Dilution Calculator
C₁V₁ = C₂V₂ — find any unknown
Solving for the highlighted term · C₁V₁ = C₂V₂
Stock volume to take (V₁)
10mL
ƒ C₁V₁ = C₂V₂
The dilution equation C₁V₁ = C₂V₂ relates a stock solution (concentration C₁, volume V₁) to the solution after dilution (C₂, V₂). Because the amount of solute is conserved, knowing any three values gives you the fourth. The most common task — finding the volume of stock (V₁) needed for a target volume at a target concentration — is the default here.
How to dilute a stock solution
Rearrange C₁V₁ = C₂V₂ for the unknown. To make 100 mL of 0.1 M from a 1 M stock: V₁ = (C₂V₂) ÷ C₁ = (0.1 × 100) ÷ 1 = 10 mL of stock, then add solvent up to 100 mL (about 90 mL).
Always add the stock to the solvent and make up to the final volume rather than adding solvent to a fixed volume of stock.
Serial dilutions
For very large dilution factors, dilute in steps (e.g. three sequential 10× dilutions = 1000×). Each step is its own C₁V₁ = C₂V₂ calculation, which keeps pipetting volumes practical and accurate.
Frequently asked questions
What is the C₁V₁ = C₂V₂ formula?
It states that the amount of solute is conserved during dilution: stock concentration × stock volume equals final concentration × final volume. Knowing any three lets you solve for the fourth.
How do I make a 10× dilution?
Take 1 part stock and add 9 parts solvent. For 10 mL of a 0.1 M solution from a 1 M stock: V₁ = (0.1 × 10) ÷ 1 = 1 mL stock, made up to 10 mL.
Does it work for any concentration unit?
Yes, as long as C₁ and C₂ use the same unit (M, mM, µM…) and V₁ and V₂ use the same unit. The calculator keeps units consistent for you.
Why must the stock be more concentrated than the final solution?
You can only dilute, not concentrate, by adding solvent — so C₁ must be greater than C₂. To go the other way you would need to evaporate or add more solute.
Need the actual compound — not just the maths?
Tech Serve Solutions supplies laboratory reagents, fine chemicals and pharmaceutical intermediates to USP, BP and EP grade, with a Certificate of Analysis and worldwide despatch.