How to find out the diameter of a circle by knowing its perimeter. Calculating the radius: how to find the circumference of a circle knowing the diameter. Diameter in calculation formulas

1. Harder to find circumference through diameter, so let's first analyze this option.

Example: Find the circumference of a circle whose diameter is 6 cm... We use the above formula for the circumference of a circle, but first we need to find the radius. To do this, we divide the diameter of 6 cm by 2 and get a radius of a circle of 3 cm.

After that, everything is extremely simple: Multiply the number Pi by 2 and by the resulting radius of 3 cm.
2 * 3.14 * 3cm = 6.28 * 3cm = 18.84cm.

2. And now let's analyze a simple option once again. find the circumference of the radius is 5 cm

Solution: The radius of 5 cm is multiplied by 2 and multiplied by 3.14. Do not be alarmed, because rearranging the multipliers does not affect the result, and circumference formula can be used in any order.

5cm * 2 * 3.14 = 10 cm * 3.14 = 31.4 cm - this is the found circumference for a radius of 5 cm!

Circumference calculator online

Our calculator of the circumference of a circle will make all these not tricky calculations instantly and write the solution in a line and with comments. We will calculate the circumference for a radius of 3, 5, 6, 8 or 1 cm, or the diameter is 4, 10, 15, 20 dm, our calculator does not matter for which value of the radius to find the circumference.

All calculations will be accurate, tested by specialist mathematicians. The results can be used in solving school problems in geometry or mathematics, as well as in working calculations in construction or in the repair and decoration of premises, when accurate calculations are required using this formula.

It often sounds like a part of a plane that is bounded by a circle. The circumference of a circle is a flat, closed curve. All points on the curve are the same distance from the center of the circle. In a circle, its length and perimeter are the same. The ratio of the length of any circle and its diameter is constant and denoted by the number π = 3.1415.

Determining the perimeter of a circle

The perimeter of a circle of radius r is equal to twice the product of the radius r and the number π (~ 3.1415)

Circle perimeter formula

Perimeter of a circle of radius \ (r \):

\ [\ LARGE (P) = 2 \ cdot \ pi \ cdot r \]

\ [\ LARGE (P) = \ pi \ cdot d \]

\ (P \) - perimeter (circumference).

\ (r \) - radius.

\ (d \) - diameter.

A circle is a geometric figure that will consist of all such points that are at the same distance from any given point.

Center of the circle we will call the point that is specified in the framework of Definition 1.

Circle radius we will call the distance from the center of this circle to any of its points.

In the Cartesian coordinate system \ (xOy \), we can also enter the equation of any circle. Let's denote the center of the circle by the point \ (X \), which will have coordinates \ ((x_0, y_0) \). Let the radius of this circle be \ (τ \). Take an arbitrary point \ (Y \), the coordinates of which we denote by \ ((x, y) \) (Fig. 2).

According to the formula for the distance between two points in the given coordinate system, we get:

\ (| XY | = \ sqrt ((x-x_0) ^ 2 + (y-y_0) ^ 2) \)

On the other hand, \ (| XY | \) is the distance from any point on the circle to our chosen center. That is, by Definition 3, we obtain \ (| XY | = τ \), therefore

\ (\ sqrt ((x-x_0) ^ 2 + (y-y_0) ^ 2) = τ \)

\ ((x-x_0) ^ 2 + (y-y_0) ^ 2 = τ ^ 2 \) (1)

Thus, we get that equation (1) is the equation of the circle in the Cartesian coordinate system.

Circumference (perimeter of a circle)

We will display the length of an arbitrary circle \ (C \) using its radius equal to \ (τ \).

We will consider two arbitrary circles. Let us denote their lengths by \ (C \) and \ (C "\), whose radii are \ (τ \) and \ (τ" \). We will inscribe in these circles regular \ (n \) -gons, the perimeters of which are \ (ρ \) and \ (ρ "\), the side lengths of which are \ (α \) and \ (α" \), respectively. As we know, the side of a regular \ (n \) -gon inscribed in a circle equals

\ (α = 2τsin \ frac (180 ^ 0) (n) \)

Then, we will get that

\ (ρ = nα = 2nτ \ frac (sin180 ^ 0) (n) \)

\ (ρ "= nα" = 2nτ "\ frac (sin180 ^ 0) (n) \)

\ (\ frac (ρ) (ρ ") = \ frac (2nτsin \ frac (180 ^ 0) (n)) (2nτ" \ frac (sin180 ^ 0) (n)) = \ frac (2τ) (2τ " ) \)

We get that the relation \ (\ frac (ρ) (ρ ") = \ frac (2τ) (2τ") \) will be correct regardless of the value of the number of sides of the inscribed regular polygons. I.e

\ (\ lim_ (n \ to \ infty) (\ frac (ρ) (ρ ")) = \ frac (2τ) (2τ") \)

On the other hand, if we infinitely increase the number of sides of inscribed regular polygons (that is, \ (n → ∞ \)), we get the equality:

