How It Works
This calculator works in 4 steps.
Enter the stock concentration and volume
Type C₁ and V₁.
Enter the diluent background
Type C_d, the solute concentration already in the diluent.
Enter the diluent volume
Type V_d.
Read both results
The calculator returns the final concentration with background and the value C₁V₁ = C₂V₂ alone predicts.
The Formula
The formula sums solute from stock and diluent and divides by the total volume.
C₂ = (C₁V₁ + C_d V_d) / (V₁ + V_d)V₁ = V₂ (C₂ − C_d) / (C₁ − C_d)- C₁ / V₁:
- Stock concentration and volume
- C_d / V_d:
- Diluent background concentration and volume
- C₂:
- Final concentration
10 mL of 10 mM calcium added to 90 mL of water carrying 1 mM calcium gives (100 + 90) / 100 = 1.9 mM, not the 1.0 mM a solute-free calculation predicts.
Conversion Table
The conversion table compares the ideal result with the background-corrected result for 6 cases (shared unit).
| Stock | Diluent background | Stock + diluent | Ideal C₂ | Corrected C₂ |
|---|---|---|---|---|
| 10 | 1 | 10 + 90 mL | 1 | 1.9 |
| 100 | 5 | 5 + 95 mL | 5 | 9.75 |
| 1 | 0.1 | 50 + 450 mL | 0.1 | 0.19 |
| 50 | 2 | 2 + 98 mL | 1 | 2.96 |
| 20 | 0.5 | 25 + 75 mL | 5 | 5.375 |
| 500 | 10 | 1 + 999 mL | 0.5 | 10.49 |
What Is the Nonzero-Diluent Concentration Calculator?
The Nonzero-Diluent Concentration Calculator is a tool that returns the final concentration when the diluent already contains some of the same solute. The calculator adds the solute from the stock and the solute from the diluent before dividing by the total volume.
Standard C₁V₁ = C₂V₂ assumes a solute-free diluent. Real diluents often carry the solute: tap water carries calcium, culture medium carries glucose, and seawater carries sodium. Ignoring that background under-states the final concentration. The calculator shows the result with and without the background so the size of the effect is clear.
Common Uses
There are 5 main uses of this calculator.
Hard water dilution
Users account for minerals in tap water used as diluent.
Media supplements
Cell culture labs add glucose to medium that already holds glucose.
Seawater experiments
Marine labs add salts to natural seawater.
Process water
Plants account for background chloride in make-up water.
Spiked matrices
Analysts add standard to samples with native analyte.