Finding a circle. How to find and what will be the circumference of a circle?

In the process of carrying out construction work at home or at work, it may become necessary to measure the diameter of a pipe that is already installed in the water supply or sewerage system. It is also necessary to know this parameter at the design stage of laying utility lines.

Hence the need arises to figure out how to determine the diameter of the pipe. The specific measurement method chosen depends on the size of the site and whether the piping location is accessible.

Determining diameter at home

Before measuring the diameter of the pipe, you need to prepare the following tools and devices:

• tape measure or standard ruler;
• calipers;
• camera - it will be used if necessary.

If the pipeline is accessible for measurements, and the ends of the pipes can be measured without problems, then it is enough to have a regular ruler or tape measure at your disposal. It should be borne in mind that this method is used when minimal requirements are imposed on accuracy.

In this case, measure the diameter of the pipes in the following sequence:

1. The prepared tools are applied to the place where the widest part of the end of the product is located.
2. Then count the number of divisions corresponding to the diameter size.

This method allows you to determine the parameters of the pipeline with an accuracy of several millimeters.

To measure the outer diameter of pipes with a small cross-section, you can use a tool such as a caliper:

1. Spread its legs and apply it to the end of the product.
2. Then they need to be moved so that they are pressed tightly against the outside of the pipe walls.
3. Based on the scale of device values, the required parameter is found out.

This method of determining the pipe diameter gives fairly accurate results, down to tenths of a millimeter.

When the pipeline is inaccessible for measurement and is part of an already functioning water supply structure or gas main, proceed as follows: a caliper is applied to the pipe, to its side surface. In this way, the product is measured in cases where the length of the measuring device’s legs exceeds half the diameter of the pipe product.

Often in everyday life there is a need to learn how to measure the diameter of a pipe with a large cross-section. There is a simple way to do this: it is enough to know the circumference of the product and the constant π equal to 3.14.

First, using a tape measure or a piece of cord, measure the girth of the pipe. Then they substitute the known quantities into the formula d=l:π, where:

d – determined diameter;

l is the length of the measured circle.

For example, the girth of the pipe is 62.8 centimeters, then d = 62.8:3.14 = 20 centimeters or 200 millimeters.

There are situations when the laid pipeline is completely inaccessible. Then you can use the copy method. Its essence lies in the fact that a measuring tool or a small object whose parameters are known is applied to the pipe.

For example, it could be a box of matches, the length of which is 5 centimeters. Then this section of the pipeline is photographed. Subsequent calculations are performed from the photograph. The photograph measures the apparent thickness of the product in millimeters. Then you need to convert all the obtained values ​​into real pipe parameters, taking into account the scale of the photograph taken.

Measuring diameters in production conditions

At large facilities under construction, pipes are subject to incoming inspection before installation begins. First of all, they check the certificates and markings applied to pipe products.

The documentation must contain certain information regarding the pipes:

• nominal dimensions;
• technical specifications number and date;
• brand of metal or type of plastic;
• product lot number;
• results of the tests performed;
• chem. smelting analysis;
• type of heat treatment;
• X-ray flaw detection results.

In addition, markings containing:

• manufacturer's name;
• heat number;
• product number and its nominal parameters;
• date of manufacture;
• carbon equivalent.

Pipe lengths under production conditions are determined using measuring wire. There are also no difficulties with how to measure the diameter of a pipe with a tape measure.

For first class products, the permissible deviation in one direction or the other from the declared length is 15 millimeters. For second class – 100 millimeters.

The outer diameter of pipes is checked using the formula d = l:π-2Δр-0.2 mm, where in addition to the above values:

Δр – thickness of tape measure material;

0.2 millimeters is the allowance for the tool to adhere to the surface.

The deviation of the external diameter from that declared by the manufacturer is allowed:

• for products with a cross-section of no more than 200 millimeters–1.5 millimeters;
• for large pipes – 0.7%.

In the latter case, ultrasonic measuring instruments are used to check pipe products. To determine the wall thickness, calipers are used, in which the division on the scale corresponds to 0.01 millimeters. The minus tolerance should not exceed 5% of the nominal thickness. In this case, the curvature cannot be more than 1.5 millimeters per 1 linear meter.

From the information described above, it is clear that it is not difficult to figure out how to determine the diameter of a pipe by its circumference or using simple measuring tools.

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 a figure based on a circle. For example: You know the volume of a ball, but you need to get its area. Nothing could be 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), area of ​​a circle and ball, and volume of a ball.