\ (lim_ (n \ to \ infty) (\ frac (ρ) (ρ ")) = \ frac (C) (C") \)

From the last two equalities we get that

\ (\ frac (C) (C ") = \ frac (2τ) (2τ") \)

\ (\ frac (C) (2τ) = \ frac (C ") (2τ") \)

We see that the ratio of the circumference of a circle to its doubled radius is always the same number, regardless of the choice of the circle and its parameters, that is

\ (\ frac (C) (2τ) = const \)

This constant is called the number "pi" and denoted by \ (π \). Approximately, this number will be equal to \ (3.14 \) (there is no exact meaning of this number, since it is an irrational number). In this way

\ (\ frac (C) (2τ) = π \)

Finally, we get that the circumference (perimeter of the circle) is determined by the formula

\ (C = 2πτ \)

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A circle is made up of many points that are equidistant from the center. It is a flat geometric figure, and its length is not difficult to find. A person encounters a circle and a circle every day, regardless of the area in which he works. Many vegetables and fruits, devices and mechanisms, dishes and furniture are round in shape. A circle is called the set of points that is located within the boundaries of the circle. Therefore, the length of the figure is equal to the perimeter of the circle.

In contact with

Figure characteristics

In addition to the fact that the description of the concept of a circle is quite simple, its characteristics are also easy to understand. With their help, you can calculate its length. The inner part of the circle consists of many points, among which two - A and B - can be seen at right angles. This segment is called the diameter, it consists of two radii.

Within the circle there are points X such, which does not change and is not equal to unity, the ratio AX / BX. In a circle, this condition must be met, otherwise this figure does not have the shape of a circle. The rule applies to each point of which the figure consists: the sum of the squares of the distances from these points to the other two always exceeds half the length of the segment between them.

Basic circle terms

In order to be able to find the length of a figure, you need to know the basic terms related to it. The main parameters of the shape are diameter, radius and chord. The radius is called the segment connecting the center of the circle with any point on its curve. The chord is equal to the distance between two points on the curve of the figure. Diameter - distance between points passing through the center of the shape.

Basic formulas for calculations

The parameters are used in the formulas for calculating the circumference:

Diameter in calculation formulas

In economics and mathematics, it is often necessary to find the length of a circle. But in everyday life, you can face this need, for example, during the construction of a fence around a round pool. How to calculate the circumference by diameter? In this case, use the formula C = π * D, where C is the desired value, D is the diameter.

For example, the width of the pool is 30 meters, and the fence posts are planned to be placed at a distance of ten meters from it. In this case, the formula for calculating the diameter: 30 + 10 * 2 = 50 meters. The required value (in this example, the length of the fence): 3.14 * 50 = 157 meters. If the posts of the fence stand at a distance of three meters from each other, then 52 of them will be needed in total.

Radius calculations

How to calculate the circumference of a circle from a known radius? For this, the formula C = 2 * π * r is used, where C is the length, r is the radius. The radius in a circle is half the diameter, and this rule can be useful in everyday life. For example, when baking a cake in a sliding pan.

To prevent the culinary product from getting dirty, it is necessary to use a decorative wrapper. How do you cut a paper circle of the right size?

Those who are somewhat familiar with mathematics understand that in this case, you need to multiply the number π by twice the radius of the form used. For example, the diameter of a mold is 20 centimeters, so its radius is 10 centimeters. According to these parameters, the required circle size is found: 2 * 10 * 3, 14 = 62.8 centimeters.

Handy calculation methods

If it is not possible to find the circumference by the formula, then you should use the available methods for calculating this value:

• With a small round object, its length can be found with a rope wrapped around once.
• The size of a large object is measured as follows: a rope is laid out on a flat plane, and a circle is rolled over it once.
• Modern students and schoolchildren use calculators for calculations. In online mode, unknown values ​​can be recognized by known parameters.

Round objects in the history of human life

The first round product invented by man is the wheel. The first structures were small rounded logs set on an axis. Then came the wheels made of wooden spokes and rims. Metal parts were gradually added to the product to reduce wear. It was in order to find out the length of the metal strips for wheel upholstery that scientists of past centuries were looking for a formula for calculating this value.

The wheel is shaped like a potter's wheel, most of the details in complex mechanisms, designs of water mills and spinning wheels. Round objects are not uncommon in construction - frames of round windows in the Romanesque architectural style, portholes in ships. Architects, engineers, scientists, mechanics and planners are faced with the need to calculate the dimensions of a circle every day in their professional field.

The circle calculator is a service specially designed for calculating the geometric dimensions of shapes online. Thanks to this service, you can easily determine any parameter of the figure, which is based on a circle. For example: You know the volume of a sphere, but you need to get its area. It couldn't be easier! Select the appropriate option, enter a numerical value, and click Calculate. The service not only gives out the results of calculations, but also provides the formulas by which they were made. With the help of our service, you can easily calculate the radius, diameter, circumference (perimeter of a circle), area of ​​a circle and a sphere, volume of a sphere.

