How It Works
This calculator works in 4 steps.
Enter the component volumes
Type V_A and V_B as measured before mixing.
Enter the measured final volume
Type V_mix read in a graduated container, or type component masses and mixture density.
Compute the contraction
The calculator returns ΔV = V_A + V_B − V_mix and the percent change.
Read the true concentration
The calculator divides the solute amount by V_mix, not by V_A + V_B.
The Formula
The formula divides the solute amount by the real final volume.
C = C_A × V_A / V_mixV_mix = (m_A + m_B) / ρ_mix%ΔV = 100 × (V_A + V_B − V_mix) / (V_A + V_B)- V_A / V_B:
- Component volumes
- V_mix:
- Real mixture volume
- m_A / m_B:
- Component masses
- ρ_mix:
- Mixture density
52 mL ethanol plus 48 mL water gives about 96.3 mL. Ethanol content is 52 / 96.3 = 54.0% v/v, not 52%.
Conversion Table
The conversion table shows approximate volume contraction for 5 liquid pairs at about 20 °C.
| Mixture | Component volumes | Sum | Measured final | Contraction |
|---|---|---|---|---|
| Ethanol + water | 52 + 48 mL | 100 mL | 96.3 mL | 3.7% |
| Ethanol 95% + water (to 70%) | 73.7 + 30 mL | 103.7 mL | 100 mL | 3.6% |
| Methanol + water | 50 + 50 mL | 100 mL | 96.5 mL | 3.5% |
| Sulfuric acid 98% + water | 10 + 90 mL | 100 mL | 98.6 mL | 1.4% |
| Isopropanol + water | 70 + 30 mL | 100 mL | 97.4 mL | 2.6% |
Values are approximate and change with temperature and composition.
What Is the Nonadditive Volume Dilution Calculator?
The Nonadditive Volume Dilution Calculator is a tool that computes concentration from a measured or modeled final volume, rather than from the sum of the component volumes. Many liquid pairs shrink on mixing, so V_A + V_B is larger than the real final volume.
Ethanol-water mixtures show volume contraction of about 3% to 4% near 50% to 60% ethanol. Sulfuric acid and water, methanol and water, and concentrated sugar solutions show the same effect. The calculator takes the measured final volume, or a density-based estimate, and returns the true concentration and the contraction percent.
Common Uses
There are 5 main uses of this calculator.
Alcohol preparation
Users correct ethanol and isopropanol strengths after mixing.
Acid dilution
Chemists correct sulfuric acid dilutions for contraction and heat.
Solvent blends
Chromatographers prepare methanol-water mobile phases by volume.
Sugar syrups
Food makers correct concentrated syrup volumes.
Teaching labs
Instructors show contraction with the 52 + 48 ethanol demonstration.