Dilution Calculator — C₁V₁=C₂V₂
Calculate solution dilutions using C₁V₁ = C₂V₂ formula. Find any unknown variable.
C₁V₁ = C₂V₂
What Is the Dilution Calculator — C₁V₁=C₂V₂?
The Dilution Calculator uses the dilution formula C₁V₁ = C₂V₂ to find any one of the four variables — initial concentration, initial volume, final concentration, or final volume — given the other three. Used in chemistry, biology, pharmacology, and food science for preparing solutions of precise concentrations.
Formula
How to Use
Enter three of the four variables: C₁ (initial concentration), V₁ (volume to take from stock), C₂ (target concentration), V₂ (final total volume). Use consistent units (both concentrations in M, g/L, etc.; both volumes in mL, L, etc.). The calculator solves for the unknown variable.
Example Calculation
Dilute a 12M HCl stock to 1M for 500 mL: C₁=12M, C₂=1M, V₂=500mL. V₁ = C₂V₂/C₁ = 1×500/12 = 41.7 mL. Add 41.7 mL of 12M HCl to approximately 400 mL water, then add water to 500 mL total. (Always add acid to water, not water to acid.)
Understanding Dilution — C₁V₁=C₂V₂
The dilution equation C₁V₁ = C₂V₂ is one of the most frequently applied formulas in laboratory science. It describes how the concentration of a solution changes when additional solvent is added — the total amount of solute is conserved while the volume increases, reducing the concentration proportionally. This relationship is valid for any dissolved substance in any solvent.
In biochemistry and molecular biology, precise dilution is critical for enzyme assays, cell culture media preparation, antibody titrations, and PCR reagent mixes. A mistake in dilution factor can invalidate an entire experiment. In clinical medicine, dilutions are used in pharmacology (drug dosing calculations), blood typing, and diagnostic test preparations.
The concept of dilution extends beyond simple solution preparation. Beer-Lambert law uses concentration and path length to determine absorbance (used in spectrophotometry). Dilution is used in environmental monitoring (diluting concentrated samples to within instrument range), food science (flavor concentration in beverages), and industrial chemistry (adjusting process stream concentrations for downstream reactions).
Frequently Asked Questions
Why is C₁V₁ = C₂V₂ valid?
The equation expresses conservation of solute: moles of solute before dilution = moles after. Since moles = concentration × volume, and adding solvent does not change solute moles, C₁V₁ = C₂V₂.
Can I dilute to any concentration?
You can dilute to any concentration between zero and the stock concentration. To get a higher concentration, you would need to concentrate the solution (evaporation, etc.), not dilute.
What is a serial dilution?
A serial dilution is a stepwise sequence of dilutions, each typically a constant factor (e.g., 1:10 each step). Used to prepare very dilute solutions (like 10⁻⁶× dilutions) that would be impractical in a single step.
What units can I use for concentration?
Any consistent concentration unit works: molar (mol/L), g/L, mg/mL, % w/v, ppm, ppb. Just ensure C₁ and C₂ use the same unit, and V₁ and V₂ use the same volume unit.
Is this calculator free?
Yes, completely free with no registration needed.
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