Dilution Calculator
Calculate dilutions using the C1V1=C2V2 formula. Find initial or final concentration, volume needed for dilution, and dilution factor.
Dilution Parameters
Solve For:
Concentration Unit:
Volume Unit:
Quick Presets:
Final Concentration (C₂)
2.0000 M
Complete Solution:
C₁ (Initial Conc.)
10.0000 M
V₁ (Initial Vol.)
50.0000 mL
C₂ (Final Conc.)
2.0000 M
V₂ (Final Vol.)
250.0000 mL
How to Prepare:
- Take 50.0000 mL of stock solution (10.0000 M)
- Add 200.0000 mL of solvent
- Mix well to get 250.0000 mL of 2.0000 M solution
Formula Used:
C₁V₁ = C₂V₂
10.0000 × 50.0000 = 2.0000 × 250.0000
Serial Dilution Series
If you continue diluting at the same factor (5.00×):
| Step | Concentration | Total Dilution |
|---|---|---|
| 1 | 10.0000 M | 1:5.00 |
| 2 | 2.0000 M | 1:25.00 |
| 3 | 0.4000 M | 1:125.00 |
| 4 | 0.0800 M | 1:625.00 |
| 5 | 0.0160 M | 1:3125.00 |
Understanding Dilution
Dilution is the process of decreasing the concentration of a solution by adding more solvent. The C₁V₁=C₂V₂ formula is based on conservation of mass - the amount of solute stays the same before and after dilution, only the concentration changes. This formula assumes ideal behavior and is widely used in laboratory settings for preparing standard solutions.
What Is Dilution?
Dilution is the process of reducing the concentration of a solution by adding more solvent. The amount of solute (dissolved substance) stays constant—only the total volume changes. Dilution is fundamental to laboratory work, from preparing reagents to making serial dilutions for assays.
| Term | Definition | Example |
|---|---|---|
| Stock solution | Concentrated starting solution | 12 M HCl, 10× buffer |
| Working solution | Diluted solution for use | 1 M HCl, 1× buffer |
| Dilution factor | Ratio of final to initial volume | 10× dilution: 1 mL stock + 9 mL solvent |
| Diluent | Solvent used to dilute | Water, buffer, saline |
Dilution Equation
Where:
- C₁= Initial (stock) concentration
- V₁= Volume of stock solution needed
- C₂= Final (desired) concentration
- V₂= Final total volume
Understanding Dilution Factor
The dilution factor describes how much a solution has been diluted. It can be expressed as a ratio, fold-dilution, or fraction.
| Expression | Meaning | Stock Needed for 100 mL | Concentration Change |
|---|---|---|---|
| 1:10 dilution | 1 part stock + 9 parts solvent | 10 mL + 90 mL | 10× less concentrated |
| 1:100 dilution | 1 part stock + 99 parts solvent | 1 mL + 99 mL | 100× less concentrated |
| 10-fold dilution | Same as 1:10 | 10 mL + 90 mL | 10× less concentrated |
| 1/5 dilution | Final is 1/5 original conc. | 20 mL + 80 mL | 5× less concentrated |
Key relationship: Dilution Factor = C₁/C₂ = V₂/V₁. A 10× dilution means the final concentration is 1/10th of the original.
Serial Dilutions
Serial dilution is a stepwise dilution where each step uses the previous dilution as stock. This is essential for creating a range of concentrations for calibration curves, dose-response studies, and bacterial counts.
| Step | Dilution Factor | Cumulative Dilution | If Starting at 1 M |
|---|---|---|---|
| Original | 1× | 1× | 1 M |
| 1st 1:10 | 10× | 10× | 0.1 M (100 mM) |
| 2nd 1:10 | 10× | 100× | 0.01 M (10 mM) |
| 3rd 1:10 | 10× | 1,000× | 0.001 M (1 mM) |
| 4th 1:10 | 10× | 10,000× | 0.0001 M (100 μM) |
Common serial dilutions: 1:2 (2-fold), 1:3 (3-fold), 1:10 (10-fold). Cumulative dilution = product of individual factors.
Proper Dilution Technique
Accurate dilution requires proper technique, especially for concentrated acids and bases.
| Solution Type | Technique | Why |
|---|---|---|
| Concentrated acids | Always add acid to water | Water splashing into acid causes violent boiling |
| Concentrated bases | Add base to water slowly | Exothermic; can splash |
| Viscous solutions | Rinse pipette tip with diluent | Ensures complete transfer |
| Volatile solvents | Work in fume hood; cover | Evaporation changes concentration |
| Precise work | Use volumetric glassware | Beakers/cylinders less accurate |
Safety mnemonic: "Do as you oughta, add acid to water" or "AAA = Always Add Acid (to water)".
