🎯 Solve for:
Initial concentration (any unit)
Enter stock concentration.
Volume of stock to use
Enter stock volume.
Desired final concentration
Enter final concentration.
Total volume after dilution
Enter final volume.
Result
—
💡
ℹ️ C1V1=C2V2 assumes ideal dilution (no volume contraction). Concentrations C1 and C2 must be in the same units. Volumes V1 and V2 must be in the same units.
Was this calculator helpful?
Sources & Methodology
C1V1=C2V2 dilution formula based on conservation of moles; per IUPAC and standard analytical chemistry references.
Skoog, West, Holler & Crouch — Fundamentals of Analytical Chemistry, 9th Ed.
Standard reference for solution preparation, dilution techniques, and concentration calculations in analytical chemistry.
IUPAC — Compendium of Chemical Terminology (Gold Book)
Defines dilution, concentration, and molar quantity. goldbook.iupac.org
NIH — Common Laboratory Methods: Solution Preparation
Standard laboratory protocols for dilution and solution preparation. nih.gov
C1V1 = C2V2 (conservation of moles of solute)
C2 = C1 x V1 / V2
V1 = C2 x V2 / C1
V2 = C1 x V1 / C2
Dilution Factor = V2 / V1 = C1 / C2
Solvent to add = V2 - V1
C2 = C1 x V1 / V2
V1 = C2 x V2 / C1
V2 = C1 x V1 / C2
Dilution Factor = V2 / V1 = C1 / C2
Solvent to add = V2 - V1
C1V1 = C2V2
Example: Dilute 50 mL of 6 M HCl to 2 M.
V2 = C1V1/C2 = (6 x 50) / 2 = 150 mL total
Add 100 mL of water to 50 mL of 6 M HCl to make 150 mL of 2 M HCl.
Dilution factor = 150/50 = 3x
V2 = C1V1/C2 = (6 x 50) / 2 = 150 mL total
Add 100 mL of water to 50 mL of 6 M HCl to make 150 mL of 2 M HCl.
Dilution factor = 150/50 = 3x
Last reviewed: April 2026
How to Use the C1V1=C2V2 Dilution Formula
The dilution formula C1V1 = C2V2 is derived from a simple principle: the number of moles of solute is conserved when you add solvent. Before dilution, moles = C1 × V1. After dilution, moles = C2 × V2. Since no solute was added or removed: C1V1 = C2V2.
This formula works for any concentration unit as long as C1 and C2 are in the same units, and V1 and V2 are in the same units. It applies to molar concentrations (M), mg/mL, percent solutions, units/mL, or any other expression of amount per volume.
Common Dilution Scenarios
| Dilution Type | Ratio | Stock + Solvent | Dilution Factor |
|---|---|---|---|
| 1:2 | 1 part stock : 2 total | 1 mL + 1 mL | 2x |
| 1:5 | 1 part stock : 5 total | 1 mL + 4 mL | 5x |
| 1:10 | 1 part stock : 10 total | 1 mL + 9 mL | 10x |
| 1:100 | 1 part stock : 100 total | 0.1 mL + 9.9 mL | 100x |
| 1:1000 | Serial 1:10 x3 | Three 1:10 dilutions | 1000x |
💡 Serial Dilution: For large dilution factors (1:1000 or greater), use serial dilutions. Perform three successive 1:10 dilutions instead of one 1:1000 dilution. Each 1:10 step requires only 0.1 mL stock into 0.9 mL diluent, giving much greater accuracy than trying to pipette 1 µL into 999 µL in a single step.
Frequently Asked Questions
C1V1 = C2V2. Stock concentration times stock volume equals final concentration times final volume. Based on conservation of moles of solute.
C2 = C1 x V1 / V2. Example: 100 mL of 5 M diluted to 500 mL: C2 = (5 x 100)/500 = 1 M. The 5x volume increase produces 5x concentration decrease.
Dilution factor = V2/V1 = C1/C2. A 1:10 dilution factor means 1 part stock in 10 parts total — not 10 parts added. To prepare, add 1 mL stock to 9 mL diluent.
1 part stock in 10 parts total. Add 1 mL stock to 9 mL diluent = 10 mL total. Concentration reduces by 10x. C2 = C1/10.
Add 0.1 mL (100 µL) to 9.9 mL diluent = 10 mL total. Or: two successive 1:10 dilutions. Final concentration = C1/100.
Stepwise dilutions where each step uses the previous diluted solution as stock. Three 1:10 serial dilutions = 1:1000 total. Used in microbiology, immunology, drug testing.
V1 = C2 x V2 / C1. Example: 200 mL of 0.1 M from 5 M stock: V1 = (0.1 x 200)/5 = 4 mL stock. Add 4 mL stock to 196 mL diluent.
Moles = C x V. Dilution does not add or remove solute, so moles before = moles after. C1V1 = n = C2V2.
C1 and C2 must be in the same unit (any concentration unit). V1 and V2 must be in the same unit (any volume unit). The concentration and volume units do not need to match each other.
Solvent to add = V2 - V1. Example: preparing 150 mL total from 50 mL stock: add 150 - 50 = 100 mL of diluent. Always add stock to diluent (not diluent to concentrated acid).
Related Calculators
Popular Calculators
AGI Calculator
Education
Ohms Law Calculator
Education
Course Pricing Calculator
Education
Stripe Fee Calculator
Finance
Pain & Suffering
Legal
TDEE Calculator
Health
Roofing Calculator
Construction
GPA Calculator
Education
Mortgage Refinance
Finance
CPM Calculator
Marketing
Markup Calculator
Finance
Angle Conversion Calculator
Education