# Potato Paradox Calculator

URL: https://speedycalculator.com/calculators/math/potato-paradox/
Last updated: 2026-10-30

> The potato paradox calculator shows how a small drop in water percentage causes a huge drop in total mass: 100 kg of potatoes that are 99% water weigh only 50 kg once they are 98% water.

## Inputs

- Initial mass (kg)
- Initial water content (%)
- New water content (%)

## Results

- Dry mass (unchanged)
- New total mass
- Water lost
- Water remaining

## Formula

```
Dry mass = M·(1 − w₁),  new mass = dry mass / (1 − w₂)
```

## Explanation

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

FieldWhat to enterInitial massIn kgInitial water contentIn %New water contentIn %

### 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)50257537.51005012562.515075200100

## 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.

## FAQ

**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.


## Sources

- [Wolfram MathWorld – Potato paradox](https://mathworld.wolfram.com/PotatoParadox.html)