Three fat rules: how much fat does a healthy body need? Ideal body fat percentage.

And water in the body. The question is relevant because by determining the proportions of fat, water and muscle mass, you can find out exactly how much fat you lost during weight loss. Perhaps only water left?

If in the process of losing weight you are losing fat, not muscle mass or water, then you are definitely on the right track. But how in the body and what is the average? There is a special table that shows all the numbers. Let's briefly go through its data.

The average is calculated depending on the age and gender of the subject. So, due to the hormone estrogen, the female audience has 5% more fat than the male audience. Therefore, the usual normal rate is 23% for women and 17% for men.

Depending on age, the percentage of normal body fat increases and muscle mass decreases.

So, for an average student aged 20 years, fat content should be approximately 15% of total body weight. And older men with a clearly sedentary lifestyle have rates of 25% or more. The ideal indicator is considered the limit of obesity. Anything higher is full-fledged clinical obesity with all the ensuing consequences.

Why is body fat needed?

As paradoxical as it sounds, the human body still needs fat. Weight loss fanatics can convince you otherwise until you are blue in the face, but still pay attention to this point so as not to cross the boundaries of acceptable weight loss.

Fat is necessary for the normal functioning of the body. Therefore, its content cannot be equal to zero.

Fat needed:

  • For thermal insulation;
  • To protect internal organs and/or the fetus during pregnancy;
  • As energy reserves. This is the so-called emergency protection of our body for a “rainy day”.

For women, the required fat level is at least 8-10%, but for men this figure is 3-5%. A low percentage of fat is extremely dangerous for health, which especially concerns the female body. So indicators below 10-13% inhibit estrogen production, disrupt reproductive function and the menstrual cycle. There is also a risk of developing osteoporosis much earlier than old age due to decreased bone density.

By the way, women often cannot get pregnant due to lack of body weight. This is why doctors recommend certain fat-building foods for those who are “morbidly thin.”

How to find out your fat percentage

There are various methods that reflect the fat content in the body. The most accurate:

  • Body composition and its analysis;
  • Waist-hip ratio;
  • Skin fold measurement.

This way you can find out what proportion of your body is occupied by fat and what proportion by other tissues. Similar studies can be easily done in sports centers and clubs. They may also offer you special products that will help you lose weight or. This means high-quality official drugs like thermogenics, and so on.

Pharmacies and not very good sports clubs often sell products that remove fat from the body. The drugs simply do not allow lipids to be absorbed during the digestion process, are harmful to the body and, moreover, can embarrass you in public.

Skinfold measurement

One of the most accurate and popular methods for determining the percentage of fat is measuring the thickness of the folds in certain places.

The scale on this instrument will show the thickness of the fat layer. Similar pinching is done in certain places - the upper back, stomach, hips, chest. Next, the indicator is inserted into a special formula and the percentage is calculated.

Believe it or not, the instrument was originally invented to determine the thickness of pig fat. Later they adapted it to human needs.

The measurement has a high degree of accuracy, but tomography is considered the most accurate. Thanks to the unit, it is possible to accurately separate adipose and non-adipose tissue in the body. But due to the high cost of the procedure, it is practically not used in practice.

Pinching

To pinch, you need to pinch the fold of skin in several places with your index finger and thumb. The help of an outsider is necessary, since you need to pinch on the hips, stomach, and slightly above the armpit. Next, trying not to spread your fingers, measure the distance between them with a ruler. If the distance is more than 2.5 cm, then you are overweight.

Body mass index

To calculate, you need to divide your weight by your height squared. The normal value is from 18.5 to 24.9. But the indicator is very inaccurate, since the same athletes have more muscle mass, and the indicators will reflect obesity at the same figures.

Clothing size

With clothes, too, everything is not clear. Clothes tend to both stretch and shrink. You simply could have eaten too much salty food and water simply accumulated in the body, that is, a banal swelling occurred, which will subside a little later. It’s enough to sit in a sauna, cut down on salt in your diet, and fit into your favorite jeans.

The principle of losing weight due to the evaporation of water is used in all kinds of weight loss shorts and creams that remove water from the body.

If you overdo it, you may lose too much water. The result is dehydration and poor health.

Body type

When taking all kinds of measurements, it is also useful to focus on your body type.

