock do I need?

You have a 10 M NaCl stock. You want 500 mL of 0.15 M NaCl.

C₁V₁ = C₂V₂
10 × V₁ = 0.15 × 500
V₁ = 75/10 = 7.5 mL of stock

Add 7.5 mL stock to 492.5 mL of water.

Example 2: What concentration did I make?

You mixed 2 mL of a 100 mM stock into a total volume of 50 mL.

C₂ = (100 × 2) / 50 = 4 mM

Scenario	C₁	V₁	C₂	V₂
Preparing PBS	10×	50 mL	1×	500 mL
Drug dilution	1 mg/mL	?	10 μg/mL	10 mL
Bleach disinfectant	5%	?	0.1%	1000 mL

Serial Dilutions

For serial dilutions (1:2, 1:10, etc.), the same formula applies at each step. If you're doing a 1:10 serial dilution starting at 1 M:

• Step 1: 1 M → 0.1 M (take 1 mL, add 9 mL)
• Step 2: 0.1 M → 0.01 M (take 1 mL, add 9 mL)
• Step 3: 0.01 M → 0.001 M

Each step applies C₁V₁ = C₂V₂ independently.

Tips

• Units must match. If C₁ is in mM and C₂ is in μM, convert before calculating. The calculator handles this if you specify units consistently.
• V₂ is total volume, not volume of diluent. This trips people up. If V₂ = 100 mL and V₁ = 10 mL, you add 90 mL of diluent — not 100 mL.
• Dilution factor = C₁/C₂ = V₂/V₁. A 1:5 dilution means V₂ is five times V₁.

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Does C1V1 = C2V2 work for all types of concentration?

Yes — molarity, percent concentration, mg/mL, and most other expressions of amount per volume all work with this equation, as long as you use the same units on both sides.

What's the difference between dilution ratio and dilution factor?

A dilution ratio of 1:10 means 1 part stock in 10 parts total (so 1 part + 9 parts diluent). A dilution factor of 10 means the final concentration is 10× less than the starting concentration. They describe the same thing from different angles.

Can I use this for percent solutions like bleach?

Absolutely. If you're diluting a 5% bleach solution to make a 0.5% disinfecting spray, plug 5% and 0.5% into C₁ and C₂ the same way you'd use molarity.

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Related calculators: Molarity Calculator · Concentration Converter · Stoichiometry Calculator