Calculate radius

The problem of calculating the radius value 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 this scheme. Regardless of what initial parameter you have chosen, the radius value is first calculated 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

Calculating diameter is the simplest type of calculation that our calculator can perform. It is not at all difficult to obtain the diameter value manually; for this you do not need to resort to the Internet at all. The diameter is equal to the radius value 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 website, you will calculate the diameter with great accuracy in a fraction of a second.

Find out the circumference

You can’t even imagine how many round objects there are 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 done either on a piece of paper or using this online assistant. The advantage of the latter is that it illustrates all calculations with pictures. And on top of everything else, 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. Being 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 a field 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 find out the area of ​​any circle without any extra effort. Our site guarantees high accuracy of 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 allowing people to calculate the area of ​​a ball quite accurately for many years. Where can this 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 scope of the formula for calculating the area of ​​a sphere is too wide.

Calculate the volume of the 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 website 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 reverse calculations, for example, to know the volume of a ball to obtain the value of its radius or diameter. Thank you for taking a quick look at the capabilities of our circle calculator. We hope you liked our site and have already bookmarked the site.

Instructions

First you need the initial data for the task. The fact is that its condition cannot explicitly say what the radius is circle. Instead, the problem may give the length of the diameter circle. Diameter circle- a segment that connects two opposite points circle, passing through its center. Having analyzed the definitions circle, we can say that the length of the diameter is twice the length of the radius.

Now we can accept the radius circle equal to R. Then for the length circle you need to use the formula:
L = 2πR = πD, where L is the length circle, D - diameter circle, which is always 2 times the radius.

note

A circle can be inscribed in a polygon or described around it. Moreover, if the circle is inscribed, then at the points of contact with the sides of the polygon it will divide them in half. To find out the radius of the inscribed circle, you need to divide the area of ​​the polygon by half its perimeter:
R = S/p.
If a circle is circumscribed around a triangle, then its radius is found using the following formula:
R = a*b*c/4S, where a, b, c are the sides of a given triangle, S is the area of ​​the triangle around which the circle is circumscribed.
If you want to describe a circle around a quadrilateral, this can be done if two conditions are met:
The quadrilateral must be convex.
The sum of the opposite angles of the quadrilateral should be 180°

Helpful advice

In addition to the traditional caliper, stencils can also be used to draw a circle. Modern stencils include circles of different diameters. These stencils can be purchased at any office supply store.

Sources:

• How to find the circumference of a circle?

A circle is a closed curved line, all points of which are at equal distances from one point. This point is the center of the circle, and the segment between the point on the curve and its center is called the radius of the circle.

Instructions

If a straight line is drawn through the center of a circle, then its segment between two points of intersection of this line with the circle is called the diameter of the given circle. Half the diameter, from the center to the point where the diameter intersects the circle is the radius
circles. If a circle is cut at an arbitrary point, straightened and measured, then the resulting value is the length of the given circle.

Draw several circles with different compass solutions. Visual comparison suggests that a larger diameter outlines a larger circle bounded by a circle with a larger length. Consequently, there is a directly proportional relationship between the diameter of a circle and its length.

In its physical meaning, the “circumference length” parameter corresponds to a bounded by a broken line. If we inscribe a regular n-gon with side b into a circle, then the perimeter of such a figure P is equal to the product of side b by the number of sides n: P=b*n. Side b can be determined by the formula: b=2R*Sin (π/n), where R is the radius of the circle into which the n-gon is inscribed.

As the number of sides increases, the perimeter of the inscribed polygon will increasingly approach L. Р= b*n=2n*R*Sin (π/n)=n*D*Sin (π/n). The relationship between the circumference L and its diameter D is constant. The ratio L/D=n*Sin (π/n) as the number of sides of an inscribed polygon tends to infinity tends to the number π, a constant value called “pi” and expressed as an infinite decimal fraction. For calculations without the use of computer technology, the value π=3.14 is taken. The circumference of a circle and its diameter are related by the formula: L= πD. For a circle, divide its length by π=3.14.

Its diameter. To do this, you just need to apply the formula for the circumference of the circle. L = p D Here: L is the circumference, p is the number Pi equal to 3.14, D is the diameter of the circle. Rearrange the required value in the formula for the circumference to the left side and get: D = L /P

Let's look at a practical problem. Suppose you need to make a cover for a round country well, which is currently not accessible. No, and unsuitable weather conditions. But do you have data on length its circumference. Let's assume this is 600 cm. We substitute the values ​​into the indicated formula: D = 600/3.14 = 191.08 cm. So, the diameter of your is 191 cm. Increase the diameter to 2, taking into account the allowance for the edges. Set the compass to a radius of 1 m (100 cm) and draw a circle.

