Dilution: formula
Enter the stock concentration, the target concentration and the final volume you need, in units that match: the two concentrations must be in the same units, such as molarity or percent, and the volume in any unit. The formula C1 times V1 equals C2 times V2 gives the volume of stock, and the rest of the final volume is diluent, usually water. Check that the target is lower than the stock, since dilution cannot increase concentration.
Dilution: worked example
| Stock concentration (C₁) | 12 |
|---|---|
| Target concentration (C₂) | 1.5 |
| Final volume (V₂) | 500 |
| Stock volume to use (V₁) | 62.5 |
| Diluent to add | 437.5 |
The formula assumes volumes add, which is approximately true for dilute solutions but not always for concentrated ones or mixtures of alcohol and water. Temperature affects volume. Serial dilutions accumulate error.
Safety data and protective equipment are essential for hazardous chemicals, and this calculator is not a substitute for lab procedures.
Dilution: changing Stock concentration (C₁)
| Stock concentration (C₁) | Stock volume to use (V₁) | Diluent to add |
|---|---|---|
| 10 | 75 | 425 |
| 11 | 68.2 | 431.8 |
| 12 (example) | 62.5 | 437.5 |
| 13 | 57.7 | 442.3 |
| 14 | 53.6 | 446.4 |
Dilution: compare input ranges
| Input | Tested from | To | Stock volume to use (V₁): low input | Stock volume to use (V₁): high input | Swing |
|---|---|---|---|---|---|
| Final volume (V₂) | 450 | 550 | 56.3 | 68.8 | 12.5 (20%) |
| Target concentration (C₂) | 1.4 | 1.7 | 58.3 | 70.8 | 12.5 (20%) |
| Stock concentration (C₁) | 11 | 13 | 68.2 | 57.7 | 10.5 (17%) |
Dilution: individual input comparisons
| Input | Value | Stock volume to use (V₁) | Diluent to add |
|---|---|---|---|
| Stock concentration (C₁) | 10 | 75 | 425 |
| 11 | 68.2 | 431.8 | |
| 12 | 62.5 | 437.5 | |
| 13 | 57.7 | 442.3 | |
| 14 | 53.6 | 446.4 | |
| Target concentration (C₂) | 1.2 | 50 | 450 |
| 1.4 | 58.3 | 441.7 | |
| 1.5 | 62.5 | 437.5 | |
| 1.7 | 70.8 | 429.2 | |
| 1.8 | 75 | 425 | |
| Final volume (V₂) | 400 | 50 | 350 |
| 450 | 56.3 | 393.8 | |
| 500 | 62.5 | 437.5 | |
| 550 | 68.8 | 481.3 | |
| 600 | 75 | 525 |
Dilution: combined input changes
| Stock concentration (C₁) / Target concentration (C₂) | 1.2 | 1.5 | 1.8 |
|---|---|---|---|
| 10 | 60 | 75 | 90 |
| 11 | 54.5 | 68.2 | 81.8 |
| 12 | 50 | 62.5 | 75 |
| 13 | 46.2 | 57.7 | 69.2 |
| 14 | 42.9 | 53.6 | 64.3 |
Dilution: which assumptions move the result?
Dilution: values and definitions
| Quantity and definition | Value used |
|---|---|
| Stock concentration (C₁) | 12 |
| Target concentration (C₂) — In the same unit as the stock concentration. | 1.5 |
| Final volume (V₂) — The total volume you want to end up with, in any unit. | 500 |
| Stock volume to use (V₁) | 62.5 |
| Diluent to add | 437.5 |
Dilution: half and double Final volume (V₂)
| Final volume (V₂) | Stock volume to use (V₁) |
|---|---|
| 250 | 31.3 |
| 500 | 62.5 |
| 1,000 | 125 |
Common error: Adding the full final volume of water to the stock. That overshoots the volume and leaves the solution weaker than the target.
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Diluting a solution keeps the amount of the dissolved substance fixed while the volume grows, so concentration times volume stays equal before and after. To make 500 milliliters at 1.5 from a stock at 12, you need 62.5 milliliters of stock and 437.5 of diluent. The same relation covers cleaning concentrates, lab reagents and garden sprays.
Add the stock to the diluent up to the final volume, not the other way around by volume. The final volume is what counts, not the volume of water added.
Compute concentrations on the molarity and ppm calculators, pH on the pH calculator, and volumes on the volume converter. The density and percent yield calculators cover other lab quantities, and the percentage and proportion pages help with scaling.
What is the dilution formula?
C1 times V1 equals C2 times V2, meaning the amount of solute stays the same when you add solvent, so concentration times volume is constant.
Why add acid to water and not water to acid?
Diluting concentrated acid releases heat, and adding it slowly to water spreads the heat and avoids dangerous splattering.
Can I make a solution more concentrated by dilution?
No. Dilution only lowers concentration. To raise it, add more solute or remove some of the solvent, for example by evaporation.