Calculate anhydrous basis, as-is assay, target moisture adjustments, and hydrate mass for chemicals from water content, molar mass, and hydration waters.
Anhydrous Basis Formula
The calculator uses one core moisture conversion plus a stoichiometric formula for hydrate masses. Each tab applies a different rearrangement.
As-is to anhydrous basis:
A_anh = A_asis × 100 / (100 − W)
Anhydrous to as-is basis:
A_asis = A_anh × (100 − W) / 100
Change moisture (current to target):
A_target = A_current × (100 − W_target) / (100 − W_current)
Hydrate mass conversion:
M_hydrate = M_anh + n × 18.01528 f = M_anh / M_hydrate mass_anh = mass_hydrate × f
- A_anh = assay reported on an anhydrous (dry) basis
- A_asis = assay on the as-is (wet) sample
- A_current, A_target = assay at current and target moisture levels
- W = water (moisture) content, in percent
- M_anh = molar mass of the anhydrous compound, g/mol
- M_hydrate = molar mass of the hydrated compound, g/mol
- n = number of waters of hydration per formula unit
- f = anhydrous factor, grams of anhydrous per gram of hydrate
- 18.01528 = molar mass of water, g/mol
Assumptions: moisture is reported in weight percent, water is the only volatile component removed on drying, and the analyte itself is non-volatile. Moisture must be less than 100%. For hydrate calculations the compound is assumed to be a pure stoichiometric hydrate with no surface or excess water.
How each tab maps to the formulas:
- As-is → anhydrous divides out the water fraction so the analyte is expressed per unit of dry mass.
- Anhydrous → as-is dilutes the dry-basis value back into the wet sample by multiplying by the dry fraction.
- Change moisture chains the two operations: it lifts the assay to the anhydrous basis, then drops it back down at the target moisture.
- Hydrate mass uses molar masses to compute the anhydrous fraction f, then scales the input mass up or down depending on direction.
Reference Tables
Use these to sanity-check your inputs and outputs. The first table shows how moisture changes the multiplier between as-is and anhydrous values. The second lists common laboratory hydrates.
| Water content (%) | As-is → anhydrous multiplier | Anhydrous → as-is multiplier |
|---|---|---|
| 0.5 | 1.0050 | 0.9950 |
| 2 | 1.0204 | 0.9800 |
| 5 | 1.0526 | 0.9500 |
| 10 | 1.1111 | 0.9000 |
| 15 | 1.1765 | 0.8500 |
| 25 | 1.3333 | 0.7500 |
| 50 | 2.0000 | 0.5000 |
| Hydrate | n (H₂O) | Anhydrous factor f | Water in hydrate (%) |
|---|---|---|---|
| MgSO₄·7H₂O | 7 | 0.4884 | 51.16 |
| CuSO₄·5H₂O | 5 | 0.6394 | 36.06 |
| Na₂CO₃·10H₂O | 10 | 0.3707 | 62.93 |
| Na₂SO₄·10H₂O | 10 | 0.4410 | 55.90 |
| CaCl₂·2H₂O | 2 | 0.7547 | 24.53 |
| C₆H₈O₇·H₂O | 1 | 0.9143 | 8.57 |
| CH₃COONa·3H₂O | 3 | 0.6029 | 39.71 |
Worked Examples and FAQ
Example 1: As-is to anhydrous. A protein sample assays at 82.4% on the as-is basis and contains 6.5% moisture. Anhydrous assay = 82.4 × 100 / (100 − 6.5) = 82.4 / 0.935 = 88.13%.
Example 2: Anhydrous to as-is. A pharmaceutical specification calls for 99.5% on a dried basis. The lot has 2.1% loss on drying. As-is value = 99.5 × (100 − 2.1) / 100 = 99.5 × 0.979 = 97.41%.
Example 3: Change moisture. A grain sample assays 11.0% protein at 14% moisture. To report at 12% moisture: A_target = 11.0 × (100 − 12) / (100 − 14) = 11.0 × 88 / 86 = 11.26%.
Example 4: Hydrate mass. You need 25 g of anhydrous MgSO₄ but only have the heptahydrate. Mass of hydrate = 25 / 0.4884 = 51.19 g.
Why convert to an anhydrous basis at all? Moisture changes from lot to lot and even hour to hour with humidity. Reporting on a dry basis removes that variability so two samples can be compared directly.
Is anhydrous basis the same as dry basis? In most analytical contexts yes. Both refer to the assay calculated as if all water were removed. The term “as-received” or “as-is” refers to the wet sample.
What if my moisture method removes more than just water? The formula assumes loss on drying equals water. If volatile organics also evaporate, the calculated anhydrous value will be biased high. Use a water-specific method like Karl Fischer titration when this matters.
Can I use ppm or mg/g instead of percent? Yes. The assay unit selector handles ppm, mg/g, fraction, and percent. Moisture must still be entered as a percent because it is always a mass fraction of the whole sample.
What does the anhydrous factor f mean? It is the grams of anhydrous compound contained in one gram of the hydrate. For CuSO₄·5H₂O, f = 0.6394, so 1 g of blue crystals delivers 0.6394 g of CuSO₄.
