Dilution Calculator C₁V₁ = C₂V₂
Precision Laboratory Solution Tool

Dilution Calculator

Calculate exact stock solution and diluent volumes for laboratory chemistry, molecular biology, pharmacy, and research workflows. Powered by the standard dilution equation C₁ × V₁ = C₂ × V₂ with real-time volume ratio visualization and step-by-step mathematical verification.

V₁ = (C₂ × V₂) / C₁ V_diluent = V₂ − V₁ Dilution Factor = C₁ / C₂

Solution Parameters

Enter stock concentration, desired target concentration, and final volume

Initial concentration of your starting stock solution (must be > 0).
Desired concentration of the diluted working solution (0 ≤ C₂ ≤ C₁).
Total final solution volume after combining stock and diluent (must be > 0).

Calculation Results

Required volumes, dilution ratio, and composition breakdown

Required Stock Volume (V₁)
10 mL
0.01 L | 10,000 µL
Diluent Volume
40 mL
0.04 L | 40,000 µL
Final Solution Volume (V₂) 50 mL
Dilution Factor 5×
Stock Percentage 20%
Stock-to-Final Volume Ratio 1 : 5
Formula Used V₁ = (C₂ × V₂) / C₁ | V_diluent = V₂ − V₁
Solution Volume Composition Total: 50 mL (100%)
Stock Solution (V₁) 10 mL (20%)
Diluent / Solvent 40 mL (80%)

Step-by-Step Calculation

How to Use the Dilution Calculator

Preparing accurate working solutions from a concentrated stock is a daily requirement in analytical chemistry, biochemistry, and clinical laboratories. Follow these steps to compute your dilution parameters:

  1. Select Your Units: Choose a Concentration Unit (such as mmol/L (mM), mol/L (M), mg/mL, or % v/v) and your preferred Volume Unit (L, mL, or µL). Both concentrations C₁ and C₂ use the same selected unit.
  2. Enter Stock Concentration (C₁): Input the known concentration of your starting stock reagent. This value must be greater than zero.
  3. Enter Target Concentration (C₂): Input the desired final concentration of your diluted solution. In a dilution, C₂ cannot exceed C₁.
  4. Enter Final Volume (V₂): Specify the total volume of diluted solution you wish to prepare.
  5. Review Results & Steps: Click Calculate Dilution (or adjust values for instant calculation) to view the required stock volume (V₁), diluent volume to add, dilution factor, visual cylinder ratio, and step-by-step math.

Dilution Formula & Dilution Factor

The Dilution Calculator is governed by the conservation of solute mass or moles during dilution. Because adding pure solvent increases total volume without changing the amount of dissolved solute, the product of concentration and volume remains constant:

C₁ × V₁ = C₂ × V₂
  • C₁ (Stock Concentration): Concentration of the initial concentrated stock solution.
  • V₁ (Required Stock Volume): Volume of stock solution to pipette, solved as V₁ = (C₂ × V₂) / C₁.
  • C₂ (Target Concentration): Final desired concentration after adding diluent.
  • V₂ (Final Volume): Total combined volume of stock solution plus diluent (V_diluent = V₂ − V₁).

Understanding Dilution Factor (DF)

The Dilution Factor expresses how many times less concentrated the final solution is compared to the original stock solution. It is calculated as DF = C₁ / C₂ (which equals V₂ / V₁). For example, diluting a 100 mM stock to 2 mM yields a 50× dilution factor (a 1 : 50 stock-to-final volume ratio), meaning 1 part stock is combined with 49 parts diluent to make 50 parts total volume.

Worked Example: Preparing a Laboratory Working Solution

Suppose a molecular biology protocol requires 50 mL of a 2 mM magnesium chloride (MgCl₂) working buffer, and your laboratory bench has a 10 mM stock solution.

