Solution Dilution Calculator (C1V1 = C2V2)
The principle of dilution comes down to one statement: the total amount of solute is conserved before and after dilution. Written as a formula:
C₁ × V₁ = C₂ × V₂
C₁/V₁ are the concentration and volume taken from the stock solution; C₂/V₂ are the target concentration and final volume after dilution. Given any three of the four quantities, the fourth is fully determined. Volume of solvent to add = V₂ − V₁.
Units do not need to be SI, but the concentration units on both sides of the equation must match, and the volume units must match — this is the most common source of errors.
Serial dilution means each step uses the product of the previous step as the new stock. For a 10-fold serial dilution, take 1 part and add 9 parts solvent per tube. Mix thoroughly at each step before transferring to the next — otherwise errors multiply at every stage. By the 6th tube, a 5% pipetting error at each step accumulates to more than 30%.
FAQ
Can C₁ and C₂ use different units?
No. The formula cancels the same concentration unit on both sides; mixing units gives a wrong result. The same applies to volume units.
Why is the error so large in the last tubes of a serial dilution?
Pipetting errors multiply at each step and accumulate. For higher accuracy, reduce the number of dilution steps or switch to a single large-factor dilution.
Related tools
Nucleic Acid Concentration Calculator: OD260, ng/µL, and pmol Conversion
Convert A260 absorbance to mass concentration and interconvert ng and pmol for dsDNA, ssDNA, RNA, and oligonucleotides.
Hemocytometer Cell Concentration Calculator – Online Tool
Enter counts per large square and dilution factor to calculate cell concentration, total cell number, and volume needed for plating.
Buffer Preparation Calculator (Henderson-Hasselbalch)
Given a target pH, calculate the acid-to-base component ratio and the mass of each component needed to prepare your buffer.
Buy me a coffee