Dilution Calculator

Dilution Calculator

Calculate dilutions using C₁V₁ = C₂V₂ formula for laboratory and chemical preparations

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Dilution Calculator: Complete Laboratory Guide

Dilution is the process of reducing concentration by adding solvent to a solution.The fundamental principle follows the conservation of mass: the amount of solute remains constant while the total volume increases, resulting in lower concentration.

Our professional dilution calculator uses the C₁V₁ = C₂V₂ formula to calculate simple dilutions, serial dilutions, and concentration adjustments for laboratory work, pharmaceutical preparations, and analytical chemistry.

Quick Answer

To calculate dilutions: Use C₁V₁ = C₂V₂ where C₁ and V₁ are initial concentration and volume, C₂ and V₂ are final concentration and volume. For example, to dilute 10 mL of 1M solution to 0.1M: (1M)(10mL) = (0.1M)(V₂), so V₂ = 100mL. Add 90mL of solvent.

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Mathematical Foundation

C₁V₁ = C₂V₂

Dilution formula based on conservation of mass principle

Formula Components:

C₁ (Initial Concentration)

Concentration of the stock solution before dilution. Can be expressed in various units: molarity (M), mg/mL, percentage, ppm, etc.

V₁ (Initial Volume)

Volume of stock solution to be diluted. This is the amount you pipette or measure from your concentrated solution.

C₂ (Final Concentration)

Desired concentration after dilution. Must be lower than initial concentration and expressed in the same units as C₁.

V₂ (Final Volume)

Total volume after dilution. This includes both the original solution volume and the volume of diluent (solvent) added.

Types of Dilutions

Simple Dilution

Single-step dilution from stock solution to desired concentration.

Example: 1M → 0.1M dilution
Take 10mL of 1M solution
Add 90mL solvent for 100mL total
Final: 0.1M in 100mL
Best for: Most laboratory preparations, reagent preparation

Serial Dilution

Multiple sequential dilutions, each using the previous dilution as stock.

Example: 10-fold serial dilution
1M → 0.1M → 0.01M → 0.001M
Each step: 1mL + 9mL solvent
Dilution factor: 10× each step
Best for: Creating concentration ranges, microbiology, standards

Concentration Calculation

Determine final concentration when adding specific volumes.

Example: Buffer preparation
5mL of 10mM buffer + 45mL water
Final concentration calculation
C₂ = (10mM × 5mL) / 50mL = 1mM
Best for: Buffer preparation, analytical chemistry

Laboratory Applications

Analytical Chemistry

Standard Curves

Create calibration standards from stock solutions for quantitative analysis and spectroscopy

Sample Preparation

Dilute samples to appropriate concentration ranges for instrument analysis

Reagent Preparation

Prepare working solutions from concentrated stock reagents for assays

Biological Sciences

Cell Culture

Prepare media, supplements, and treatment concentrations for cell biology experiments

Protein Studies

Dilute protein stocks, enzyme preparations, and antibody solutions for assays

Microbiology

Serial dilutions for colony counting, MIC testing, and culture maintenance

Laboratory Protocols

Protocol 1: Buffer Dilution

Prepare 100mL of 50mM Tris buffer from 1M stock

Calculation: C₁V₁ = C₂V₂
(1M)(V₁) = (0.05M)(100mL)
V₁ = 5mL of 1M stock needed
Protocol:
1. Add 5mL of 1M Tris stock to beaker
2. Add ~80mL distilled water
3. Adjust pH if required
4. Make up to 100mL final volume

Protocol 2: Serial Dilution for Plate Counting

10-fold serial dilution for bacterial enumeration

Materials: 9mL sterile water tubes
Protocol:
1. Add 1mL sample to first tube (10⁻¹ dilution)
2. Mix thoroughly, transfer 1mL to next tube (10⁻² dilution)
3. Repeat for desired range (10⁻³, 10⁻⁴, etc.)
4. Plate 100μL from appropriate dilutions
5. Count colonies and calculate CFU/mL

Protocol 3: Drug Concentration Series

Prepare concentration range for dose-response studies

Target: 100μM, 50μM, 25μM, 12.5μM, 6.25μM
Stock: 10mM in DMSO
Protocol:
1. 100μM: 10μL stock + 990μL media
2. 50μM: 500μL of 100μM + 500μL media
3. Continue 2-fold serial dilutions
4. Final DMSO concentration: 1%

Common Dilution Mistakes

Calculation Errors

  • Unit mismatches (mL vs L, mM vs M)
  • Confusing initial volume vs final volume
  • Incorrect dilution factor interpretation

Practical Errors

  • Adding solvent before transferring stock
  • Inadequate mixing between dilution steps
  • Cross-contamination in serial dilutions

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