How It Works
This calculator works in 4 steps.
Enter the stock concentration (C₁)
Type the concentration of the concentrate.
Enter the target concentration (C₂)
Type the required strength. C₂ must be lower than C₁.
Enter the fixed diluent volume (V_d)
Type the volume of water or buffer already in the container.
Read the stock volume and total
The calculator returns V₁ = C₂V_d / (C₁ − C₂) and the total volume V_d + V₁.
The Formula
The formula divides the target concentration times the diluent volume by the concentration difference.
C₁ × V₁ = C₂ × (V₁ + V_d)V₁ = (C₂ × V_d) / (C₁ − C₂)V₂ = V₁ + V_d- V₁:
- Stock volume to add
- V_d:
- Fixed diluent volume
- C₁:
- Stock concentration
- C₂:
- Target concentration
A bottle holds 200 mL of water and needs a 1× solution from 5× concentrate. V₁ = 1 × 200 / (5 − 1) = 50 mL. The bottle then holds 250 mL of 1× solution.
Conversion Table
The conversion table shows the stock volume and resulting total volume for 6 fixed diluent amounts (any matching concentration unit).
| Stock (C₁) | Target (C₂) | Diluent on hand | Stock to add | Total volume |
|---|---|---|---|---|
| 10 | 1 | 90 mL | 10 mL | 100 mL |
| 5 | 1 | 200 mL | 50 mL | 250 mL |
| 100 | 1 | 99 mL | 1 mL | 100 mL |
| 2 | 0.5 | 30 mL | 10 mL | 40 mL |
| 50 | 2 | 480 mL | 20 mL | 500 mL |
| 1,000 | 10 | 495 mL | 5 mL | 500 mL |
What Is the Fixed Diluent Volume Calculator?
The Fixed Diluent Volume Calculator is a dilution tool that returns the stock volume to add to a set amount of diluent already in a container, so the mixture reaches a target concentration. The tool fits cases where the diluent is pre-measured, such as a 500 mL bottle of water, a filled tank, or a 9 mL dilution blank.
The final volume in this method is the diluent volume plus the stock volume, so the stock volume appears on both sides of the dilution equation. The calculator solves this rearranged form and reports the total volume produced. Results assume additive volumes.
Common Uses
There are 5 main uses of this calculator.
Microbiology dilution blanks
Microbiologists add sample to 9 mL or 99 mL pre-filled blanks for 1:10 and 1:100 dilutions.
Pre-filled bottles
Users add concentrate to a factory-filled 500 mL (16.9 US fl oz) bottle of water.
Tank and bucket mixing
Operators add concentrate to a tank holding a known water volume.
Media bottle supplements
Cell culture staff add a supplement to a 500 mL medium bottle.
Field test kits
Field technicians add reagent to a fixed volume of sample water.