Potato Paradox Calculator — Water Content & Weight Loss
The Potato Paradox shows that a tiny drop in water percentage can cause a surprisingly large weight loss. Enter the initial weight, starting water %, and target water % to see the counterintuitive result — and the exact maths behind it.
lb
%
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Dry matter is conserved — only water is lost
- 1
Initial dry-matter fraction
1 − 99 ÷ 100 = 0,01 - 2
Dry matter mass (constant)
100 × 0,01 = 1 - 3
Final dry-matter fraction
1 − 98 ÷ 100 = 0,02 - 4
Final weight after drying
1 ÷ 0,02 = 50Dry matter is conserved — only water evaporates.
¿Cómo funciona esta calculadora?
The Potato Paradox: dry matter is conserved during drying. New weight = initial weight × (1 − initial water%) ÷ (1 − final water%). A 99% → 98% water drop halves the weight because the dry fraction doubles. Enter any weight and water percentages to see the maths work out.
Fórmula
How this is calculated
The key insight is that the dry matter (the non-water portion) is conserved during drying — only water evaporates. If 100 lb of potatoes are 99% water, the dry matter is just 1 lb. After drying to 98% water, that same 1 lb of dry matter now represents 2% of the total weight, so the total weight must be 1 ÷ 0.02 = 50 lb. The potato lost half its weight by shedding one single percentage point of water.
The general formula is: new weight = W₀ × (1 − Wᵢ/100) ÷ (1 − W_f/100), where Wᵢ is the initial water percentage and W_f is the final water percentage. This result feels paradoxical because we focus on the small change in the water percentage (99% → 98%) rather than the large change in the dry-matter fraction (1% → 2%), which doubled.
This principle applies to any dehydration scenario: food drying, concentrating solutions, shrinkage of concrete, or wood seasoning. Real potatoes are about 78–80% water, not 99%, but the same maths applies — try entering 80% initial and 70% final to see a real-world drying example.
Preguntas frecuentes
The name comes from Martin Gardner's popular version of the puzzle: 100 lb of potatoes are 99% water; after drying, they are 98% water — how much do they weigh? The answer, 50 lb, feels wrong because the water percentage barely changed, yet half the weight vanished. The "paradox" is a cognitive illusion, not a logical contradiction.
Yes — the formula applies to any substance losing only water (or any single solvent). It is used in food technology for drying calculations, in concrete engineering to account for water loss during curing, and in wood seasoning to estimate shrinkage. The more water-rich the initial material, the more dramatic a small drop in water percentage becomes.
Fresh table potatoes contain approximately 78–80% water and 20–22% dry matter. After typical home cooking (boiling) little water is lost. Industrial drying for crisps or freeze-dried potato products reduces the moisture to 2–10%, concentrating the weight dramatically — consistent with the paradox formula.
También conocido como
TG we-Calculate Editorial Team. (2026). Potato Paradox Calculator — Water Content & Weight Loss [Online calculator]. TG we-Calculate. https://we-calculate.com/es/calculator/potato-calculator
TG we-Calculate Editorial Team. "Potato Paradox Calculator — Water Content & Weight Loss." TG we-Calculate. 2026. https://we-calculate.com/es/calculator/potato-calculator.
TG we-Calculate Editorial Team, "Potato Paradox Calculator — Water Content & Weight Loss," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/es/calculator/potato-calculator
@misc{wecalculate_potato_calculator, title = {Potato Paradox Calculator — Water Content & Weight Loss}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/es/calculator/potato-calculator}}, year = {2026}, note = {TG we-Calculate} }
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