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 can easily determine the value of any other parameter of a circle or ball. Our site is built exactly on such a scheme. Regardless of which initial parameter you have chosen, the first step is to calculate the value of the radius, and all subsequent calculations are based on it. For greater accuracy of calculations, the site uses Pi rounded to the 10th decimal place.

Calculate diameter

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

Find out the circumference

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

Calculate the area of ​​a circle

The area of ​​a 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 to all, without exception, segments of the population. It is difficult to imagine a field of science and technology in which you would not need to know the area of ​​a circle. The formula for the calculation is again easy: S = PR 2. This formula and our online calculator will help you easily find the area of ​​any circle. Our site guarantees high accuracy of calculations and their lightning-fast execution.

Calculate the area of ​​the ball

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 ball for many years. Where can it be applied? Yes, everywhere! For example, you know that the area of ​​the globe is 510,100,000 square kilometers. It is useless to list where knowledge of this formula can be applied. The area of ​​application of the formula for calculating the area of ​​a ball is too wide.

Calculate the volume of a ball

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 allows you to calculate the volume of a ball in a matter of seconds, if you know any of the following parameters: radius, diameter, length of a circle, area of ​​a circle or area of ​​a ball. You can also use it for the reverse calculation, for example, in order to know the volume of a ball, to get the value of its radius or diameter. Thank you for taking a quick look at the capabilities of our lap calculator. We hope you liked our site and you have already bookmarked the site.

Many objects in the surrounding world are round in shape. These are wheels, round window openings, pipes, various dishes and much more. You can calculate what the circumference of a circle is, knowing its diameter or radius.

There are several definitions of this geometric shape.

• It is a closed curve made up of points that are equidistant from a given point.
• This is a curve consisting of points A and B, which are the ends of the line segment, and all points from which A and B are visible at right angles. In this case, the segment AB is the diameter.
• For the same segment AB, this curve includes all points C, such that the AC / BC ratio is unchanged and does not equal 1.
• This is a curve consisting of points for which the following is true: if you add the squares of the distances from one point to two given other points A and B, you get a constant number greater than 1/2 of the segment connecting A and B. This definition is derived from the Pythagorean theorem.

Note! There are other definitions as well. A circle is an area within a circle. The perimeter of a circle is its length. According to various definitions, a circle may or may not include the curve itself, which is its boundary.

Defining a circle

Formulas

How to calculate the circumference of a circle in terms of the radius? This is done using a simple formula:

where L is the required value,

π is pi, approximately equal to 3.1413926.

Usually, to find the desired value, it is enough to use π to the second decimal place, that is, 3.14, this will provide the required accuracy. Calculators, in particular engineering calculators, may have a button that automatically enters the value of the number π.

Designations

To find through the diameter, there is the following formula:

If L is already known, the radius or diameter can be easily found. To do this, L must be divided by 2π or π, respectively.

If a circle is already given, you need to understand how to find the circumference of a circle from this data. The area of ​​the circle is S = πR2. From here we find the radius: R = √ (S / π). Then

L = 2πR = 2π√ (S / π) = 2√ (Sπ).

It is also easy to calculate the area in terms of L: S = πR2 = π (L / (2π)) 2 = L2 / (4π)

In summary, we can say that there are three basic formulas:

• through the radius - L = 2πR;
• through the diameter - L = πD;
• through the area of ​​the circle - L = 2√ (Sπ).

Pi

Without the number π, it will not be possible to solve the problem under consideration. The number π was first found as the ratio of the circumference of a circle to its diameter. This was done by the ancient Babylonians, Egyptians and Indians. They found it quite accurately - their results differed from the now known value of π by no more than 1%. The constant was approximated by such fractions as 25/8, 256/81, 339/108.

Further, the value of this constant was considered not only from the point of view of geometry, but also from the point of view of mathematical analysis through the sum of the series. The designation of this constant by the Greek letter π was first used by William Jones in 1706, and it became popular after the work of Euler.

It is now known that this constant is an infinite non-periodic decimal fraction, it is irrational, that is, it cannot be represented as a ratio of two integers. With the help of calculations on supercomputers in 2011, we learned the 10-trillionth sign of a constant.

It is interesting! Various mnemonic rules have been invented to memorize the first few digits of π. Some allow you to store a large number of numbers in memory, for example, one French poem will help you memorize pi up to 126 characters.

If you need circumference, an online calculator can help you with that. There are many such calculators, in them you only need to enter the radius or diameter. Some of them have both of these options, others calculate the result only through R. Some calculators can calculate the required value with different precision, you need to specify the number of decimal places. Also, using online calculators, you can calculate the area of ​​a circle.

Such calculators are easy to find by any search engine. There are also mobile applications that will help you solve the problem of how to find the length of a circle.

Useful video: circumference

Practical use

It is most often necessary for engineers and architects to solve such a problem, but knowledge of the necessary formulas can also be useful in everyday life. For example, you want to wrap a paper strip on a cake baked in a shape with a diameter of 20 cm. Then it will not be difficult to find the length of this strip.