Helpful advice

It is convenient to draw circles of relatively large diameters at home with a compass, which can be quickly made. It's done like this. Two nails are driven into the lath at a distance from each other equal to the radius of the circle. Drive one nail shallowly into the workpiece. And use the other one, rotating the staff, as a marker.

A circle is a geometric figure on a plane that consists of all points of this plane that are at the same distance from a given point. The given point is called the center circle, and the distance at which the points circle are from its center - radius circle. The area of ​​the plane bounded by a circle is called a circle. There are several calculation methods diameter circle, the choice of a specific one depends on the available initial data.

Instructions

In the simplest case, if the circle is of radius R, then it will be equal to
D = 2 * R
If radius circle is not known, but it is known, then the diameter can be calculated using the length formula circle
D = L/P, where L is length circle, P – P.
Same diameter circle can be calculated knowing the area limited by it
D = 2 * v(S/P), where S is the area of ​​the circle, P is the number P.

Sources:

• circle diameter calculation

In the course of high school planimetry, concept circle is defined as a geometric figure consisting of all points of the plane lying at a distance of a radius from a point called its center. Inside a circle you can draw many segments connecting its points in different ways. Depending on the construction of these segments, circle can be divided into several parts different ways.

Instructions

Finally, circle can be divided by constructing segments. A segment is a part of a circle made up of a chord and an arc of a circle. In this case, a chord is a segment connecting any two points on a circle. Using segments circle can be divided into an infinite number of parts with or without a formation at its center.

Video on the topic

note

The figures obtained by the above methods - polygons, segments and sectors - can also be divided using appropriate methods, for example, diagonals of polygons or bisectors of angles.

A flat geometric figure is called a circle, and the line that bounds it is usually called a circle. The main property is that every point on this line is the same distance from the center of the figure. A segment with a beginning at the center of the circle and ending at any point on the circle is called a radius, and a segment connecting two points on the circle and passing through the center is called a diameter.

Instructions

Use Pi to find the length of a diameter given the known circumference. This constant expresses a constant relationship between these two parameters of the circle - regardless of the size of the circle, dividing its circumference by the length of its diameter always gives the same number. It follows from this that to find the length of the diameter, the circumference should be divided by the number Pi. As a rule, for practical calculations of the length of a diameter, accuracy to hundredths of a unit is sufficient, that is, to two decimal places, so the number Pi can be considered equal to 3.14. But since this constant is an irrational number, it has an infinite number of decimal places. If there is a need for a more precise definition, then the required number of signs for pi can be found, for example, at this link - http://www.math.com/tables/constants/pi.htm.

Given the known lengths of the sides (a and b) of a rectangle inscribed in a circle, the length of the diameter (d) can be calculated by finding the length of the diagonal of this rectangle. Since the diagonal here is the hypotenuse in a right triangle, the legs of which form sides of known length, then according to the Pythagorean theorem, the length of the diagonal, and with it the length of the diameter of the circumscribed circle, can be calculated by finding from the sum of the squares of the lengths of the known sides: d=√(a² + b²).

Dividing into several equal parts is a common task. This way you can build a regular polygon, draw a star, or prepare the basis for a diagram. There are several ways to solve this interesting problem.

You will need

• - a circle with a designated center (if the center is not marked, you will have to find it in any way);
• - protractor;
• - compass with stylus;
• - pencil;
• - ruler.

Instructions

The easiest way to divide circle into equal parts - using a protractor. Dividing 360° into the required number of parts, you get the angle. Start from any point on the circle - the corresponding radius will be the zero mark. Starting from there, make marks on the protractor corresponding to the calculated angle. This method is recommended if you need to divide circle by five, seven, nine, etc. parts. For example, to build a regular pentagon, its vertices must be located every 360/5 = 72°, that is, at 0°, 72°, 144°, 216°, 288°.

To share circle into six parts, you can use the property of a regular one - its longest diagonal is equal to twice the side. A regular hexagon is, as it were, made up of six equilateral triangles. Set the compass opening equal to the radius of the circle, and make notches with it, starting from any arbitrary point. The serifs form a regular hexagon, one of the vertices of which will be at this point. By connecting the vertices through one, you will build a regular triangle inscribed in circle, that is, it is divided into three equal parts.

To share circle into four parts, start with an arbitrary diameter. Its ends will give two of the required four points. To find the rest, set the compass opening equal to the circle. Place the compass needle on one end of the diameter and make notches outside the circle and below. Repeat the same with the other end of the diameter. Draw an auxiliary line between the intersection points of the serifs. It will give you a second diameter, strictly perpendicular to the original one. Its ends will become the remaining two vertices of the square inscribed in circle.