There are three types of physique:

  • thin. It is distinguished by narrow bones, elongated arms and legs. This type of person does not have much fat and muscle in their body. They have an intense metabolism, so ectomorphs simply cannot imagine what “” is. Even the most unhealthy foods like mayonnaise and buns will not make them fat.
  • have wide bones, muscles predominate over fatty tissue. Their body responds to physical activity as quickly as possible. It is mesomorphs who quickly earn beautiful relief.
  • the bone has average parameters, but the metabolism is slow. Adipose tissue predominates over muscle tissue. It is endomorphs who have problems with excess weight. Even foods such as lean steamed fish can cause obesity.

Having determined your body type, you can calmly determine where exactly to start and transform your body shape.

What is your body fat percentage? Why do you even need to know this?
We all know that in order to look better and be healthy, you need to avoid fatty foods in your diet and exercise a lot to burn excess body fat (ballast).
How can we estimate the amount we already have?
Is it a lot or a little?
Bodybuilders, for example, compete with around 5% body fat.
How much do we have? 10-15?
How much is needed?
Let's tell...

This is the part of the body that is represented by fat. For example, if you weigh 70 kg and have 7 kg of fat, then the percentage is 10.

It's simple.

This means that fat content is a constantly changing number. Fluctuates as you gain or lose weight, as you gain or lose muscle.

For example, if both and your weight increases from 70 to 80 kg, and at the same time you gain 3 kg of fat, then the new figure will be 8%. If you then stop training for a year and lose, for example, 5 kg of muscle, your body fat content will be 7.5%.

So this figure is constantly changing as lifestyle changes.

Why body fat percentage is more important than BMI

Some people confuse body fat percentage with BMI, but these are two completely different indicators. BMI—body mass index—expresses the relationship between height and weight.
Calculated using the formula: weight, kg / ((height, m) squared).

According to this formula, people with large muscles may fall into the "overweight" category. This is the main problem with BMI. It is very useful for analyzing large populations, but is not particularly suitable for athletes. In this sense, the percentage of body fat is much better.

Can body fat percentage be determined based on BMI?
No.

BMI is based on height and weight only. It can be high for a number of reasons. It can also be the same in a person with highly developed muscles and a low amount of fat tissue and in a person with a large amount of fat deposits and poor muscle development.

What percentage of body fat is considered normal for men and women?

Although it is commonly viewed with hostility, human fat is not just a layer of disgusting, unnecessary flesh. It performs many vital functions in the body, including protecting organs from damage, maintaining body temperature, producing hormones, other chemicals, and more. This is why there is a limit to how much body fat you can burn without compromising your health. Here are two charts for men and women:

Why such a difference?

In women, additional fat deposits are found in the breasts, thighs and buttocks.

Numerous studies have shown that the minimum percentage of body fat in a man cannot be less than 4 - 5%, and in women - 10 -12%. This is explained as follows: when you become so “dry”, all that remains in the body is “vital” fat, which is contained in nerve cells, brain tissue, joints, palms of the hands and soles of the feet, in the membranes of such organs, like the heart and intestines. That's why he is needed to stay alive.
Once you reach this percentage in the body, you are literally on the edge of the abyss. Further fat burning can lead to cardiac arrest and loss of consciousness (coma). At the same time, the body protects itself and begins to destroy internal organs and muscles to produce energy instead of using fat. This is why many studies show that people who starved to death still had vital fat tissue.

For clarity: this is what a man with 4% and a woman with 10% look like. Horror.

Unless you're a professional bodybuilder and don't know what you're doing, don't ever try to push yourself to that point. Hormonal imbalances and disruptions in the functioning of internal organs will begin. If you avoid all this, then all the same, the process of returning to normal will be very long and difficult. Fortunately, most likely, like most people, you are not striving for this. You will be quite satisfied with 7-10% for men and 13-20% for women. This is the percentage that is called “relief”.

(We share photos of famous athletes because a lot of research has been done on them. For example, we know that the best male athletes in most sports have a percentage of 6-10%, and women - 13-20%).
Anyone can look like this with exercise, but it is very difficult to maintain this shape for a long time. While this percentage of body fat is normal, there is no need to be this lean to stay healthy.

Another illustration - 15% man and 25% woman:

As you can see, they look great and athletic.
But when your body fat percentage rises above a healthy level, you begin to look clearly “overweight.”
Like in this photo:

How to Calculate Body Fat Percentage

Smart floor scales and weight loss monitor

  • Smart floor scales (body composition scales)
  • Fat loss monitor

These are the simplest ways. These instruments use a technique called bioimpedance testing (BIA), which involves measuring the resistance of different areas of the body to electrical current.

Muscles are good conductors of electricity because they are 70% water. Fat conducts current less well. The worse the body passes current, the more fatty tissue it contains. This sounds pretty reasonable, but there are serious problems with the BIA. When current passes through a body, it follows the path of least resistance. For example, through the fatty tissues of internal organs, and not subcutaneous ones.

Most of these devices contain two electrodes, so even large areas of the body are often ignored. For example, the scale may not take into account the entire upper body (electrical current will flow from leg to leg). And manual devices will miss the entire lower part. This seriously distorts the results.
Another problem with bioimpedance testing is that it uses mathematical equations that translate test scores into percentage body fat.

Why are their formulas not correct? When companies create BIA meters they use another imperfect method of measuring body fat percentage such as hydrostatic weighing.

Some studies have proven that hydrostatic weighing itself can produce an error of 6%, depending on the race, nationality of the person, etc. In other words, a person with 10% body content may get a result of between 4-16% on a hydrostatic weighing.

Many factors influence the results. If you conduct a study in a state of dehydration, you will get a very high result due to reduced conductivity. But if you test after eating, you will get the opposite effect - the readings are too low. Body conductivity is also better after training. Therefore, when conducting a test after physical activity, incorrect and low results are obtained. This is why these devices are not suitable for correctly estimating your body fat percentage.

How about purchasing one of these to track changes over time?

That's no good either. These devices make mistakes differently each time. There is no clear pattern.

Calipers and skinfold thickness

Calipers are used to measure the thickness of skin folds in different areas of the body. These measurements are plugged into the formula. As a result
And there are disadvantages here. Grab too little skin and the readings will be too low; too much and the readings will be higher.

Photos and mirror

This is the simplest and most obvious way to assess your body fat levels. People with the same body percentage look very similar if they have the same body type. However, if not, the same percentage of body fat can look very different in people with different body types.

For example, an 80 kg guy with 10% body fat has 8 kg of body fat, while a 95 kg guy with the same percentage has only 1.5 kg more, but a little more muscle, which gives him a completely different look.

For the training athlete, the pictures below should help to approximately determine the percentage of fat tissue in the body.

For men:
For women:

Dual-energy X-ray absorptiometry (DXA)

DXA (sometimes called DEXA) uses x-rays of the entire body. It is based on the fact that tissues containing and not containing fat absorb X-rays differently. Therefore, everything can be measured and calculated. Most people previously believed that DXA was an error-free method, but numerous studies have proven that it can be wrong by 4-8, and sometimes even 10%.

Causes of errors: different manufacturers of devices, different algorithms used to interpret data. Body size, state of dehydration and some other factors also influence.

Plethysmography (Bod Pod)

A plethysmograph (Bod Pod) is a machine that works similar to hydrostatic weighing, but uses air instead of water. Sit in a sealed capsule and a sensor measures how much air your body displaces (Archimedes' principle). Then, using mathematical formulas, this is all translated into the percentage of fat tissue in the body. Unfortunately, the accuracy of the Bod Pod method is no better than all previous ones. It is negatively affected by hair, humidity, body temperature and clothing.

The most accurate way to calculate body fat

It is called 4-component analysis. It includes several methods, dividing a person's body weight into four categories:

  1. bone
  2. muscle
  3. fat masses
  • Hydrostatic weighing is used to measure the density of a body.
  • Deuterium dissolution is used to determine the amount of water in the body.
  • DXA is used to measure bone mass.

The results obtained are processed and calculated using various formulas. The result is always an accurate measurement of body fat percentage. This is interesting, but useless information for us. Because this method requires a whole team of scientists.

Fortunately, there is a method that deserves our attention.

How to Measure and Track Your Body Fat Percentage

  • Weigh yourself daily. Calculate the average over 7-10 days. If the average goes up, you gain weight. Therefore, weigh yourself every day in the morning after washing your face, before breakfast.
  • Take measurements with calipers once a week. If your skin becomes thicker, you gain weight. If you are thinner, you lose body fat. In this sense, the use of calipers is very useful.
  • Measure your waist circumference once a week. Waist size measured at the navel is a reliable indicator of fat gain or loss.
  • Photography once a week. For most gym goers, the main goal is how they look in the mirror. And when they look at themselves every day, they can lose motivation because they don’t notice changes. Photos from the front, side and back solve this problem.

Using these methods, you will know exactly what is happening to your body and make changes to your diet and exercise program.

Good luck!

Today's topic of the article will be dedicated to girls who are not completely happy with their figure and would like to change it a little or more thoroughly. When we talk about excess weight, we mean those extra fat deposits that prevent us from feeling comfortable and liking ourselves in the mirror. Those ugly extra pounds are defined by nothing more than percentage of body fat. Today we will find out what should be the norm of fat in the female body, and also determine what percentage of body fat is in a woman is the lower threshold, after which problems with health and reproductive function begin. In general, in this article we will analyze in detail and bit by bit how the female body and its nature reacts to changes in the percentage of fat and a decrease in the fat layer on its body. I think it will be interesting for every girl to know what normal body fat which is acceptable and which is dangerous...


Minimum percentage of fat in the female body

In fact, there is no one value that would accurately state that “this” indicator or “this” is the ideal percentage of fat in the female body (and in the male too). Fat norm for each person is determined individually and is based on many factors - gender, age, activity level, lifestyle, genetics, dietary habits and others. But despite this, scientists were able to determine minimum range of female body fat percentage, below which women should not go, due to the appearance of significant disturbances in the vital functions of the body. This percentage varies from 13 to 16 depending on age differences (Table 1).

Table 1 Minimum acceptable fat content depending on the woman’s age

AGE

≤ 30 30 – 50 50+
Fat percentage 13% 15% 16%

As we can see, the lower threshold of a woman’s normal body fat percentage increases the older she gets. This is due to a decrease in her motor activity and metabolism in general.

Normal percentage fat in the female body

Now let's move on to consider the average value normal body fat percentage for women. As we already know, there are no two completely identical organisms, therefore this indicator will not be one specific number, but a range of several values, which will characterize the acceptable percentage of fat for the female body. In Table 2 you can see what these values ​​are for different age groups of women.

Table 2 Normal percentage of fat in the female body

AGE ≤ 30 30 – 50 50+
Fat percentage 16 – 20% 18 – 23% 20 – 25%

But it is worth noting that even within these values ​​there may be disruptions and irregularities in the menstrual cycle in women.

For example, if for a twenty-year-old young girl the normal fat percentage is 19%, (this is what happened “historically”), and when she lost weight, then the fat percentage dropped to 17%, but still remained within her normal range and fits into the range "safe" minimum fat percentage, then the girl may still develop disturbances in the functioning of the ovaries at a more serious level. And all because normal body fat indicated in tables 1 and 2 or prescribed in physiology textbooks is still more conditional meaning, which only approximately determine this normal percentage . But in fact, the body itself decides what is the ACCEPTABLE percentage of fat for it, what is MINIMUM, and what is EXCESSIVE. And we, unfortunately, do not participate in this distribution.

How to measure your body fat percentage?

There are several ways to measure your body fat percentage. The infographic below shows the most popular (picture clickable).

But keep in mind that the resulting figure will only be approximate, since this method is not the most accurate of all those presented above.


Low or negative body fat percentage energy balance?

There are studies that show that low fat percentage does not in any way affect the absence of menstruation and the appearance of amenorrhea in girls. It's all about negative energy balance, not fat percentage per se. When a girl starts to lose weight and lose her kilograms, she does it by calorie deficit, that is, it spends more energy than it receives from food, thereby creating negative energy balance.

So it is this factor that is key in stopping menstruation and disrupting a girl’s reproductive function, and not the low percentage of fat itself.

If you believe these studies, it turns out that, in principle, a girl can have 6 packs on her stomach and not have problems with her cycle. Is it really?

If we think logically, then to get the desired muscle definition, just NEED TO REDUCE its fat component, that is REDUCE body fat percentage to its minimum (13-14%). And this in turn can ONLY be done through a calorie deficit, which is created by reducing the amount of calories consumed from food and increasing energy expenditure during training.

And here the question arises: are there girls who perform in the “” or “Body Fitness” nominations and at the same time their cycle does not disappear? How is this possible? After all, most of them bring their body fat percentage below the minimum acceptable norm of 13%.

I allow this option:

 those girls who were able to maintain their menstrual cycle during drying and a strict diet (and there are not so many such girls), they still managed to maintain their energy balance at the proper level, without creating a large calorie deficit due to sports supplements food and .

After all, in order to prepare and compete in bodybuilding and bikini fitness competitions, you definitely need additional help in the form of special help, otherwise there is no other way. Training and strict nutrition deplete the body’s energy reserves so much that sometimes girls not only lose their cycle, they simply faint right on stage. This all shows how illiterate and incorrectly the coach or the girl herself approaches the issue of preparation and preparation for competitions. It is clear that the diet of performing athletes contains the minimum possible amount of carbohydrates (the main source of energy), but, perhaps, some also do not receive the normal amount of proteins and fats from food. We cannot know this for sure, but it is true that sports nutrition supplements can partly reduce the energy balance created in the body of athletes.

Where am I leading with all this? And besides, if you want to have a low percentage of body fat (less than 15%) in order to see your six-pack on your stomach, you need to take this issue VERY seriously! Firstly, you need to find out your minimum percentage of fat with which your body continues to function normally, and secondly, do not forget about additional nutrition for athletes.

remember, that norm of fat in the female body is still directly related to the negative energy balance created. The higher it is, the faster you lose weight and reduce your fat percentage. And if at this time you do not help your body and do not support it in the form of additional sports nutrition and vitamins, then you risk losing your cycle, and subsequently getting even more problems with your health:

And there is one more important point that I would like to mention. After the girl fully realizes that her weight loss is not at all the result she dreamed of, and she decides to increase her fat percentage to her “historical” norm, then this girl will inevitably face the realities of her weight loss. Unfortunately, not all the consequences of this weight loss will go away as completely as they appeared. Yes, she will most likely be able to return her menstrual cycle to normal in a couple of weeks, but, for example, the loss of some minerals that are responsible for bone strength may be an irreversible process for her. The consequences of amenorrhea never go completely without a trace, this is a scientifically proven fact. So, remember this if you suddenly want to lose weight and reduce your normal fat percentage to a minimum.

Fat percentage from low to high

Well, let's summarize all of the above.

So, minimum percentage of fat in the female body should be 13-16% depending on the woman’s age. Below this threshold, women begin to have serious health problems, remember this.

Normal percentage of body fat in a woman ranges from 16 to 25%. Falling into this range, a woman looks and feels good, all her organ systems and, most importantly, her reproductive function are in perfect order.

We didn’t discuss the diagnosis of obesity here, but I will say that more than 32% body fat indicates that a woman is already included in the “overweight” category.

I hope this article was useful to you and you learned a lot of useful and necessary information for you.

And I wish you to be healthy and not focus on six-pack abs, because health is a thousand times more important than some six-pack. We have only one, and it can be easily and irretrievably lost! And we have six cubes, they are with us forever and you can always buy them if you wish =))

Sincerely yours, Janelia Skripnik!

If you are an athlete or just a person who is concerned about his health, you were probably interested in how to determine there are several ways to do this. Each of them has a different level of difficulty. The fat calculator offered by many Internet users is often inaccurate, so we will look at the most correct formulas and other ways you can control your weight. Today, many new techniques have been developed that allow you to find out the most accurate result, but they all require financial investments. Choose the most appropriate method for yourself and then focus on it.

Why calculate your body fat amount?

Every time you step on the scale, you notice a certain dynamic. You either gain weight or lose weight, albeit slightly. But the pounds you lose are not always fat. This could be muscle mass or simple dehydration. If you want to lose weight or gain weight, you should be interested in subcutaneous fat. Additionally, the formula is more accurate if you know how much excess deposits you have in your body. Therefore, it is imperative to find out this indicator, and today we will talk about how to do this.

The simplest ways to determine the amount of body fat

Weight based on height and age is determined taking into account the amount of body fat. It may be large, but it will consist only of muscles, water and bones. Let's look at how to determine your body fat percentage:

  • Special scales that determine the amount of fat in the body. Only you can decide whether to trust this invention of mankind, since it is impossible to accurately verify whether the information you receive is true.
  • You can carefully examine yourself in the mirror and determine the amount of excess fat. But it is difficult to evaluate yourself objectively, so this method is rarely accurate.
  • Use to measure your waist and forearm. If there are fewer centimeters on your waist, and more on your arms, then your fat layer decreases and muscle mass increases.

Any of these methods are available to every person, but with their help you cannot know the exact results. In addition, by assessing the general condition of the fat layer, you will not get specific numbers.

To find out your body fat percentage using the Lyle MacDonald method, you must calculate your BMI. To do this, use the formula: BMI = weight in kilograms/height in meters squared. Next, find your indicator:

  • BMI = 13-20. Then the percentage of fat is 13.5-24;
  • BMI = 21-30. The percentage of fat is 25.5-39;
  • BMI = 31-40. The percentage of fat is 40.5-54.

This method of determining the thickness of the fat layer is quite popular among girls, but there are other methods that allow you to calculate this indicator more accurately.

The most effective way to determine the amount of fat in the body

If you are interested in how to determine your body fat percentage using medical equipment, then you should evaluate your financial capabilities. Even in government agencies, this method requires money, but it is the most accurate of all possible. It is used by professional athletes before competitions when it is necessary to provide official data on the condition of the body.

The essence of the method is this: special electrodes are attached to the wrists and ankles, through which a weak electric current passes. The body's tissues resist it, and the level of this resistance is measured by medical devices. You will know the result immediately after the procedure.

But this method has a significant drawback. If your body is not properly hydrated, the equipment may give incorrect results. Therefore, the procedure is usually performed twice. When swelling in the body disappears, the devices may show a lower fat percentage than the previous time.

There is no need to carry out such an analysis without the need or a special referral from a doctor; it is better to use other methods to calculate the amount of body fat.

Underwater weighing method

Ideal weight based on height and age can only be determined by taking into account the amount of fat in the body. The underwater weighing method gives the most accurate result of all methods known today.

The essence of the underwater measurement is this: when a person is completely immersed in water, he loses the amount of weight that was displaced from the container in which he is located. After the procedure, the person is weighed on ordinary medical scales, and specialists compare the weight in the water with the body weight on land. After certain calculations are carried out, the amount of fat in the body is calculated.

Using a caliper for women

To find out your body fat percentage (the norm for women must be strictly observed, since this greatly affects overall health indicators), use a caliper. This is a device that is used to measure the thickness of the fat layer in any area of ​​the body.

So, how to determine your body fat percentage using a caliper:

  1. Find out the thickness of one fold of fat on the back of the shoulder;
  2. Calculate the thickness of the side fold between the ribs and the thigh bone;
  3. Measure the thickness slightly away from the navel;
  4. Use the formula: (the sum of all three folds in centimeters + the same figure squared + 0.03661 * the number of your years) + 4.03653.

You need to practice to calculate your body fat percentage yourself. The norm for women is that accurate results are calculated 3 times. Using this device you can calculate the amount of fat in men.

Using a caliper for women and men

The fat calculator below is quite accurate, but you need to practice using the device to get reliable results. So, to find out your indicator, follow the instructions:

  • Find out the thickness of the fold on the back of the shoulder.
  • Measure the thickness of the fat fold on the front of the shoulder.
  • Calculate the thickness of the fold on the stomach.
  • Add up all the obtained indicators.

To find out the amount of fat in the male body, use the following data:

50 or more years

To find out the fat content in the female body, use the table:

50 or more years

This method allows you to find out accurate indicators. Plus, once you get the hang of it, it's easy to use. The disadvantage is that it is sometimes difficult to take measurements on your own and requires the help of another person.

The human body is a very complex mechanism. The normal fat content in it is different for an ordinary person and an athlete. From 10% for women and from 3% for men - this is the necessary indicator. A low percentage of body fat indicates that you urgently need to gain weight, otherwise you may experience health problems.

Up to 31% body fat for women and up to 25% body fat for men are normal numbers. If your indicators exceed them, you need a special diet and exercise to reduce body fat. The sooner you start fighting excess weight, the more time your body will have to normalize all metabolic processes.

So, a person needs to know the percentage of subcutaneous fat in the body in order to control body weight and prevent health problems associated with being under or overweight.

Which indicator to choose is up to you. But do not neglect even the simplest methods in order to at least approximately know how normal your body fat is. Remember that not only your appearance, but also your health depends on its quantity.

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