The lap calculator is a service specially designed to calculate geometric dimensions figures online. Thanks to this service, you can easily determine any parameter of a figure based on a circle. For example: You know the volume of a sphere, but you need to get its area. There is nothing easier! Select the appropriate option, enter a numeric value, and click the Calculate button. The service not only displays the results of calculations, but also provides the formulas by which they were made. Using our service, you can easily calculate the radius, diameter, circumference (perimeter of a circle), the area of ​​a circle and a ball, and the volume of a ball.

Calculate Radius

The task of calculating the value of the radius is one of the most common. The reason for this is quite simple, because knowing this parameter, you special work you can determine the value of any other parameter of the circle or ball. Our site is built exactly on such a scheme. Regardless of which initial parameter you choose, the radius value is calculated first and all subsequent calculations are based on it. For greater accuracy of calculations, the site uses the number Pi rounded to the 10th decimal place.

Calculate Diameter

Diameter calculation is the simplest type of calculation that our calculator can perform. Getting the diameter value is not difficult at all and manually, for this you do not need to resort to the help of the Internet at all. Diameter equals the value radius multiplied by 2. Diameter - the most important parameter circle, which is extremely often used in Everyday life. Absolutely everyone should be able to calculate it correctly and use it. Using the capabilities of our site, you will calculate the diameter with great accuracy in a fraction of a second.

Find out the circumference of a circle

You can't even imagine how many round objects around us and what an important role they play in our lives. The ability to calculate the circumference is necessary for everyone, from an ordinary driver to a leading design engineer. The formula for calculating the circumference is very simple: D=2Pr. The calculation can be easily carried out both on a piece of paper and with the help of given internet assistant. The advantage of the latter is that it will illustrate all the calculations with drawings. And to everything else, the second method is much faster.

Calculate the area of ​​a circle

The area of ​​the circle - like all the parameters listed in this article, is the basis of modern civilization. To be able to calculate and know the area of ​​a circle is useful for all segments of the population without exception. It is difficult to imagine an area of ​​science and technology in which it would not be necessary to know the area of ​​a circle. The formula for calculation is again not difficult: S=PR 2 . This formula and our online calculator will help you without extra effort find the area of ​​any circle. Our site guarantees high precision calculations and their lightning-fast execution.

Calculate the area of ​​a sphere

The formula for calculating the area of ​​a ball is no more complicated than the formulas described in the previous paragraphs. S=4Pr 2 . This simple set of letters and numbers has been giving people the ability to accurately calculate the area of ​​a sphere for many years. Where can it be applied? Yes, everywhere! For example, you know that the area the globe equal to 510,100,000 square kilometers. It is useless to list where knowledge of this formula can be applied. The scope of the formula for calculating the area of ​​a ball is too wide.

Calculate the volume of a sphere

To calculate the volume of the ball, use the formula V=4/3(Pr 3). It was used to create our online service. The site site makes it possible to calculate the volume of a ball in a matter of seconds, if you know any of the following parameters: radius, diameter, circumference, area of ​​a circle or area of ​​a ball. You can also use it for inverse calculations, for example, to know the volume of a ball, get the value of its radius or diameter. Thank you for briefly reviewing the capabilities of our lap calculator. We hope you enjoyed your stay with us and have already added the site to your bookmarks.

So the circumference ( C) can be calculated by multiplying the constant π per diameter ( D), or by multiplying π by twice the radius, since the diameter is equal to two radii. Consequently, circumference formula will look like this:

C = πD = 2πR

where C - circumference, π - constant, D- circle diameter, R is the radius of the circle.

Since a circle is the boundary of a circle, the circumference of a circle can also be called the length of a circle or the perimeter of a circle.

Problems for the circumference

Task 1. Find the circumference of a circle if its diameter is 5 cm.

Since the circumference is π multiplied by the diameter, then the circumference of a circle with a diameter of 5 cm will be equal to:

C≈ 3.14 5 = 15.7 (cm)

Task 2. Find the circumference of a circle whose radius is 3.5 m.

First, find the diameter of the circle by multiplying the length of the radius by 2:

D= 3.5 2 = 7 (m)

Now find the circumference of the circle by multiplying π per diameter:

C≈ 3.14 7 = 21.98 (m)

Task 3. Find the radius of a circle whose length is 7.85 m.