Given Parameters:
  • Stock Concentration (C₁) = 10 mM
  • Target Concentration (C₂) = 2 mM
  • Final Volume (V₂) = 50 mL
Step-by-Step Solution:
  • 1. Calculate Required Stock Volume (V₁): V₁ = (2 mM × 50 mL) / 10 mM = 100 / 10 = 10 mL
  • 2. Calculate Diluent Volume: V_diluent = 50 mL − 10 mL = 40 mL
  • 3. Calculate Dilution Factor: DF = 10 mM / 2 mM = 5× (Stock percentage = 20%)

Laboratory Procedure: Measure 10 mL of the 10 mM stock solution and bring the final volume up to 50 mL by adding 40 mL of deionized water or buffer.

Laboratory Units and Conversion Reference Table

When applying C₁V₁ = C₂V₂, ensure both concentrations share identical dimensions. Note that converting between mass-based units (such as g/L or mg/mL) and molarity-based units (such as mol/L or mM) requires the compound's molecular weight (g/mol).

Category Unit Symbol Full Unit Name Equivalent / Conversion Relation
Molar Concentration mol/L (M) Molar (Moles per Liter) 1 M = 1,000 mM = 1,000,000 µM
Molar Concentration mmol/L (mM) Millimolar 1 mM = 0.001 M = 1,000 µM
Molar Concentration µmol/L (µM) Micromolar 1 µM = 0.001 mM = 10⁻⁶ M
Mass Concentration g/L & mg/mL Grams per Liter / Milligrams per mL 1 g/L = 1 mg/mL = 1,000 µg/mL
Mass Concentration mg/L & µg/mL Milligrams per Liter / Micrograms per mL 1 mg/L = 1 µg/mL = 1,000 ng/mL
Percentage & Parts % w/v, % v/v, ppm, ppb Percent Weight/Volume, Volume/Volume, Parts per Million/Billion 1% w/v = 10 g/L | 1 ppm ≈ 1 mg/L (dilute aqueous) | 1 ppm = 1,000 ppb
Solution Volume L, mL, µL Liter, Milliliter, Microliter 1 L = 1,000 mL = 1,000,000 µL | 1 mL = 1,000 µL

Frequently Asked Questions (FAQ)

Click on any question below to expand detailed laboratory guidance and mathematical explanations.

A dilution calculator is a scientific tool based on the conservation of solute equation (C₁V₁ = C₂V₂). It determines the exact volume of concentrated stock solution and solvent (diluent) required to prepare a target solution of a lower concentration and specific final volume.
The universal dilution formula is C₁ × V₁ = C₂ × V₂, where C₁ is the starting stock concentration, V₁ is the required stock volume, C₂ is the desired target concentration, and V₂ is the total final solution volume.
Rearrange the dilution equation to solve for V₁: multiply the desired target concentration (C₂) by the total final volume (V₂), and divide that product by the stock concentration (C₁). Formula: V₁ = (C₂ × V₂) / C₁.
Assuming additive liquid volumes, subtract the calculated stock volume (V₁) from the desired total final volume (V₂). Formula: Diluent Volume = V₂ − V₁. In high-precision analytical work with concentrated acids or alcohols where volume contraction can occur, add stock solution to a portion of diluent first, mix, and bring to the final calibration mark in a volumetric flask.
You can use any concentration unit—such as mol/L (M), mM, µM, mg/mL, % w/v, or ppm—as long as both the stock concentration (C₁) and target concentration (C₂) share the exact same unit. Converting between mass concentration (e.g., mg/mL) and molar concentration (e.g., mM) requires knowing the solute's molecular weight.
A simple dilution can only decrease or maintain concentration by adding solvent. If your desired target concentration (C₂) is higher than your stock concentration (C₁), you cannot reach it by adding diluent; instead, you must prepare a fresh concentrated solution or evaporate solvent.

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Disclaimer & Limitations of Use: The values generated by this Dilution Calculator represent theoretical mathematical calculations based on additive volume assumptions (C₁V₁ = C₂V₂). Before performing any laboratory, clinical, pharmaceutical, or industrial preparation, users must independently verify unit compatibility, chemical reactivity, non-ideal volume contraction effects, safety data sheets (SDS), and standard laboratory safety protocols (such as always adding concentrated acid slowly to water).