How It Works
This calculator works in 4 steps.
Choose the flask size (V₂)
Select a volumetric flask volume, such as 100 mL, 250 mL, or 1 L.
Enter stock and target concentrations
Type C₁ and C₂ in the same unit, such as molarity (M).
Read the stock volume (V₁)
The calculator returns V₁ = C₂V₂ / C₁ for transfer with a volumetric or graduated pipette.
Fill to the calibration mark
Add diluent until the meniscus bottom touches the mark at 20 °C (68 °F), then cap and invert 10 to 15 times.
The Formula
The formula uses the flask volume as the fixed final volume.
V₁ = (C₂ × V_flask) / C₁V₂ = V_flask (filled to mark)- V₁:
- Stock volume to place in the flask
- V_flask:
- Nominal volumetric flask volume
- C₁:
- Stock concentration
- C₂:
- Target concentration
To make 1 M hydrochloric acid (HCl) in a 500 mL flask from 12.1 M concentrated HCl, V₁ = 1 × 500 / 12.1 = 41.3 mL. Add the acid to about 300 mL of water in the flask, cool, then fill to the mark.
Conversion Table
The conversion table lists the stock volume per flask size for 6 molar dilutions.
| Stock (C₁) | Target (C₂) | Flask size | Stock volume (V₁) | Diluent |
|---|---|---|---|---|
| 1 M | 0.1 M | 100 mL | 10 mL | Fill to mark |
| 12.1 M | 1 M | 500 mL | 41.32 mL | Fill to mark |
| 10 M | 1 M | 1 L | 100 mL | Fill to mark |
| 100 M | 2 M | 250 mL | 5 mL | Fill to mark |
| 5 M | 0.05 M | 50 mL | 0.5 mL | Fill to mark |
| 18 M | 0.5 M | 2 L | 55.56 mL | Fill to mark |
What Is the Make-to-Volume Calculator?
The Make-to-Volume Calculator is a dilution tool that returns the stock volume to place in a volumetric flask before filling the flask to its calibration mark. The tool follows the q.s. (quantum satis, "as much as suffices") method, so the final volume is exact even when the liquids do not add linearly.
Make-to-volume preparation is the standard method in analytical chemistry and pharmacy compounding. The calculator matches the result to Class A flask sizes from 10 mL to 2 L (0.53 US gal) and states the fill step instead of a diluent volume.
Common Uses
There are 5 main uses of this calculator.
Analytical standards
Analysts prepare calibration solutions in Class A flasks for HPLC and ICP-MS.
Acid dilution
Chemists dilute concentrated acids where heat and volume change make additive estimates inaccurate.
Titrant preparation
Labs make standard titrants, such as 0.1 M sodium hydroxide (NaOH), to a fixed volume.
Pharmacy compounding
Pharmacists make solutions q.s. to a labeled final volume.
Nonadditive mixtures
Users prepare ethanol-water and solvent blends where volumes contract on mixing.