Dilution Calculator: Solve C1V1 = C2V2 Instantly

How to use the dilution calculator

1. Enter the initial concentration (C1) and initial volume (V1) of your stock solution.
2. Enter either the final concentration (C2) or the final volume (V2) you need.
3. Leave exactly one field blank so the dilution calculator can solve for it.
4. Read the result below the form. The calculation uses the formula C1 x V1 = C2 x V2.

How the C1V1 = C2V2 formula works

The dilution equation states that the amount of solute stays constant before and after adding solvent. Concentration multiplied by volume gives the total quantity of solute, so C1 x V1 = C2 x V2.

For example, if you have a 10 M stock solution and need 500 mL of a 1 M working solution, solve for V1: V1 = (C2 x V2) / C1 = (1 x 500) / 10 = 50 mL. You would measure 50 mL of the stock and add enough solvent to reach 500 mL total.

The formula assumes volumes are additive, which is a good approximation for dilute aqueous solutions but may introduce small errors with concentrated acids or organic solvents where mixing causes contraction or expansion.

Common dilution reference table

This table shows typical scenarios solved with the dilution calculator. All rows assume consistent units throughout.

Unit consistency matters

The dilution calculator does not convert units automatically. You must use the same unit for both concentrations and the same unit for both volumes. If C1 is in molarity (M), then C2 must also be in molarity. If V1 is in milliliters, V2 must be in milliliters.

Mixing units is the most common source of error. For instance, entering C1 as 1 mol/L and V1 as 500 mL while setting C2 as 0.5 mmol/mL will give a numerically correct but physically meaningless answer unless you first normalize everything to matching units.

When working with percent concentrations, ensure both percentages are the same type: weight/weight (w/w), weight/volume (w/v), or volume/volume (v/v). A 10% w/v solution diluted to 100 mL total volume requires different handling than a 10% v/v solution.

Serial dilutions

A serial dilution applies the C1V1=C2V2 principle repeatedly. Each step uses the diluted solution from the previous step as the new stock. This technique is standard in microbiology for reducing bacterial counts to a countable range and in biochemistry for creating standard curves.

For a 10-fold serial dilution across five tubes, you transfer 1 mL into 9 mL of solvent each time. After five steps the overall dilution factor is 10⁵, or 100,000. You can verify each step with this dilution calculator by setting C1 to the previous tube's concentration and solving for C2.

Always mix thoroughly between transfers. Incomplete mixing at an early step compounds through every subsequent step, producing large errors in the final concentration.

Practical applications

Laboratory technicians use the dilution equation daily to prepare buffers, reagents, and standards from concentrated stocks. Pharmacists apply it when compounding medications to achieve precise dosages from bulk ingredients.

In agriculture, concentrated fertilizers and pesticides are diluted to safe application rates. Aquarium hobbyists use it to adjust water chemistry parameters like salinity or mineral hardness without shocking fish.

The math is identical to what you might encounter in a percentage calculator when converting between percentage-based and molar concentrations, though the dilution calculator handles the algebra directly.

Laboratory safety

The calculator gives the arithmetic only. For acids, bases and other hazardous chemicals follow your lab protocol and safety data sheet, wear suitable protection, and add concentrated stock to the diluent (not the other way round) unless your procedure says otherwise. Check the result against your own records before using it for anything that matters.

Worked examples

Each result below was produced by the same code the tool runs, so you can check your own numbers against them.