How It Works
This calculator works in 4 steps.
Enter the stock % w/w
Type the mass percent from the label or certificate.
Enter the target % w/w
Type the required mass percent.
Enter the final mass
Type the total mass of solution in g or kg.
Read the masses
The calculator returns the concentrate mass, the diluent mass, and optional volumes from density.
The Formula
The formula keeps the solute mass constant across the dilution.
w₁ × m₁ = w₂ × m₂m₁ = w₂ × m₂ / w₁m_d = m₂ − m₁- w₁ / w₂:
- Stock and target mass fractions (% w/w)
- m₁:
- Concentrate mass
- m₂:
- Final solution mass
- m_d:
- Diluent mass
To make 1,000 g of 10% w/w HCl from 37% w/w HCl, m₁ = 10 × 1,000 / 37 = 270.3 g of acid. Add the acid to 729.7 g of water.
Conversion Table
The conversion table gives concentrate and diluent masses for 6 % w/w dilutions.
| Stock | Target | Final mass | Concentrate | Diluent |
|---|---|---|---|---|
| 37% w/w | 10% w/w | 1,000 g | 270.3 g | 729.7 g |
| 98% w/w | 20% w/w | 500 g | 102 g | 398 g |
| 50% w/w | 5% w/w | 2,000 g | 200 g | 1,800 g |
| 30% w/w | 3% w/w | 100 g | 10 g | 90 g |
| 25% w/w | 1% w/w | 1,000 g | 40 g | 960 g |
| 70% w/w | 35% w/w | 400 g | 200 g | 200 g |
What Is the Weight/Weight Percent Dilution Calculator?
The Weight/Weight Percent Dilution Calculator is a tool that dilutes solutions expressed as grams of solute per 100 g of solution (% w/w) by mass balance. The calculator returns the mass of concentrate and the mass of diluent, so both components go on a balance.
Mass does not change with temperature or mixing, so % w/w dilution by weighing is exact for nonadditive systems such as concentrated acids, alcohols, and syrups. Concentrated reagents such as 37% hydrochloric acid and 98% sulfuric acid carry % w/w labels. The calculator outputs grams and, when a density is given, the matching volume in mL.
Common Uses
There are 5 main uses of this calculator.
Acid dilution by weight
Chemists dilute 37% HCl and 98% H₂SO₄ on a balance.
Industrial batching
Plants mix concentrates by weight on load cells.
Cosmetic formulation
Formulators state ingredient levels in % w/w.
Food syrups
Food makers dilute syrups labeled in mass percent.
Gravimetric standards
Metrology labs prepare standards by mass for lower uncertainty.