Dilution Calculator – Molarity & mg/mL Solution Dilution
Calculate solution dilutions with our free dilution calculator. Perform molarity dilutions, mg/mL conversions, serial dilutions, and more using the C₁V₁ = C₂V₂ formula. Perfect for chemistry students, lab professionals, and researchers.
C₁V₁ = C₂V₂ Formula: Calculate any one variable when you know the other three. Select which value to calculate below.
mol/L
mL
mol/L
mL
Dilution is the process of reducing the concentration of a solute in a solution by adding more solvent. In chemistry and biology labs, dilution is one of the most fundamental techniques used to prepare working solutions from concentrated stock solutions. The key principle is that the amount of solute remains constant during dilution—only the volume changes.
Why Dilution Matters
Dilution is essential in laboratories because concentrated stock solutions are more stable for storage and take up less space. When needed, these stocks are diluted to the appropriate working concentration. This approach:
- Saves money: Concentrated solutions are more economical to purchase and store
- Reduces errors: It's easier to accurately measure larger volumes than very small ones
- Improves safety: Working with diluted solutions is often safer than handling concentrated chemicals
- Ensures consistency: All lab members can prepare the same concentration from a single stock
Common Applications
Chemistry Labs
- Preparing standard solutions
- Making calibration curves
- Titration preparations
- Adjusting pH buffers
Biology & Medicine
- Cell culture media
- Protein and DNA samples
- Drug dilutions
- Antibody preparations
The fundamental dilution equation is C₁V₁ = C₂V₂, which states that the amount of solute before dilution equals the amount after dilution. This formula is the cornerstone of all dilution calculations.
C₁V₁ = C₂V₂
C₁ = Initial concentration (stock solution)
V₁ = Initial volume (stock volume needed)
C₂ = Final concentration (after dilution)
V₂ = Final volume (total volume after dilution)
When to Use This Formula
The C₁V₁ = C₂V₂ formula is used whenever you need to calculate any one of the four variables (C₁, V₁, C₂, or V₂) when you know the other three. Most commonly, you'll use it to find V₁—the volume of stock solution needed to prepare a desired final concentration and volume.
Important Rules
- Units must match: C₁ and C₂ must be in the same concentration units (both M, or both mg/mL)
- Volume units must match: V₁ and V₂ must be in the same volume units (both mL, or both µL)
- Conservation principle: The formula assumes no chemical reaction occurs during dilution
- Temperature consideration: Volumes can change slightly with temperature, especially for organic solvents
Molarity (M) is the most common concentration unit in chemistry, expressing moles of solute per liter of solution. Our molarity dilution calculator makes it simple to prepare solutions with precise molar concentrations.
Understanding Molarity
Molarity (M) = moles of solute / liters of solution
Common units: M (mol/L), mM (mmol/L), µM (µmol/L), nM (nmol/L)
Molarity Dilution Example
Problem:
You have a 1 M stock solution and need to prepare 100 mL of 0.1 M solution. How much stock do you need?
Given:
• C₁ = 1 M (stock concentration)
• C₂ = 0.1 M (desired concentration)
• V₂ = 100 mL (desired final volume)
• V₁ = ? (stock volume needed)
Solution:
V₁ = (C₂ × V₂) ÷ C₁
V₁ = (0.1 M × 100 mL) ÷ 1 M
V₁ = 10 mL
Answer: Take 10 mL of 1 M stock and add 90 mL of solvent to reach 100 mL total volume.
Common Molarity Conversions
| From | To | Multiply By |
|---|---|---|
| M (mol/L) | mM | ×1000 |
| M (mol/L) | µM | ×1,000,000 |
| mM | M | ÷1000 |
| µM | nM | ×1000 |
Mass concentration (mg/mL, µg/mL, ng/mL) is commonly used in biochemistry, pharmacology, and clinical laboratories. Our mg/mL dilution calculator helps you prepare accurate mass-based dilutions for proteins, drugs, and other biomolecules.
Understanding Mass Concentration
Mass concentration expresses the mass of solute per unit volume of solution. It's particularly useful when the molecular weight is unknown or when working with complex biological mixtures.
Common Mass Concentration Units
- g/L or mg/mL: Grams or milligrams per milliliter (1 g/L = 1 mg/mL)
- µg/mL: Micrograms per milliliter (common for proteins and antibodies)
- ng/mL: Nanograms per milliliter (common for hormones and cytokines)
- % w/v: Weight per volume percentage (g per 100 mL)
mg/mL Dilution Example
Problem:
You have a 10 mg/mL protein stock and need to prepare 50 mL of 2 mg/mL solution. How much stock do you need?
Given:
• C₁ = 10 mg/mL (stock concentration)
• C₂ = 2 mg/mL (desired concentration)
• V₂ = 50 mL (desired final volume)
• V₁ = ? (stock volume needed)
Solution:
V₁ = (C₂ × V₂) ÷ C₁
V₁ = (2 mg/mL × 50 mL) ÷ 10 mg/mL
V₁ = 100 ÷ 10 = 10 mL
Answer: Take 10 mL of 10 mg/mL stock and add 40 mL of buffer to reach 50 mL total volume.
