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Solution Dilution Calculator (C1V1 = C2V2)

Calculate the volume needed to dilute a stock solution to a target concentration.

Result

Stock Solution Needed (V1)
50 mL
Diluent (Water/Solvent) to Add
450 mL

About the Dilution Calculator

This calculator applies the dilution equation C1V1 = C2V2 to determine how much of a stock solution and how much diluent are needed to reach a target concentration and volume. It serves lab technicians, students, and anyone preparing a diluted solution from a more concentrated stock.

How It Works

You enter the stock solution's concentration (C1), the target concentration you want to reach (C2), and the target final volume (V2) in milliliters. The calculator solves for the volume of stock solution needed (V1), then subtracts that from the target volume to find how much diluent, such as water, needs to be added.

V1 = (C2 * V2) / C1. Diluent volume = V2 - V1

Formula & Methodology

The dilution equation rests on the fact that the total amount of solute stays constant when diluent is added; only the concentration and volume change. Rearranging C1V1 = C2V2 to solve for the unknown stock volume gives V1 = (C2 * V2) / C1. Once V1 is known, the remaining volume needed to reach V2 is simply V2 minus V1, and that remainder is the amount of diluent to add.

Examples

Preparing a working solution from concentrated stock

Starting from a 10x stock concentration and wanting a final 1x concentration in 500 mL total volume, V1 = (1 * 500) / 10 = 50 mL of stock solution, so the remaining 450 mL is added as diluent.

Small-scale reagent dilution

A stock at concentration 4 needs to be diluted to concentration 0.5 in a final volume of 200 mL. V1 = (0.5 * 200) / 4 = 25 mL of stock, meaning 175 mL of diluent is added to reach the full 200 mL.

Advantages

  • Automatically calculates both the stock volume and the diluent volume in one step, rather than requiring a second manual subtraction
  • Detects and flags the case where the target concentration exceeds the stock concentration, which would otherwise silently produce a negative and meaningless diluent volume
  • Works with any consistent concentration units, since C1V1 = C2V2 is a ratio-based equation that does not require a specific unit system as long as C1 and C2 share the same units

Common Mistakes

  • Entering the target final volume as the amount of diluent to add rather than the total finished volume, which the calculator expects as V2
  • Mixing concentration units between C1 and C2, such as one in molarity and the other in percent, which invalidates the ratio
  • Requesting a target concentration higher than the stock concentration, not realizing that a true dilution can only lower concentration, never raise it

Edge Cases to Watch For

  • If the stock concentration C1 is entered as zero or negative, the calculator returns an error, since it would require dividing by zero or produce a physically meaningless result.
  • If the target concentration C2 is higher than the stock concentration C1, the calculated diluent volume would be negative; the calculator catches this and displays a note explaining that dilution isn't possible with those values, while clamping the displayed diluent amount at zero.
  • The calculator assumes the volumes of stock solution and diluent add linearly to reach the final volume, which is a standard simplifying assumption for dilute solutions but is not exactly true for all solute-solvent mixtures.

Common Use Cases

  • Laboratory technicians preparing reagent or buffer solutions at a specified working concentration
  • Students completing dilution problems for chemistry or biology coursework
  • Researchers scaling a stock solution to a specific final volume for an experiment
Written & fact-checked by the Calculateus TeamLast updated August 5, 2026How we verify our formulas

Frequently asked questions

What is C1V1 = C2V2?

It's the dilution equation: the concentration times volume before dilution equals the concentration times volume after, since the total amount of solute doesn't change when you add solvent - only its concentration changes as the volume increases.

Conclusion

C1V1 = C2V2 is one of the most frequently used relationships in a wet lab, and this calculator removes the manual algebra and subtraction needed to find both the stock and diluent volumes. Its built-in check for an impossible target concentration helps prevent an obviously invalid dilution from being carried into the lab.