Dilution Calculator
Calculate dilution using the C1V1 = C2V2 formula.
Formula: C1 × V1 = C2 × V2
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What it does
The Dilution Calculator applies the dilution relationship to find any missing value among initial concentration, initial volume, final concentration, and final volume. It is used whenever a stock solution is thinned out with solvent to a lower concentration. The same relationship covers everything from making a 1× working buffer out of a 10× stock to preparing concentration standards for an assay curve.
How it works
Dilution keeps the amount of solute constant while you add solvent, so the product of concentration and volume is conserved: C1 x V1 = C2 x V2. Here C1 and V1 are the stock concentration and volume, C2 and V2 the diluted concentration and volume. The calculator solves for whichever one you leave blank. All concentrations must use the same unit and all volumes the same unit. The equation assumes volumes are additive and solute is conserved. For concentrated acids or very dilute targets, volume contraction is small but real — prepare to the mark in a volumetric flask rather than adding a calculated volume of water.
Worked example
You have 10 M stock and need 500 mL of 2 M solution. Using C1V1 = C2V2: V1 = (C2 x V2) / C1 = (2 x 500) / 10 = 100 mL. Pipette 100 mL of stock and add solvent up to 500 mL final volume. To prepare 1 L of 1× PBS from 10× stock: V1 = (1 × 1000) / 10 = 100 mL of stock, then bring to 1000 mL. Scaled down the same way, 5 mL of 10× stock makes 50 mL of 1×.
When to use it
Use it to work out how much concentrated stock to pipette for a working solution. Use it to find the final concentration after you add a known volume of solvent. Use it to plan serial or one-step dilutions in assays. It also helps verify dilutions made by others: if someone added 50 mL of stock to 450 mL of water, plugging the numbers in confirms the resulting 10-fold dilution.
FAQ
- What is the dilution formula C1V1 = C2V2?
- It states that the moles of solute before and after dilution are equal: initial concentration times initial volume equals final concentration times final volume. Use it to solve for any one unknown.
- Do units matter in the dilution calculator?
- The equation is unit-consistent: keep all concentrations in the same unit (for example mol/L) and all volumes in the same unit (for example mL). You do not need to convert mL to L as long as both volumes match.
- How do I calculate the volume of stock needed for a dilution?
- Rearrange to V1 = (C2 x V2) / C1. This gives the volume of concentrated stock to dilute up to the desired final volume.
- What is a 1 to 10 dilution?
- A 1:10 dilution means one part stock plus nine parts solvent to make ten parts total, lowering the concentration to one tenth of the original.