To find the radius of a circle given its length, divide the circumference by 2. π

Area of ​​a circle

The area of ​​a circle is equal to the product of the number π to the square of the radius. The formula for finding the area of ​​a circle:

S = pr 2

where S is the area of ​​the circle, and r is the radius of the circle.

Since the diameter of a circle is twice the radius, the radius is equal to the diameter divided by 2:

Problems for the area of ​​a circle

Task 1. Find the area of ​​a circle if its radius is 2 cm.

Since the area of ​​a circle is π multiplied by the radius squared, then the area of ​​a circle with a radius of 2 cm will be equal to:

S≈ 3.14 2 2 \u003d 3.14 4 \u003d 12.56 (cm 2)

Task 2. Find the area of ​​a circle if its diameter is 7 cm.

First, find the radius of the circle by dividing its diameter by 2:

7:2=3.5(cm)

Now we calculate the area of ​​the circle using the formula:

S = pr 2 ≈ 3.14 3.5 2 \u003d 3.14 12.25 \u003d 38.465 (cm 2)

This task can be solved in another way. Instead of first finding the radius, you can use the formula for finding the area of ​​a circle in terms of the diameter:

Task 3. Find the radius of the circle if its area is 12.56 m 2.

To find the radius of a circle given its area, divide the area of ​​the circle π , and then extract from the result Square root:

r = √S : π

so the radius will be:

r≈ √12.56: 3.14 = √4 = 2 (m)

Number π

The circumference of objects surrounding us can be measured using a centimeter tape or a rope (thread), the length of which can then be measured separately. But in some cases it is difficult or almost impossible to measure the circumference, for example, the inner circumference of a bottle or just the circumference drawn on paper. In such cases, you can calculate the circumference of a circle if you know the length of its diameter or radius.

To understand how this can be done, let's take a few round objects, from which you can measure both the circumference and the diameter. We calculate the ratio of length to diameter, as a result we get the following series of numbers:

From this we can conclude that the ratio of the circumference of a circle to its diameter is a constant value for each individual circle and for all circles as a whole. This relationship is denoted by the letter π .

Using this knowledge, you can use the radius or diameter of a circle to find its length. For example, to calculate the circumference of a circle with a radius of 3 cm, you need to multiply the radius by 2 (so we get the diameter), and multiply the resulting diameter by π . Finally, with the number π we learned that the circumference of a circle with a radius of 3 cm is 18.84 cm.

A circle is a series of points equidistant from one point, which, in turn, is the center of this circle. The circle also has its own radius, equal to distance these points from the center.

The ratio of the length of a circle to its diameter is the same for all circles. This ratio is a number that is a mathematical constant, which is denoted by the Greek letter π .

Determining the circumference of a circle

You can calculate the circle using the following formula:

L= π D=2 π r

r- circle radius

D- circle diameter

L- circumference

π - 3.14

A task:

Calculate circumference with a radius of 10 centimeters.

Formula for calculating the dyne of a circle looks like:

L= π D=2 π r

where L is the circumference, π is 3.14, r is the radius of the circle, D is the diameter of the circle.

Thus, the circumference of a circle with a radius of 10 centimeters is:

L = 2 × 3.14 × 10 = 62.8 centimeters

Circle is a geometric figure, which is a collection of all points on the plane, remote from a given point, which is called its center, at a distance that is not equal to zero and is called the radius. Scientists knew how to determine its length with varying degrees of accuracy already in ancient times: historians of science believe that the first formula for calculating the circumference of a circle was compiled around 1900 BC in ancient Babylon.

With such geometric shapes like circles we collide daily and everywhere. It is its shape that has the outer surface of the wheels, which are equipped with various vehicles. This detail, despite its external simplicity and unpretentiousness, is considered one of greatest inventions humanity, and it is interesting that the natives of Australia and the American Indians, until the arrival of Europeans, had absolutely no idea what it was.

In all likelihood, the very first wheels were pieces of logs that were mounted on an axle. Gradually, the design of the wheel improved, their design became more and more complex, and for their manufacture it was necessary to use a lot of different tools. First, wheels appeared, consisting of a wooden rim and spokes, and then, in order to reduce wear on their outer surface, they began to upholster it with metal strips. In order to determine the lengths of these elements, it is necessary to use the formula for calculating the circumference (although in practice, most likely, the craftsmen did this “by eye” or simply girding the wheel with a strip and cutting off the required section of it).

