Potato Calculator

Created by Komal Rafay and Anna Szczepanek, PhD
Reviewed by Rijk de Wet
Last updated: Jun 02, 2023

Did you ever imagine that you would need the assistance of a potato calculator? We had a hunch it might come in handy for many of you math enthusiasts.

Yes, you read it correctly — math enthusiasts. And that must have you thinking, "what do potatoes have to do with math"? Well, we are dealing with the potato paradox, which deals with the variation in the mass of potatoes caused by dehydration. So, in actuality, our tool is a potato paradox calculator.

The highlights of this informative article are:

• What is the dehydrating potato problem?
• How to use the potato calculator? and
• What is the significance of the potato paradox problem?

The potato paradox: what is the potato problem

What exactly is the potato paradox? Is it a problem? Is it a riddle? Well, you can stop scratching your head — because we are here with satisfying answers.

The potato paradox is a mathematical puzzle in which the decrease in water content due to dehydration makes it seem as if the mass of potatoes increases. The paradox goes as follows:

"100 kg of potatoes consist of 99% water. After dehydration, they consist of 98% water. What is their new weight?"

Go ahead, make a guess. 2 kg? 102 kg?

Nope.

The correct answer is 🥁 ... 50 kg.

Jump into the next section to understand how we deduced this result.

🙋 Would you like to take a look at our volume calculator? Since we are talking about changes in the mass of objects and its impacts on volume, it might help to have an understanding of the concept.

The potato paradox says that the water content is 99% of 100 kg of potatoes. It means that out of 100% potatoes, 1% is potato and 99% is water. So, the first thing to know is what is 99% of 100.

$\frac {99}{100} \times 100 = 99$

This means that the potatoes are 99 kg water and 1 kg dry weight.

After dehydration, the new percentage of water is 98%. Since the percentage is reduced by 2% of the total, our main question is 2% of what is 1 kg? Let's dive into our algebra arsenal and create the equation to determine this unknown, our beloved $x$.

We can write 2% as $\frac {2}{100}$, so the equation looks like:

$\frac {2}{100} \cdot x = 1$

Multiplying both sides by 100 to cancel out the 100 in the denominator, the equation becomes:

$2 \cdot x = 100$

Now, to determine the value of $x$, divide both sides by 2.

$x = \frac {100}{2}$

$x = 50$

So, there you have it. After dehydration, we have 50 kg of potatoes. These potatoes are 49 kg water and 1 kg dry potato mass.

So, is it safe to say that you do need a potato paradox calculator in your life?

The significance of the potato paradox problem

The potato paradox is a significant mathematical puzzle as it oppugns our assumptions about the connection between weight, volume, and density. It also has practical applications in many fields ranging from food science and agriculture to engineering, where accurate weight and volume measurements are essential.

🙋 Speaking of volume and density, it would be interesting to try our density calculator. Just saying!

One application of the potato paradox is in production of dehydrated foods, such as potato chips, which rely on removing water to extend their shelf life. Understanding the paradox can help manufacturers optimize their dehydration processes to ensure the final product meets weight and quality specifications.

In the field of agriculture, the potato paradox can be used to estimate the water content of potatoes and other crops, which can be important for determining optimal storage and transportation conditions. It can also help farmers to estimate crop yields and plan irrigation schedules.

💡 Another strange food paradox: people in France consume greater amounts of saturated fat than Americans, yet suffer less from heart disease.

Using the potato calculator

If you enjoy solving puzzles, you surely would have enjoyed our first riddle in our potato calculator — and if not, you can take any guess and jump straight into the calculations.

After the main paradox riddle, the calculations in the remainder of the tool are divided into two sections where you can enter the values before dehydration or after dehydration. There, you can play around with the paradox using a different percentage of water and the potato weight.

To start, input the values before dehydration for:

1. The total mass of the object, expressed in kilograms(kg). In this case, since we are looking at the potato problem, it's the total mass of potatoes.
2. The water percentage.

The tool automatically determines:

1. The dry mass, also in kg; and
2. The water mass in kg.

In the after dehydration section, all you have to input is the new water percentage. And the tool will do the rest for you. It displays:

1. The new water mass;
2. The dry potato mass; and
3. The *new total mass, all of which are expressed in kilograms.

Notice the one thing that doesn't change during all these calculations is the dry potato mass. That is where we get puzzled about this paradox. That dehydration impacts the water weight, but we tend to get confused, assuming the dry mass of the potatoes increases.

Our potato calculator does make you wonder about percentages. You may want to look at our percentage decrease calculator. It will help you understand the concept of a decrease in percentage.

FAQ

Yes, the potato paradox is true. But thinking otherwise might be correct as well.

The potato paradox makes us think as if the weight of the potatoes increases after dehydration, whereas we know that it's not possible. It is a mathematical puzzle in which the volume of the potatoes remains the same after dehydration, but they appear to take up more space and have a greater weight per unit volume.

Can I apply the potato paradox problem to other objects?

Yes, you may apply the potato paradox problem to many other situations that involve an impact due to dehydration.

For instance, the reduced total mass of dry fruits after dehydration. And remember, dehydrating a substance is not inherently bad — it was the best method of food preservation for much of history.

Does dehydration impact the dry weight of potatoes?

Dehydration has no impact on the dry weight of potatoes. Dehydration means the removal or loss of water from something. Hence, it only affects the water content.

What is the weight of 8 kg potatoes with 98% water after dehydrating?

After dehydrating 8 kg of potatoes with 98% water content, the new weight is 3.2 kg, assuming the water content after dehydration is 95%.

The 8 kg and 98% water content potatoes have 0.16 kg dry mass and 7.84 kg water mass. Since dehydration only impacts the water mass, the dry weight would remain the same after dehydration, i.e., 0.16 kg. And the water content at 95% hydration becomes 3.04 kg.

Komal Rafay and Anna Szczepanek, PhD
🥔 Start here!
We all love to eat potatoes, one way or the other. Let's try something different with potatoes today.

Imagine you are arranging a family dinner. You decide to make your famous mashed potatoes using 100 kg of potatoes, but they have an unusual water content of 99%. So, you decide to let them dehydrate until they are 98% water. However, this changes their weight — do you know what their new weight is?
Make a guess...
kg
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