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Potato paradox calculator

Find the mass of potatoes after their water percentage changes, keeping the dry solids fixed. Compare water loss with total mass loss.

Calculator

Final total mass
50
Dry solids
1
Initial water mass
99
Final water mass
49
Water lost (negative means gained)
50

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How this calculator works

The unchanged quantity is dry solids, rather than water percentage. Multiply the initial mass by its dry fraction to find the solids. Divide those solids by the new dry fraction to recover the new total. This idealised model assumes no solids are added or lost and ignores changes in composition other than water.

Formula

Dry mass D = M₁(1 - w₁). Final mass M₂ = D/(1 - w₂). Water lost = M₁ - M₂.

Worked example

An 80 kg batch at 75% water contains 20 kg of dry material. At 50% water those solids are half the total, so the batch weighs 40 kg and has lost 40 kg of water.

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Frequently asked questions

Why can a small percentage change cause a large mass change?

Near 100% water, the dry fraction is small. Doubling that dry fraction halves the total mass when the solids stay fixed.

Can the final water content be higher?

Yes. The result then describes water being added, and water lost becomes negative.

Does this estimate actual drying time?

No. Drying speed depends on airflow, temperature, humidity and the material. This calculation is a mass balance only.

Sources

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