It should be noted that wheel is used not only in vehicles. For example, its form is Potter's wheel, as well as elements of gears of gears widely used in technology. Since ancient times, wheels have been used in the construction of water mills (the oldest structures of this kind known to scientists were built in Mesopotamia), as well as spinning wheels used to make threads from animal wool and plant fibers.

circles often found in construction. Their shape is quite widespread round windows, very characteristic of the Romanesque. architectural style. The manufacture of these structures is a very difficult task and requires high skill, as well as the availability special tool. One of the varieties of round windows are portholes installed in ships and aircraft.

Thus, to solve the problem of determining the circumference of a circle, it is often necessary for design engineers who develop various machines, mechanisms and units, as well as architects and designers. Since the number π necessary for this is infinite, then it is not possible to determine this parameter with absolute accuracy, and therefore the calculations take into account that degree of it, which in one way or another specific case is necessary and sufficient.

A circle is found in everyday life no less than a rectangle. And for many people, the task of how to calculate the circumference of a circle is difficult. And all because she has no corners. With them, everything would be much easier.

What is a circle and where does it occur?

This flat figure is a number of points that are located at the same distance from another one, which is the center. This distance is called the radius.

In everyday life, it is not often necessary to calculate the circumference, except for people who are engineers and designers. They design mechanisms that use, for example, gears, portholes and wheels. Architects create houses that have round or arched windows.

Each of these and other cases requires its own precision. Moreover, it is absolutely impossible to calculate the circumference of a circle with absolute accuracy. This is due to the infinity of the main number in the formula. "Pi" is still being specified. And most often the rounded value is used. The degree of accuracy is chosen so as to give the most correct answer.

Notation of quantities and formulas

Now it is easy to answer the question of how to calculate the circumference of a circle from a radius, this will require the following formula:

Since the radius and diameter are related to each other, there is another formula for calculations. Since the radius is two times smaller, the expression will change slightly. And the formula for how to calculate the circumference of a circle, knowing the diameter, will be as follows:

l \u003d π * d.

What if you need to calculate the perimeter of a circle?

Just remember that a circle includes all points inside the circle. So, its perimeter coincides with its length. And after calculating the circumference, put an equal sign with the perimeter of the circle.

By the way, they have the same designations. This applies to the radius and diameter, and the Latin letter P is the perimeter.

Task examples

Task one

Condition. Find the circumference of a circle whose radius is 5 cm.

Solution. Here it is easy to understand how to calculate the circumference of a circle. You just need to use the first formula. Since the radius is known, all you need to do is plug in the values ​​and count. 2 multiplied by a radius of 5 cm gives 10. It remains to multiply it by the value of π. 3.14 * 10 = 31.4 (cm).

Answer: l = 31.4 cm.

Task two

Condition. There is a wheel whose circumference is known and equal to 1256 mm. You need to calculate its radius.

Solution. In this task, you will need to use the same formula. But only the known length will need to be divided by the product of 2 and π. It turns out that the product will give the result: 6.28. After division, the number remains: 200. This is the desired value.

Answer: r = 200 mm.

Task three

Condition. Calculate the diameter if the circumference is known, which is 56.52 cm.

Solution. Similar to the previous problem, you need to divide the known length by the value of π, rounded up to hundredths. As a result of such an action, the number 18 is obtained. The result is obtained.

Answer: d = 18 cm.

Task four

Condition. The clock hands are 3 and 5 cm long. It is necessary to calculate the lengths of the circles that describe their ends.

Solution. Since the arrows coincide with the radii of the circles, the first formula is required. It needs to be used twice.

For the first length, the product will consist of factors: 2; 3.14 and 3. The result will be the number 18.84 cm.

For the second answer, you need to multiply 2, π and 5. The product will give a number: 31.4 cm.

Answer: l 1 = 18.84 cm, l 2 = 31.4 cm.

Task five

Condition. A squirrel runs in a wheel with a diameter of 2 m. How much distance does it run in one complete revolution of the wheel?

Solution. This distance is equal to the circumference of the circle. Therefore, you need to use the appropriate formula. Namely, multiply the value of π and 2 m. The calculations give the result: 6.28 m.

Answer: Squirrel runs 6.28 m.