Calculate solution strength, molarity, dilution, reconstitution, and serial dilution from mass, volume, concentration, and molecular weight.
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Solution Strength Formula
The calculator supports percent strength, reconstitution, molarity, dilution, and serial dilution. The three percent conventions are defined below.
Weight/volume strength (% w/v):
Weight/weight percent (% w/w):
Volume/volume percent (% v/v):
Variables:
- mass of solute: the dissolved substance, by mass
- volume of solute: the dissolved liquid, by volume
- final volume of solution: total volume after mixing, not just solvent added
- total mass of solution: solute mass plus solvent mass
- density: if a liquid solute is weighed, first calculate its volume separately as mass / density
Select the quantity to solve and enter the displayed known values. Percent modes use solute mass or volume and the final solution amount. Reconstitution uses mass = concentration × final volume; molarity additionally uses molar mass. Dilution uses C1V1 = C2V2 with compatible mass or molar concentrations. Serial dilution uses Cn = C0 / factorn with whole-number steps. Supported units are µg, mg, g, kg; µL, mL, L; molar concentrations; and the displayed mass concentrations. For a weighed liquid solute, divide mass by density separately before entering solute volume.
Reference Values
Common solution strengths used in labs, kitchens, and industry:
| Solution | Type | Strength |
|---|---|---|
| Normal saline | w/v | 0.9% (9 g/L NaCl) |
| D5W (dextrose IV) | w/v | 5% (50 g/L) |
| Household bleach | w/w | ~5–6% NaOCl |
| Hydrogen peroxide (drugstore) | w/w | 3% |
| Isopropyl alcohol (rubbing) | v/v | 70% or 91% |
| Ethanol (denatured cleaner) | v/v | 95% |
| Concentrated HCl | w/w | ~37% |
| Concentrated H₂SO₄ | w/w | ~98% |
Approximate reference densities for separate mass-to-volume conversions. Use the actual reagent density at its measurement temperature for precise work; acid percentages below are w/w. Acid-stock density converts stock-solution mass to stock-solution volume, not pure-acid equivalent volume.
| Liquid | Approximate density (g/mL at 20°C) |
|---|---|
| Water | 0.9982 |
| Ethanol | 0.789 |
| Methanol | 0.792 |
| Isopropanol | 0.786 |
| Acetone | 0.791 |
| Glycerol | 1.261 |
| Concentrated H₂SO₄ (98%) | 1.840 |
| Concentrated HCl (37%) | 1.190 |
Worked Examples
Example 1 — w/v. You need 250 mL of 0.9% saline. How much NaCl?
mass = (0.9 / 100) × 250 mL × 1 g/mL = 2.25 g NaCl. Dissolve in water and bring the final volume to 250 mL.
Example 2 — v/v with density. You have 55.2 g of ethanol (density 0.789 g/mL) and want to dilute to 100 mL final volume. What is the resulting % v/v?
Solute volume = 55.2 / 0.789 = 69.96 mL. % v/v = 69.96 / 100 × 100 = 69.96%, essentially 70% v/v.
FAQ
Is % w/v the same as % w/w? No. w/v uses solution volume in the denominator (g per 100 mL), while w/w uses solution mass (g per 100 g). They only match when the solution density is exactly 1 g/mL.
Should I add solvent up to the final volume, or add the listed amount of solvent? Bring the solution up to the final volume. Mixing liquids often causes a small volume change, so adding “solute volume + solvent volume” will not give the right concentration.
Why does my w/w result come out over 100%? You probably entered solvent mass instead of total solution mass. The denominator is solute + solvent combined.
When do I need density for v/v? When the liquid solute is weighed, divide its mass by its density separately to obtain solute volume, then use the v/v mode.
