C1V1 Dilution Calculator
C1V1 = C2V2 is the working equation behind almost every dilution on a plant floor or in a QC lab. This calculator solves it for the stock volume and the diluent volume and checks that the target is actually achievable.
Your numbers
Concentration of the stock, in any unit as long as C2 uses the same one.
Concentration you want after dilution.
Total volume of diluted solution you need.
Your results
Assumes volumes are additive. For strong acids, bases and some solvents, volumes are not exactly additive and heat is released. Always add concentrate to diluent slowly, wearing the PPE listed on the SDS.
Stock and diluent volume vs final volume
Sweeps Final volume needed (V2) from 1 to 100, holding your other inputs fixed.
Digitise your dilution and make-up recipes
Optional: a short review of moving make-up solutions and dilution instructions into controlled ERP or MES recipes.
Optional. The tool and every export work without this. No spam.
How to use it
Enter the stock concentration C1, the target concentration C2 and the final volume V2. The calculator gives V1, the volume of stock to measure, and the diluent to add so the total equals V2. Concentration units are free as long as C1 and C2 use the same one (percent, molarity, g/L, ppm). Volume units come back in whatever you entered for V2. If C2 is higher than C1 the validity flag drops to zero because dilution can only lower concentration.
- Make up to the final volume in a graduated vessel rather than adding a fixed volume of diluent.
- Label the container with concentration, date and preparer.
- Use a fresh calculation if the stock concentration changes by lot.
The equation and its limits
The amount of solute is conserved, so C1 times V1 equals C2 times V2. Rearranged, V1 equals C2 times V2 divided by C1. The dilution factor is C1 divided by C2, so a 37 percent stock diluted to 5 percent is a factor of 7.4, one part stock plus 6.4 parts diluent. The equation assumes ideal additivity of volumes; with concentrated sulfuric acid, caustic or ethanol-water blends the final volume is slightly less than the sum, which is why you top up to the mark.
Worked example and mistakes
To make 20 L of 5 percent solution from a 37 percent stock, V1 is 5 x 20 / 37 = 2.70 L of stock and 17.30 L of diluent. Common errors: mixing weight percent with volume percent, using molarity for one value and percent for the other, adding the full V2 of diluent on top of the stock, and forgetting that the stock label may be a nominal value that drifts with age or evaporation.
- Confirm the stock assay on the certificate of analysis.
- Check density if mixing weight percent by volume.
- Add acid to water, never water to acid.
Frequently Asked Questions
What does C1V1 = C2V2 mean?
It states that the amount of solute before dilution (stock concentration times stock volume) equals the amount after dilution (final concentration times final volume). It works for any consistent concentration unit because the solute amount is unchanged by adding diluent.
Can I use it for percent solutions?
Yes, if both values are the same type, for example both weight percent or both volume percent. Mixing weight percent and volume percent without a density correction gives wrong answers, especially for dense or viscous stocks.
Why can the final volume be less than stock plus diluent?
Some mixtures contract, such as ethanol and water or strong acids and water. That is why procedures say to dilute to a mark in a calibrated vessel. For routine plant dilutions the error is small, but for assays it matters.
Is this safe for acids and bases?
The arithmetic is, but the handling needs care. Strong acids and bases release heat when diluted. Follow your SDS and site procedure, add concentrate slowly to diluent with stirring, and wear the specified PPE.
If dilution recipes are scattered across spreadsheets and paper batch sheets, Netray can help move them into your ERP or MES as controlled, auditable formulas.
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