Dilution Calculator

Stretching a Stock Solution Without Guesswork

Almost no one prepares a working solution from scratch every time — it's far more common to keep a concentrated stock on the shelf and dilute a small amount of it down as needed. The relationship that governs this is deceptively simple, but getting a variable wrong means either a solution that's too weak to work or too strong to be safe.

The Formula

C1 × V1 = C2 × V2

C1 and V1 describe the concentrated stock before dilution; C2 and V2 describe the final, diluted solution. Because the total moles of solute don't change during dilution — only the volume does — this equation holds for any pair of consistent units.

Where This Calculation Matters

  • Preparing lab reagents — scaling a concentrated stock down to a working concentration for an assay or reaction.
  • Cleaning and disinfecting solutions — diluting a concentrate to a target percentage for safe, effective use.
  • Pharmaceutical compounding — adjusting a stock drug concentration to a prescribed dose concentration.
  • Serial dilutions — each step in a dilution series applies this same relationship in sequence.

Worked Examples

Volume of stock needed to prepare a diluted solution (C1V1 = C2V2)
Stock Concentration (C1)Target Concentration (C2)Target Volume (V2)Stock Volume Needed (V1)
10 mol/L1 mol/L1 L0.100 L
5 mol/L0.5 mol/L0.5 L0.050 L

In the first example, 100 mL of the 10 mol/L stock is brought up to a total of 1 L to reach 1 mol/L — the remaining 900 mL is solvent.

How to Use This Calculator

  1. Choose which value you're solving for — C1, V1, C2, or V2.
  2. Fill in the three known values among C1 – Initial Concentration (mol/L), V1 – Initial Volume (L), C2 – Final Concentration (mol/L), and V2 – Final Volume (L).
  3. Select Calculate to solve for the missing quantity.

Related Calculations

Working from a stock:diluent ratio like 1:4 instead of concentrations? The Dilution Ratio Calculator handles that form directly. To determine the stock concentration itself from a mass, start with the Molarity Calculator.