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Solution Dilution Calculator (C1V1 = C2V2)

Preparing working laboratory solutions from concentrated stock reagents relies on the principle of solute conservation: C₁V₁ = C₂V₂.

Choose which variable you need to determine.

Concentration of concentrated stock (Molar, mM, %, mg/mL).

Volume of stock solution in mL.

Desired final diluted concentration (in identical units as C₁).

Total desired volume of working solution in mL.

Calculated Result
10.00 mL

Required Stock Volume (V₁)

Stock Volume (V₁)

10.00 mL

Stock Concentration (C₁)

10.00

Final Volume (V₂)

100.00 mL

Target Concentration (C₂)

1.00

Solvent to Add

90.00 mL

Dilution Factor

10.0×

Calculation Breakdown

  1. Conservation of Solute Mass in DilutionStock: C₁=10, Target: C₂=1C1V1=C2V2C_1 V_1 = C_2 V_2
  2. Algebraic Solution for V1V1 = 10.00 mLV1=C2V2C1V_1 = \frac{C_2 V_2}{C_1}
  3. Dilution Ratio & Diluent Preparation10.0× Dilution (Add 90.00 mL solvent/water)DF=C1C2=V2V1,Vsolvent=V2−V1\text{DF} = \frac{C_1}{C_2} = \frac{V_2}{V_1}, \quad V_{\text{solvent}} = V_2 - V_1

Stock vs Diluent Volume Distribution for 100 mL Total (C1 = 10 M)

Interactive visualization based on your current inputs

Stock Volume (V₁)
0.0132538500.5 M (20×)1.0 M (10×)2.0 M (5×)5.0 M (2×)Target Conc (C₂)Volume (mL)

What Is the Solution Dilution Calculator (C1V1 = C2V2)?

The dilution equation C₁V₁ = C₂V₂ (or M₁V₁ = M₂V₂) is the primary mathematical tool used by scientists and laboratory technicians to prepare working chemical solutions.

It applies universally across chemistry, molecular biology, pharmacology, and clinical diagnostics.

How Does the Solution Dilution Calculator (C1V1 = C2V2) Work?

Multiplying concentration (moles/volume) by volume gives total moles of solute.

Because adding solvent does not alter the absolute quantity of solute, n_initial = n_final.

Solution Dilution Calculator (C1V1 = C2V2) Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

C1V1=C2V2  ⟹  V1=C2V2C1,Vsolvent=V2−V1C_1 V_1 = C_2 V_2 \implies V_1 = \frac{C_2 V_2}{C_1}, \quad V_{\text{solvent}} = V_2 - V_1

Solute mass or molar amount remains strictly constant before and after dilution; only solvent volume increases.

How to Use the Solution Dilution Calculator (C1V1 = C2V2)

  1. Select the target variable you need to calculate.
  2. Input known stock and target concentrations.
  3. Input initial or final volumes.

Step-by-Step Example Calculation

Preparing 100 mL of 1 M from 10 M Stock

Input Values:

solveFor:V1
conc1:10
vol1:10
conc2:1
vol2:100
Worked Steps: Pipette 10.0 mL of 10 M stock into a volumetric flask and add 90.0 mL of water/diluent to prepare 100 mL of 1 M solution (10× dilution).

Understanding Your Result

Stock Volume Needed (V₁): Volume of concentrate to measure.

Diluent Volume: Volume of water or buffer to add to reach total volume.

Dilution Factor: Overall concentration reduction multiplier.

Factors That Affect the Result

  • Pipetting Accuracy: Use calibrated positive-displacement or air-displacement micropipettes for small volumes.
  • Volumetric Expansion: Mixing certain solvents (e.g., ethanol and water) causes non-ideal volume contraction.

When Should You Use This Calculator?

  • Preparing buffer reagents, drug dosages, cell culture media, and PCR master mixes.

Assumptions & Limitations

  • Assumes additive volumes (V₂ = V₁ + V_solvent), which holds accurately for dilute aqueous solutions.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Deterministic mass conservation solution with 100% mathematical precision.

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