Solution Dilution Calculator: How to Use C1V1 = C2V2 (With Examples)

Dilutions are one of those lab skills that feel simple — until you’re in a hurry, converting units (mM → µM), or trying to figure out how much stock to pipette without second‑guessing yourself.

The good news: most day-to-day dilution prep can be handled by a single relationship:

C₁V₁ = C₂V₂

The Tooladex Solution Dilution Calculator lets you solve this instantly (for C1, C2, V1, or V2) and gives you clear “stock + diluent” mixing instructions.

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🧪 What is a dilution?

A dilution lowers concentration by adding more solvent (diluent). In practical terms, you take a stock solution (more concentrated), measure a volume of it, and add buffer/water until you reach a target concentration and final volume.

This assumes the amount of solute you care about is conserved during mixing (no reaction, no precipitation, no evaporation during the calculation).

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🧮 The core dilution equation (C₁V₁ = C₂V₂)

• C1: stock concentration
• V1: volume of stock you will use
• C2: final (target) concentration
• V2: final total volume after dilution

The conservation idea is:

(amount of solute before) = (amount of solute after)

And for many common concentration units, “amount” is captured by concentration × volume, which gives the classic equation:

C₁V₁ = C₂V₂

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🔁 Dilution factor (DF) and “X” dilutions

Two super useful shortcuts:

• Dilution factor (DF): DF = C1 / C2
• Stock fraction (the fraction of the final solution that is stock): V1 / V2 = C2 / C1

So if C1 is 10× higher than C2:

• DF = 10
• V1/V2 = 1/10
• That means 10% stock and 90% diluent

This matches common lab language like 10× → 1×.

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✅ How to solve for each variable

Starting from C₁V₁ = C₂V₂:

• Solve for V1: V1 = (C2 × V2) / C1
• Solve for V2: V2 = (C1 × V1) / C2
• Solve for C2: C2 = (C1 × V1) / V2
• Solve for C1: C1 = (C2 × V2) / V1

Tooladex supports all four modes.

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🧰 Real dilution examples

Example 1: Make 100 mL of 0.1 M from a 1.0 M stock

You know:

• C1 = 1.0 M
• C2 = 0.1 M
• V2 = 100 mL

Solve for V1:

• V1 = (C2 × V2) / C1
• V1 = (0.1 × 100) / 1.0 = 10 mL

Then add diluent:

• Diluent = V2 − V1 = 100 − 10 = 90 mL

So: 10 mL stock + 90 mL diluent.

Example 2: Convert units (mM → µM) for a tiny prep

Make 1,000 µL (1 mL) of 10 µM from a 1 mM stock.

Because 1 mM = 1000 µM, this is a 100× dilution:

• DF = 1 mM / 10 µM = 100
• V1 = V2 / DF = 1 mL / 100 = 0.01 mL = 10 µL

So: 10 µL stock + 990 µL diluent.

Example 3: % (w/v) dilutions

Percent weight/volume is common for buffers and reagents.

• 1% (w/v) means 1 g per 100 mL

If you have a 10% (w/v) stock and want 1% (w/v) final, that’s also a 10× dilution (same ratio logic):

• V1 = V2 / 10
• Diluent = V2 − V1

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⚠️ Common dilution mistakes (and how to avoid them)

• Mixing incompatible concentration types: You can’t convert molar (M) to mass/volume (mg/mL) without molecular weight. Keep C1 and C2 in the same family unless you’ve done that conversion separately.
• Trying to “dilute up”: If C2 > C1, adding diluent won’t get you there — you’d need a more concentrated stock or a different prep.
• Forgetting that V2 is total volume: V2 already includes the stock volume.

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🚀 Use the Tooladex Solution Dilution Calculator

The calculator is built to be practical for real prep work:

• Solve for any one variable (C1, C2, V1, or V2)
• Get dilution factor and stock fraction
• See stock + diluent amounts clearly
• Keep everything private (runs entirely in your browser)

Try it here: