Solution Dilution
Calculator

A solution dilution calculator uses the equation C₁V₁ = C₂V₂ to determine volumes and concentrations when preparing solutions from concentrated stocks. Enter three of four values — stock concentration (C₁), stock volume (V₁), desired concentration (C₂), or total volume (V₂) — and the tool solves for the unknown. This covers every routine dilution task in chemistry, biology, and pharmaceutical work.

The solution dilution calculator handles all concentration units used in laboratory and industrial settings. Researchers preparing phosphate-buffered saline (PBS) from 10× stock, diluting Tris buffer from 1 M to 50 mM, or adjusting sodium hydroxide concentration for titration all use C₁V₁ = C₂V₂. Chemical suppliers like Sigma-Aldrich, Fisher Scientific, and VWR International provide stock solution concentrations on their product labels and certificates of analysis.

Every solution dilution obeys one principle: the total amount of solute stays constant when you add solvent. C₁V₁ = C₂V₂ expresses this mathematically. C₁ is the stock concentration, V₁ is the volume of stock you take, C₂ is the final concentration after dilution, and V₂ is the total final volume.

Rearrange the equation to solve for any unknown:

This solution dilution formula works for any solute in any solvent — from sodium chloride in water to pharmaceutical compounds in DMSO. The equation assumes the volumes are additive and the solution behaves ideally. For highly concentrated solutions (above 1 M for many solutes), volumetric addition may introduce small errors. In such cases, weigh the solvent instead. For routine laboratory work at millimolar concentrations, C₁V₁ = C₂V₂ is precise and reliable.

The dilution factor equals C₁ ÷ C₂ = V₂ ÷ V₁. A 10× PBS stock diluted to 1× working strength has a dilution factor of 10. This means you need 1 part stock for every 10 parts total volume — or 100 mL stock in 1 L final.

Common buffer stocks come at standard concentrations designed for easy dilution factors: 10× PBS, 5× TAE, 50× Tris-acetate. Manufacturers like Bio-Rad, Invitrogen (Thermo Fisher), and New England Biolabs formulate stocks at these concentrations specifically so scientists can perform simple integer dilutions. This solution dilution factor calculator handles both standard and non-standard factors.

Follow these steps to calculate your dilution:

Serial dilution of solutions creates a range of working concentrations from a single stock. This approach is standard for enzyme kinetics studies, where substrate concentrations spanning two orders of magnitude are needed, and for calibration curve preparation in analytical chemistry.

Analytical chemistry laboratories certified under ISO 17025 use serial dilutions to create multi-point calibration standards for instruments like ICP-MS (Agilent, PerkinElmer), HPLC (Waters, Shimadzu), and GC-MS (Thermo Fisher). Each dilution step must be traceable to a certified reference material (CRM). This solution dilution calculator generates the concentration at every step, ensuring audit-ready documentation.

Problem: A researcher needs 200 mL of 50 mM Tris-HCl buffer, pH 7.5, from a 1 M Tris-HCl stock purchased from Sigma-Aldrich.