The potato paradox surprises almost everyone. The key is that the dry matter stays the same: going from 99% to 98% water doubles the dry share from 1% to 2%, so the total must halve. The same reasoning applies to drying fruit, timber and concentration problems.
How to use the Potato Paradox Calculator
- Initial mass
- Initial water content
- New water content
Results update as you type, and everything is calculated in your browser.
How it works
Enter the initial mass, the initial water percentage and the new water percentage.
Inputs explained
| Field | What to enter |
|---|---|
| Initial mass | In kg |
| Initial water content | In % |
| New water content | In % |
What each result means
- Dry mass (unchanged) = [Initial mass]×(1 – [Initial water content]÷100)
- New total mass = [Dry mass (unchanged)]÷(1 – [New water content]÷100)
- Water lost = [Initial mass] – [New total mass]
- Water remaining = [New total mass] – [Dry mass (unchanged)]
Example values
How the main result changes when Initial mass changes and everything else stays at the example values above:
| Initial mass (kg) | New total mass (kg) |
|---|---|
| 50 | 25 |
| 75 | 37.5 |
| 100 | 50 |
| 125 | 62.5 |
| 150 | 75 |
| 200 | 100 |
Formula
Dry mass = M·(1 − w₁), new mass = dry mass / (1 − w₂)
Worked example
Inputs — Initial mass: 100 kg; Initial water content: 99 %; New water content: 98 %.
Results — Dry mass (unchanged) = 1 kg; New total mass = 50 kg; Water lost = 50 kg; Water remaining = 49 kg.
Key terms
- Dry matter
- The part of the mass that is not water.
Frequently asked questions
Why do the potatoes lose half their weight?
The dry part goes from 1% to 2% of the total, so the total halves.
Is it really a paradox?
No – just counter-intuitive; it is a veridical paradox.
Does it work for other foods?
Yes – any drying process with constant dry matter.
What if the water drops to 50%?
100 kg becomes just 2 kg.