Potato Calculator - Mass, Dry Matter, Water %

A potato calculator answers the famous potato paradox, the counter-intuitive math puzzle about how the total mass of a hydrated material changes as its water percentage changes.

• • Math class and puzzle nights: Show students and friends why 100 kg of potatoes at 99% water becomes 50 kg of potatoes at 98% water, and walk through the dry-mass identity that makes the answer click.
• • Food science and dehydration: Estimate the weight of dried potatoes, fruit leather, beef jerky, or any other food that loses water during processing, using the same dry-mass identity that anchors the paradox.
• • Reverse engineering from a target dry matter: Work backwards from a known dry matter percentage to back out the initial mass before dehydration, which is useful for storage, transport, and yield planning.
• • Sanity check for percentage and mass problems: Verify the relationship between a percentage and a raw mass in homework, lab work, or pricing problems where the answer needs to make physical sense, not just arithmetic sense.

The potato paradox was popularised in Darling's "The Universal Book of Mathematics" and survives in math education, contest problem sets, and a Car Talk puzzler, but the underlying identity is general: any hydrated material obeys the same dry-mass conservation, so the calculator works for fruit, soil, sludge, or laundry, not just potatoes.

The page is built so that you can run the paradox forward (initial mass plus starting water % plus a lower target water %) and read the surprising new total mass in real time. You can also rehydrate a sample by entering a higher target water %, and the page reports a negative water-evaporated value to show that the sample gained mass.

Because the math is short, the calculator is also useful as a teaching aid. Watching the dry mass stay fixed while the water mass and total mass change is the visual payoff of the page, and it is exactly the move that makes the 100 kg, 99% water riddle feel obvious after you see it once.

When the question is reframed as how much smaller one number is than another, the Percentage Decrease Calculator applies the same percentage-of-total thinking to any starting and ending pair of values.

The math is two short identities chained together: the dry mass never changes, and the new total mass is whatever the dry mass has to be in order to land on the requested water percentage.

• initialMass: Total mass of the hydrated material in kilograms before any dehydration happens.
• waterPercentBefore: Share of the initial total mass that is water, expressed as a percentage from 0 to 100.
• waterPercentAfter: Target share of the new total mass that is water, expressed as a percentage from 0 to 100.

Step 1: the calculator reads the initial total mass and the starting water percentage, then multiplies them to expose the dry mass. Step 2: it takes the new water percentage, flips it into a dry fraction, and divides the dry mass by that new dry fraction to recover the new total mass. Step 3: it subtracts the dry mass from the new total to give the new water mass, and subtracts the new total from the initial total to give the water evaporated.

Each of those steps is exactly the algebra that makes the classic 100 kg, 99% water riddle fall apart, and each one is reproducible by hand on a sheet of paper, so the page can be used as a worked-example generator as well as a calculator.

According to Wolfram MathWorld, after 100 pounds of 99%-water potatoes dehydrate to 98% water, the surprising weight is 50 pounds, because the dry mass of 1 pound is now 2% of the total.

If you need the raw mass difference in kilograms instead of the percentage, the Absolute Change Calculator gives the signed magnitude between any two numbers in the same units.

Four short ideas drive the math; once each one is clear, the 100 kg, 99% water riddle stops being a surprise.

These four concepts are enough to derive the formula on the page. They also explain why the same formula behaves dramatically differently at different water percentages, which is the source of the surprise in the original puzzle.

The relationship between the starting mass, the final mass, and the water percentage is the same signed difference that the Percentage Change Calculator measures between any two values.

Five short steps get you from the riddle to a defensible new total mass, and the page does the algebra in the background so you can focus on the result.

1. 1 Enter the initial total mass: Type the total mass of the hydrated material in kilograms. For the classic paradox, this is 100.
2. 2 Enter the starting water percentage: Type the share of the initial mass that is water. For the classic paradox, this is 99%.
3. 3 Read the initial dry mass and water mass: The page shows the dry mass and the water mass of the starting sample. The dry mass is the value the rest of the math anchors to.
4. 4 Enter the target water percentage: Type the water percentage you want after dehydration, which can be lower (dehydration) or higher (rehydration) than the starting value.
5. 5 Read the new total mass and the water evaporated: The page shows the new total mass, the new water mass, the unchanged dry mass, and the water evaporated, all in kilograms, all updated in real time as you type.

To verify the classic 100 kg, 99% to 98% riddle, type 100, 99, and 98 into the three fields. The page should show a dry mass of 1 kg, a new total mass of 50 kg, and 50 kg of water evaporated, which matches the textbook answer.

If you are working out baker's percentages in a kitchen, the Bakers Percentage Calculator covers the same percentage-to-ingredient math from a culinary angle.

The same identity that makes the paradox click is also useful for a handful of practical problems, which is why the page goes beyond a yes-or-no answer.

• • Show the paradox step by step: Walk through the dry-mass identity with students, friends, or co-workers and watch the new total mass update live as the target water percentage changes.
• • Estimate dehydrated food yields: Plan the weight of dried potatoes, fruit, herbs, or jerky from a starting fresh weight and a target final water content, and avoid surprise shortages or excess.
• • Plan harvest and storage logistics: Pre-dehydration weights feed into transport, packaging, and storage cost models, and the page gives a quick answer to how much weight is lost at the target water content.
• • Solve reverse-direction problems: Enter a higher target water percentage to rehydrate a sample, and the page reports a negative water evaporated value, which is the same identity used in reverse.
• • Sanity check percentage and mass intuitions: Catch common percentage errors where a one-point move is treated as a small change, when it is in fact a large change at high water percentages.

For a kitchen use case that depends on a fixed water ratio, the Rice to Water Ratio Calculator solves the same forward ratio problem with a different unit.

Three things determine how big the surprise is, and three caveats keep the model honest when the page is used outside the original puzzle.

• • The math assumes a single, uniform water percentage throughout the sample, which is a fair model for a well-mixed batch of potatoes or a thin layer of drying food, but a poor model for layered or partially dried material where the surface and the centre have very different water contents.
• • The identity treats all mass loss as water, so it does not capture small amounts of volatile flavour and aroma compounds that can leave alongside water during real dehydration, and it does not model sugar or salt migration.
• • The page is a teaching and planning tool, not a lab instrument, so the result should be read as a target or a back-of-the-envelope estimate, not as a measurement of a real sample.

According to Wikipedia, the potato paradox is a veridical paradox in which 100 kg of 99%-water potatoes that dehydrate to 98% water weigh 50 kg, since the unchanged 1 kg of dry matter now has to be 2% of the total mass.