Dilution with Different Concentration Units
C₁V₁ = C₂V₂ works with any concentration unit as long as both concentrations use the same unit.
| Unit Type | Example Calculation | Notes |
|---|---|---|
| Molarity (M) | 6 M × 10 mL = 1 M × V₂ | Most common in chemistry |
| Percent (%) | 70% × V₁ = 10% × 100 mL | Commercial reagents |
| mg/mL | 50 mg/mL × V₁ = 5 mg/mL × 10 mL | Protein solutions |
| Fold (×) | 10× × V₁ = 1× × 50 mL | Buffers, media |
| Parts per million | 1000 ppm × V₁ = 100 ppm × V₂ | Trace analysis |
Volume units: Must also match (both in mL, both in L, etc.) or be converted.
Common Laboratory Dilutions
Many standard dilutions are used repeatedly in laboratories. Here are frequently needed calculations.
| Application | Stock | Final | Preparation (per 100 mL) |
|---|---|---|---|
| HCl working solution | 12 M (conc.) | 1 M | 8.3 mL stock + 91.7 mL H₂O |
| 10× PBS to 1× | 10× PBS | 1× PBS | 10 mL stock + 90 mL H₂O |
| Ethanol dilution | 95% | 70% | 73.7 mL stock + 26.3 mL H₂O |
| Bleach sanitizer | 5.25% | 0.5% | 9.5 mL stock + 90.5 mL H₂O |
| NaOH working | 10 M | 0.1 M | 1 mL stock + 99 mL H₂O |
Applications of Dilution
Dilution is used throughout science, medicine, and industry for various purposes.
| Field | Application | Example |
|---|---|---|
| Analytical Chemistry | Calibration standards | Serial dilutions for standard curves |
| Microbiology | Viable cell counts | 10-fold serial dilutions for plating |
| Pharmacy | Medication preparation | Diluting IV drugs to correct dose |
| Environmental | Sample analysis | Diluting samples into detector range |
| Food Industry | Flavor/additive adjustment | Concentrate to ready-to-drink |
| Research | Dose-response curves | Drug concentration series |
Worked Examples
Basic Dilution Calculation
Problem:
How do you prepare 500 mL of 0.5 M NaCl from a 5 M stock solution?
Solution Steps:
- 1Identify knowns: C₁ = 5 M, C₂ = 0.5 M, V₂ = 500 mL
- 2Apply C₁V₁ = C₂V₂: 5 M × V₁ = 0.5 M × 500 mL
- 3Solve for V₁: V₁ = (0.5 × 500) / 5 = 250 / 5 = 50 mL
- 4Dilution factor check: 5/0.5 = 10× dilution ✓
Result:
Add 50 mL of 5 M NaCl stock to enough water to make 500 mL total volume. This is a 10-fold dilution (add 50 mL stock + 450 mL water).
Preparing Working Acid Solution
Problem:
Prepare 250 mL of 2 M H₂SO₄ from concentrated H₂SO₄ (18 M).
Solution Steps:
- 1C₁ = 18 M, C₂ = 2 M, V₂ = 250 mL
- 2V₁ = (C₂ × V₂) / C₁ = (2 × 250) / 18 = 27.8 mL
- 3Safety: NEVER add water to concentrated acid!
- 4Procedure: Add ~150 mL water to flask first, slowly add 27.8 mL conc. H₂SO₄ while swirling, cool, then dilute to 250 mL mark
Result:
Use 27.8 mL of 18 M H₂SO₄. Always add acid to water to prevent violent boiling. Allow solution to cool before bringing to final volume.
Serial Dilution for Bacterial Count
Problem:
Create a 6-step 10-fold serial dilution from a bacterial culture for colony counting.
Solution Steps:
- 1Label tubes 10⁻¹ through 10⁻⁶
- 2Add 9 mL sterile diluent to each tube
- 3Transfer 1 mL from original culture to tube 10⁻¹ (1:10 dilution)
- 4Mix well, transfer 1 mL from 10⁻¹ to 10⁻², repeat to 10⁻⁶
- 5Each step: 1 mL sample + 9 mL diluent = 10 mL total
- 6Final dilution: 10⁻⁶ (1 million-fold)
Result:
Serial dilution complete. If 150 colonies grow from 0.1 mL of the 10⁻⁵ dilution: CFU/mL = 150 × 10 × 10⁵ = 1.5 × 10⁸ bacteria/mL in original.
Tips & Best Practices
- ✓Always add acid to water (AAA), never water to acid—prevents violent exothermic reactions.
- ✓Use the dilution factor to verify your calculation: C₁/C₂ should equal V₂/V₁.
- ✓For precise work, add stock to partial diluent, mix, then bring to final volume in a volumetric flask.
- ✓C₁V₁ = C₂V₂ only works when solute amount doesn't change—no reactions, no precipitation.
- ✓Serial dilutions improve accuracy for large dilution factors (>100×).
- ✓Label all dilutions clearly with concentration, date, and preparer.
- ✓Account for thermal expansion if diluting solutions with significant heat of mixing.
Frequently Asked Questions
Sources & References
Last updated: 2026-01-22