Potato Calculator

How to use the potato paradox calculator

What this calculator does

This calculator applies a mass-balance identity to a wet material made of water and dry solids. It estimates the water mass and dry mass before a moisture change, then calculates the new total mass needed for the unchanged dry solids to represent the selected final water percentage. Although the classic example uses potatoes, the same arithmetic can describe fruit, vegetables, dough, timber, sludge, or another material when dry matter is conserved. It is a mathematical estimate, not a food-safety test, moisture-meter reading, or process-engineering specification.

When to use it

Use it to solve the classic 99%-to-98% potato puzzle, check homework involving percentages by mass, estimate yield after idealized dehydration, or explain why percentage-point changes near 100% can have large effects on total mass. The percentage interpretation follows the standard definition of mass percentage as component mass divided by total mass.

How to calculate

1. The calculator opens with a complete demonstration: 100 kg total mass, 99% initial water, and 98% final water. The results and a validated example XLSX workbook are ready immediately.
2. Replace Initial total mass with the starting mass in kilograms. Then enter the starting and ending moisture percentages in Initial water percentage and Final water percentage.
3. Read New total mass first, then compare the water and dry-solids values in the result cards, chart, and table. All views update from the same calculation.
4. Select Download Excel to export the current inputs and calculated values. Select Reset to clear the demonstration and all results; Excel export remains unavailable until a complete valid set of inputs is entered again.

Input guide

Initial total mass is required, measured in kilograms, and must be greater than zero. Enter a plain decimal such as 100 or a correctly grouped value such as 1,250.5. A decimal comma, scientific notation, negative value, or unit typed into the field is rejected rather than silently reinterpreted. Increasing this input scales every mass result proportionally while leaving the percentage relationship unchanged. The kilogram is the SI unit of mass; see the NIST guide to mass and the kilogram.

Initial water percentage is required and accepts a decimal from 0 through values below 100. You may type 99 or 99%. It represents water mass divided by initial total mass. Raising it reduces the conserved dry-solids mass, so a modest later percentage change can produce a much smaller final total. Do not confuse a change from 99% to 98% with a 1% loss of the original mass; it is a one-percentage-point change in composition.

Final water percentage is required and also ranges from 0 to below 100. A realistic dehydration example normally uses a value no greater than the initial water percentage, but the formula also evaluates a higher value as an idealized rehydration case. Lowering the value increases the dry-solids share of the final material and therefore lowers total mass. Values of 100% are impossible here because a material containing conserved dry solids cannot be entirely water.

Output guide

New total mass is the primary estimated mass after the moisture percentage changes. Initial dry mass and Final dry mass are identical by assumption; they are the conserved non-water component. Initial water mass and Final water mass show the water component at each stage. The summary pills repeat starting mass, dry solids, and final mass for quick scanning. The Before-and-after mass composition chart uses a common kilogram scale: blue represents water and teal represents dry solids. The table lists the same two components and their total, so each row must satisfy water mass plus dry solids equals total mass.

Worked example

With 100 kg at 99% water, dry solids are 100 × (1 – 0.99) = 1 kg. At 98% water, dry solids are 2% of the new total. Therefore new total mass = 1 ÷ 0.02 = 50 kg. The final water mass is 50 × 0.98 = 49 kg, while dry solids remain exactly 1 kg. This is why a one-percentage-point drop in water content cuts the total mass in half in the classic example.

Learn more

Real drying decisions require more than composition arithmetic. Removing moisture can affect microbial growth and preservation, but percentage water content is not the same as water activity. For practical food handling, consult the USDA explanation of how drying preserves food by removing moisture and the FDA overview of water activity in foods.