Common Mistakes with mg/mL Dilutions
Unit Confusion
Mixing up mg/mL with µg/mL leads to 1000× errors. Always double-check units!
Forgetting Total Volume
V₂ is the TOTAL final volume, not just the diluent volume to add.
Protein Precipitation
Some proteins precipitate at low concentrations. Dilute in appropriate buffer, not just water.
Example 1: Basic Dilution Calculation
Problem:
Prepare 500 mL of 0.05 M NaCl from a 1 M stock solution.
Step 1: Identify known values
C₁ = 1 M, C₂ = 0.05 M, V₂ = 500 mL, V₁ = ?
Step 2: Use the formula C₁V₁ = C₂V₂
V₁ = (C₂ × V₂) ÷ C₁
Step 3: Substitute values
V₁ = (0.05 M × 500 mL) ÷ 1 M
V₁ = 25 ÷ 1 = 25 mL
Answer: Measure 25 mL of 1 M stock and add water to reach 500 mL total volume.
Example 2: Serial Dilution
Problem:
Create a 1:1000 dilution using three 1:10 serial dilutions.
Step 1: First dilution (1:10)
Take 1 mL stock + 9 mL diluent = 10 mL total
Concentration = C₀ ÷ 10
Step 2: Second dilution (1:10)
Take 1 mL from Step 1 + 9 mL diluent = 10 mL
Concentration = C₀ ÷ 100
Step 3: Third dilution (1:10)
Take 1 mL from Step 2 + 9 mL diluent = 10 mL
Concentration = C₀ ÷ 1000
Result: Final dilution is 1:1000 (10 × 10 × 10 = 1000)
Example 3: Reverse Calculation
Problem:
You used 15 mL of a 2 M stock and added water to make 150 mL. What is the final concentration?
Step 1: Identify known values
C₁ = 2 M, V₁ = 15 mL, V₂ = 150 mL, C₂ = ?
Step 2: Use the formula C₁V₁ = C₂V₂
C₂ = (C₁ × V₁) ÷ V₂
Step 3: Substitute values
C₂ = (2 M × 15 mL) ÷ 150 mL
C₂ = 30 ÷ 150 = 0.2 M
Answer: The final concentration is 0.2 M (or 200 mM)
⚠️ Educational Use Disclaimer
This dilution calculator is intended for educational and laboratory planning purposes. Always verify calculations and follow laboratory protocols.
Common Dilution Ratios
DF=2
DF=5
DF=10
DF=20
DF=50
DF=100
Unit Conversions
Molarity:
1 M = 1000 mM = 1,000,000 µM
Volume:
1 L = 1000 mL = 1,000,000 µL
Mass:
1 g/L = 1 mg/mL = 1000 µg/mL
C₁V₁ = C₂V₂
Calculate any variable from the dilution equation
Dilution Factor
Quick calculations using dilution ratios (1:10, 1:100, etc.)
Serial Dilution
Multi-step dilutions for extreme concentrations
Always add stock to diluent, not diluent to stock (especially for acids/bases)
Mix thoroughly after dilution—inversion or gentle swirling works best
For viscous solutions, allow extra mixing time to ensure homogeneity
Label all diluted solutions with concentration, date, and your initials
Use volumetric flasks for precise final volumes in analytical work
Chemistry Labs
Standard solutions, titrations, buffer preparation
Molecular Biology
DNA/RNA dilutions, enzyme preparations, PCR reagents
Biochemistry
Protein dilutions, antibody preparations, substrate solutions
Pharmacology
Drug dilutions, dose preparations, IC50 assays
Dilution Calculator for Antibody & DNA Samples
This dilution calculator can also be used as an antibody dilution calculator and DNA dilution calculator in molecular biology and biotechnology laboratories. Antibodies, DNA, RNA, and enzymes are often supplied as concentrated stock solutions and must be diluted accurately before use in experiments such as ELISA, Western blotting, PCR, and sequencing.
Using the C₁V₁ = C₂V₂ formula, you can easily calculate how much stock antibody or DNA solution is required to prepare a working concentration while maintaining experimental accuracy and reproducibility.
Antibody Dilution Calculator
An antibody dilution calculator is commonly used in immunology and diagnostic labs to prepare primary and secondary antibodies at specific working concentrations. Antibody dilutions are critical for techniques such as ELISA, Western blot, immunofluorescence, and immunohistochemistry.
For example, if an antibody datasheet recommends a 1:1000 dilution, you can use this calculator to determine the exact volume of antibody and diluent required for your final reaction volume.
Always practice safe dilution techniques:
- Wear appropriate PPE (gloves, goggles, lab coat)
- Work in a fume hood when diluting volatile or hazardous chemicals
- Add acid to water, never water to acid
- Use appropriate containers for chemical compatibility
- Dispose of waste according to institutional guidelines
- Double-check calculations before preparing solutions