💡 C₁ = Stock concentration | V₁ = Stock volume | C₂ = Final concentration | V₂ = Final volume | Units must match on both sides
📖 What is Dilution?
Dilution is the process of reducing the concentration of a solute in a solution,
usually by adding more solvent (like water). When you dilute a solution, the amount of solute stays the same,
but the total volume increases — so the concentration decreases.
This calculator uses the standard dilution equation used in every chemistry lab:
Problem: You have a 5 M stock solution of HCl. You need 250 mL of 1 M HCl. How much stock do you need?
Given: C₁ = 5 M | C₂ = 1 M | V₂ = 250 mL | V₁ = ? Formula: V₁ = (C₂ × V₂) / C₁ Calculation: V₁ = (1 × 250) / 5 = 50 mL Procedure: Measure 50 mL of 5 M HCl, add to a 250 mL volumetric flask, and fill with distilled water up to the mark.
🧪 Common Lab Applications
Preparing working solutions from concentrated stock
Serial dilutions for microbiology and cell culture
Titration experiments — diluting titrants to working strength
Buffer preparation — adjusting concentration
Pharmaceutical compounding — preparing doses from stock
Always add acid to water — never the other way around (exothermic reaction).
Use calibrated volumetric flasks and pipettes for accurate results.
Wear gloves, goggles, and lab coat when handling concentrated acids/bases.
Verify units match on both sides of the equation (M × mL = M × mL, etc.).
Label every prepared solution with name, concentration, and date.
⚠️ Limitations & Assumptions
📌 Important Notes
Assumes ideal behavior — no volume contraction on mixing.
Does not account for temperature effects on volume (thermal expansion).
For very high concentrations (>1 M), volume changes may be significant.
Ensure C₁ and C₂ use the same unit (M, mM, %, etc.), and V₁ and V₂ use the same unit (mL, L, etc.).
Results are theoretical estimates — verify with a calibrated instrument when accuracy is critical.
📚 Sources & References
Authoritative Sources
OpenStax — Chemistry: Atoms First (Chapter on Solutions)
Khan Academy — Dilution and Molarity
CRC Handbook of Chemistry and Physics
NIH / CDC Laboratory Safety Guidelines
❓ Frequently Asked Questions
What does C₁V₁ = C₂V₂ mean?
The equation states that the amount of solute before dilution (C₁V₁) equals
the amount after dilution (C₂V₂). This is because dilution only changes the volume, not the amount of solute.
Can I use any units in this calculator?
Yes, as long as the units are consistent. C₁ and C₂ must use the same concentration unit (M, mM, %, etc.),
and V₁ and V₂ must use the same volume unit (mL, L, µL, etc.).
How much water do I add to dilute the solution?
Water to add = V₂ − V₁. For example, if V₁ = 50 mL and V₂ = 250 mL, add 200 mL of solvent.
Does dilution change pH?
Yes. For acidic solutions, dilution increases pH (moves toward neutral). For basic solutions,
dilution decreases pH. The change is approximately logarithmic.
Can I use this for serial dilutions?
Yes. Use the calculator once for each step in the serial dilution. For example, for a 1:10 serial dilution,
use V₁ = 1 and V₂ = 10 (or any multiple).
This Dilution Calculator is provided for informational and educational purposes only.
Results are based on the ideal dilution equation C₁V₁ = C₂V₂ and assume no volume contraction on mixing.
Real-world results may vary due to temperature, solvent effects, and measurement uncertainty.
Always follow proper laboratory safety protocols, use calibrated equipment, and consult a qualified
chemist or lab supervisor when preparing solutions for critical applications.