Solution Dilution Calculator
Calculate dilution volumes and concentrations using the C1V1 = C2V2 equation. Solve for any unknown variable with step-by-step solutions.
Solution Dilution Calculator
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Formula: C1 x V1 = C2 x V2
Worked example — Use 41.67 mL of stock, add 458.33 mL water
Formula
C1 x V1 = C2 x V2
The dilution equation states that the product of concentration and volume is conserved. C1 and V1 are the initial concentration and volume, while C2 and V2 are the final concentration and volume after dilution.
Worked Examples
Example 1: Standard Lab Dilution
Problem:You have a 12 M HCl stock and need 500 mL of 1 M HCl. How much stock do you need?
Solution:C1V1 = C2V2 12 x V1 = 1 x 500 V1 = 500 / 12 = 41.67 mL Add 41.67 mL stock to 458.33 mL water
Result:Use 41.67 mL of stock, add 458.33 mL water
Example 2: Buffer Dilution
Problem:Dilute 10 mL of 5x PBS to 1x. What is the final volume?
Solution:C1V1 = C2V2 5 x 10 = 1 x V2 V2 = 50 / 1 = 50 mL Add 40 mL water to 10 mL of 5x PBS
Result:Final volume = 50 mL (add 40 mL water)
Frequently Asked Questions
What is the dilution equation C1V1 = C2V2?
The dilution equation C1V1 = C2V2 is a fundamental chemistry formula that relates the concentration and volume of a stock solution (C1, V1) to the concentration and volume of the diluted solution (C2, V2). It works because the amount of solute (moles) remains constant during dilution — you are only adding more solvent. The equation assumes that the volumes are additive and the solution behaves ideally, which is a good approximation for most laboratory dilutions.
How do you perform a serial dilution?
A serial dilution involves making a series of successive dilutions from a single stock solution. Each dilution uses a fixed dilution factor, typically 1:2, 1:5, or 1:10. For a 1:10 serial dilution, take 1 mL of the previous solution and add 9 mL of solvent to make 10 mL total. After n dilutions of factor f, the final concentration is the original concentration divided by f raised to the power n. Serial dilutions are essential in microbiology for plate counts and in immunology for antibody titrations.
What are common mistakes in dilution calculations?
The most common mistake is confusing the volume of solvent to add with the final volume. If C1V1 = C2V2 gives V2 = 100 mL and V1 = 10 mL, you add 90 mL of solvent (not 100 mL). Another common error is using inconsistent units between concentration and volume values. Always ensure that C1 and C2 use the same concentration unit, and V1 and V2 use the same volume unit. Also be careful that C2 must always be less than C1 for a dilution.
When does C1V1 = C2V2 not apply?
This equation does not apply when a chemical reaction changes the amount of solute, when mixing concentrated solutions where volumes are not additive (like mixing ethanol and water), or when the solute dissociates or associates differently at different concentrations. It also fails for gases where pressure and temperature must be considered. For very concentrated solutions, activity coefficients deviate significantly from unity and the simple dilution equation becomes inaccurate.
What is the correct, safe order of operations when diluting a concentrated acid?
Always add the concentrated acid slowly to the water — never add water to the acid. Concentrated acids like sulfuric acid release a large amount of heat when they mix with water, and if water is added to a small volume of concentrated acid, the heat can boil that small volume almost instantly, spattering hot corrosive acid outward. Adding acid gradually to a larger, cooler volume of water lets the heat dissipate safely across a much greater volume. This rule ('AAA' — always add acid) is taught before any C1V1 = C2V2 calculation is performed with concentrated acids or bases in a working lab.
How do you manage stock solutions to avoid repeated dilution errors?
Well-run labs label every stock solution with its exact concentration, preparation date, and preparer's initials, and store concentrated stocks separately from working dilutions to avoid mix-ups. Before every dilution calculation, verify the stock concentration on the label rather than assuming it matches a previous batch, since even small formulation or lot differences change C1 and therefore every downstream V1 calculation. Many labs also keep a dilution log recording each C1V1 = C2V2 calculation performed, which makes it fast to spot an error if a later titration or assay gives an unexpected result.
Can C1V1 = C2V2 be used with percent or ppm units instead of molarity?
Yes. The equation only requires that the amount of solute is conserved, so it works with molarity, % w/v, mg/mL, ppm, or a fold-strength label such as 5x buffer — provided C1 and C2 share one unit and V1 and V2 share another. Diluting a 500 ppm standard to 50 ppm in 100 mL needs V1 = (50 × 100)/500 = 10 mL of standard topped up to 100 mL. Mixing units, such as molarity on one side and % w/v on the other, is what breaks the calculation.
How is the dilution factor defined, and why is the 1:10 notation ambiguous?
The dilution factor is the final volume divided by the stock volume, V2/V1, which equals C1/C2. Taking 10 mL of stock to a final 100 mL is a factor of 10, so the concentration drops tenfold. The ambiguity lies in ratio notation: some protocols read 1:10 as one part stock made up to ten parts total (factor 10), others as one part stock plus ten parts diluent (factor 11). Stating the final volume, as Solution Dilution Calculator does, removes the guesswork — important when factors compound across a serial dilution.
What is the difference between molarity and molality when diluting?
Molarity is moles of solute per litre of solution, so it depends on the final volume and shifts slightly with temperature as the solution expands or contracts. Molality is moles per kilogram of solvent and is temperature-independent because mass does not change. The dilution equation is written in volume terms and therefore applies to molarity and other per-volume units. For colligative-property work such as freezing-point depression, or for solutions used across a wide temperature range, convert to molality instead.
Which glassware gives an accurate dilution, and how should the final volume be reached?
Measure the stock with a volumetric or calibrated air-displacement pipette, deliver it into a volumetric flask of the target final volume, then add solvent until the meniscus sits on the graduation mark with the flask at the calibration temperature. Do not measure the solvent separately and add it, because V2 is the total solution volume, not stock plus solvent, and volume contraction on mixing makes those two differ. A graduated cylinder is typically an order of magnitude less accurate than a volumetric flask, so reserve it for rough working dilutions.
References
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Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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