Stock solutions in a lab are almost always stronger than what an experiment actually calls for, because storing one concentrated bottle is easier than storing a dozen weaker ones for every possible use. Diluting that stock down to the exact concentration you need is one of the most common calculations in any chemistry lab, and it comes down to a single, elegant equation.
How to Use the Dilution Calculator
Choose which of the four quantities to solve for — initial concentration, initial volume, final concentration, or final volume — then enter the other three known values. Concentrations are in moles per liter and volumes are in liters, though the equation works with any consistent pair of units as long as you use the same one for both concentrations and the same one for both volumes.
A Note on Units
This calculator assumes both concentrations use the same unit and both volumes use the same unit, but it doesn't require any particular choice of units — molarity, percentage, milligrams per milliliter, and parts per million all work identically, because the equation is really just a statement that "amount of solute" doesn't change during dilution, expressed as concentration times volume on each side.
The Dilution Equation
C₁V₁ = C₂V₂
The concentration before dilution times the volume before dilution equals the concentration after dilution times the volume after dilution. This works because dilution never changes the actual amount of solute present — only how much solvent it's spread through — so the product of concentration and volume, which represents total moles of solute, stays constant on both sides.
Using the calculator's default example: starting with 2 mol/L stock solution, taking 0.1 liters of it, and diluting until the concentration drops to 0.5 mol/L, the final volume works out to (2 × 0.1) ÷ 0.5, or 0.4 liters. That means you'd take 100 mL of the 2 M stock and add solvent until the total volume reaches 400 mL — an additional 300 mL of solvent.
Why This Matters Beyond the Lab
The dilution equation isn't limited to chemistry benches — it's the same math behind diluting concentrated juice, mixing cleaning solutions from concentrate, or calculating how much medication concentration drops when a dose is mixed into a larger volume of IV fluid. Anywhere a concentrated substance gets spread through more volume without changing the total amount present, C₁V₁ = C₂V₂ applies exactly the same way.
Finding How Much Solvent to Add
The single most common real-world use of this equation is figuring out exactly how much water (or other solvent) to add to a known amount of stock solution. Solve for final volume using your stock's concentration, the volume you're starting with, and your target concentration — then subtract the initial volume from the result to get the volume of solvent to add. In the example above, that's 400 mL minus 100 mL, or 300 mL of solvent.
Working the Other Direction
Sometimes you know what final solution you need — say, 500 mL at 0.2 mol/L — and you need to figure out how much of your concentrated stock to measure out. Solve for initial volume: V₁ = (C₂V₂) / C₁. If your stock is 4 mol/L, that's (0.2 × 0.5) ÷ 4, or 0.025 liters — 25 mL of stock, topped up to 500 mL total with solvent. This is exactly the calculation behind "serial dilution," where a strong stock is diluted in a series of controlled steps to reach very low, precisely known concentrations that would be difficult to measure out directly.
