Potato Calculator
Solve the famous Potato Paradox and explore dehydration mathematics
The Potato Paradox Calculator
Choose between the classic riddle or custom calculations
🥔 The Classic Potato Paradox
Here's the riddle:
"You have 100 kg of potatoes that are 99% water. After dehydration, they become 98% water. What is their new weight?"
Most people guess around 99 kg or 101 kg - what do you think?
Initial weight of the object
Water content before dehydration
Water content after dehydration
Dehydration Results
Before Dehydration
After Dehydration
💡 The Paradox Explained
The dry mass stays constant at 1.00 kg, but it now represents 2.0% instead of 1.0% of the total. This seemingly small change in water percentage causes a dramatic change in total mass!
Step-by-Step Solution
Calculate initial water mass
99% of 100 kg = (99/100) × 100
Initial water mass = 99.00 kg
Calculate dry mass (remains constant)
100 kg - 99.00 kg
Dry mass = 1.00 kg
Calculate final total mass
Dry mass ÷ (100% - 98%) = 1.00 ÷ 0.02
Final total mass = 50.00 kg
Calculate final water mass
50.00 kg - 1.00 kg
Final water mass = 49.00 kg
Example Problems
Example 1: Classic Potato Paradox
Problem: 100 kg potatoes, 99% → 98% water
Solution:
Initial water: 99 kg, Dry mass: 1 kg
Final mass = 1 kg ÷ (100% - 98%) = 1 ÷ 0.02 = 50 kg
Result: 50 kg final mass (50% reduction!)
Example 2: Extreme Dehydration
Problem: 50 kg potatoes, 95% → 80% water
Solution:
Initial water: 47.5 kg, Dry mass: 2.5 kg
Final mass = 2.5 kg ÷ (100% - 80%) = 2.5 ÷ 0.20 = 12.5 kg
Result: 12.5 kg final mass (75% reduction)
Example 3: Small Change, Big Impact
Problem: 200 kg potatoes, 90% → 89% water
Solution:
Initial water: 180 kg, Dry mass: 20 kg
Final mass = 20 kg ÷ (100% - 89%) = 20 ÷ 0.11 = 181.8 kg
Result: 181.8 kg final mass (9% reduction from 1% water change)
Why the Paradox?
Percentage Confusion
Small percentage changes can have huge absolute effects
Constant Dry Mass
The dry mass never changes during dehydration
Ratio Change
Changing the water-to-dry ratio changes everything
The Mathematics
Key Formula
Final Mass = Dry Mass ÷ (100% - Final Water %)
Why 99% → 98%?
Dry mass goes from 1% to 2% of total, doubling its proportion!
Inverse Relationship
As water % decreases, the multiplier effect increases exponentially
Real-World Uses
Food dehydration and preservation
Agricultural crop water content analysis
Industrial drying process optimization
Understanding percentage vs. absolute changes
Teaching mathematical paradoxes
Understanding the Potato Paradox
What Makes It a Paradox?
The potato paradox seems to challenge our intuition about weight and percentage. When we remove water from potatoes, we expect the weight to decrease slightly. However, the mathematical reality shows that a small change in water percentage can lead to dramatic changes in total weight.
The Key Insight
The paradox arises because we're looking at percentages of the total mass, not absolute amounts. The dry mass remains constant, but its percentage of the total changes dramatically. When dry mass goes from 1% to 2% of the total, the total mass must halve to maintain this relationship.
Mathematical Foundation
If water = W% of total mass M:
Water mass = (W/100) × M
Dry mass = M - (W/100) × M = M(1 - W/100)
Since dry mass is constant, this creates the paradox!
Practical Applications
This paradox has real applications in food science, agriculture, and manufacturing. Understanding how water content affects total mass is crucial for processes like food dehydration, crop storage, and quality control.
Extreme Examples of the Paradox
Dramatic Change
99.9% → 99% water
100 kg → 10 kg
90% weight reduction!
From 0.1% to 1% dry mass
Moderate Change
95% → 90% water
100 kg → 50 kg
50% weight reduction
From 5% to 10% dry mass
Small Change
80% → 75% water
100 kg → 80 kg
20% weight reduction
From 20% to 25% dry mass