Using the method described above, you can find the middle of any segment. As a consequence, with this method you can double the number of equal parts into which you circle. Having found the midpoint of each side of the correct n- inscribed in circle, you can draw perpendiculars to them, find the point of their intersection with circle yu and thus construct the vertices of a regular 2n-gon. This procedure can be repeated as many times as you like. So, the square turns into, that - into, etc. Starting with a square, you can, for example, divide circle into 256 equal parts.

note

To divide a circle into equal parts, dividing heads or dividing tables are usually used, which make it possible to divide the circle into equal parts with high accuracy. When it is necessary to divide a circle into equal parts, use the table below. To do this, you need to multiply the diameter of the circle being divided by the coefficient given in the table: K x D.

Helpful advice

Dividing a circle into three, six and twelve equal parts. Two perpendicular axes are drawn, which, intersecting the circle at points 1,2,3,4, divide it into four equal parts; Using the well-known technique of dividing a right angle into two equal parts using a compass or square, they construct bisectors of right angles, which, intersecting with the circle at points 5, 6, 7, and 8, divide each fourth part of the circle in half.

When constructing various geometric shapes, it is sometimes necessary to determine their characteristics: length, width, height, and so on. If we are talking about a circle or circle, then we often have to determine its diameter. A diameter is a straight line segment that connects the two points furthest from each other located on a circle.

You will need

• - yardstick;
• - compass;
• - calculator.

We are surrounded by many objects. And many of them are round in shape. It is given to them for convenient use. Take, for example, a wheel. If it were made in the shape of a square, how would it roll along the road?

In order to make a round object, you need to know what the formula for circumference through diameter looks like. To do this, we first define what this concept is.

Circle and circumference

A circle is a set of points that are located at equal distances from the main point - the center. This distance is called the radius.

The distance between two points on a given line is called a chord. In addition, if a chord passes through the main point (center), then it is called a diameter.

Now let's look at what a circle is. The set of all points that are inside the outline is called a circle.

What is circumference?

After we have covered all the definitions, we can calculate the diameter of a circle. The formula will be discussed a little later.

First, we will try to measure the length of the outline of the glass. To do this, we will wrap it with thread, then measure it with a ruler and find out the approximate length of the imaginary line around the glass. Because the size depends on the correct measurement of the item, and this method is not reliable. But nevertheless, it is quite possible to make accurate measurements.

To do this, let us again remember the wheel. We have repeatedly seen that if you increase the spoke in the wheel (radius), the length of the wheel rim (circumference) will also increase. And also, as the radius of the circle decreases, the length of the rim also decreases.

If we carefully follow these changes, we will see that the length of an imaginary circular line is proportional to its radius. And this number is constant. Next, let's look at how the diameter of a circle is determined: the formula for this will be used in the example below. And let's look at it step by step.

Circle formula through diameter

Since the length of the outline is proportional to the radius, it is correspondingly proportional to the diameter. Therefore, we will conventionally denote its length by the letter C, and its diameter by d. Since the ratio of the length of the outline and the diameter is a constant number, it can be determined.

Having done all the calculations, we will determine a number that is approximately equal to 3.1415... For the reason that during the calculations a specific number did not work out, we will denote it with the letter π . This icon will be useful to us in order to derive the formula for the circumference of a circle through its diameter.

Let's draw an imaginary line through the central point and measure the distance between the two extreme ones. This will be the diameter. If we know the diameter of a circle, the formula for determining its length will look like this: C = d * π.

If we determine the length of different outlines, then if their diameter is known, the same formula will be applied. Because the sign π - this is an approximate calculation, it was decided to multiply the diameter by 3.14 (a number rounded to hundredths).

How to calculate diameter: formula

This time, let's try using this formula to calculate other quantities besides the length of the outline. To calculate the diameter from the circumference, the same formula is used. Only for this purpose we divide its length by π . It will look like this d = C / π.

Let's look at how this formula works in practice. For example, we know the length of the outline of a well, we need to calculate its diameter. It is impossible to measure it because there is no access to it due to weather conditions. Our task is to make a lid. What should we do in this case?

You need to use the formula. Let's take the length of the well outline - for example, 600 cm. We put a specific number in the formula, namely C = 600 / 3.14. As a result, we get approximately 191 cm. Let's round the result to 200 cm. Then, using a compass, draw a round line with a radius of 100 cm.

Since an outline with a large diameter must be drawn with an appropriate compass, you can make such a tool yourself. To do this, take a strip of the required length and drive a nail at each end. We install one nail into the workpiece and drive it in lightly so that it does not move from the intended place. And with the help of the second we draw a line. The device is very simple and convenient.

Modern technologies allow you to use an online calculator to calculate the length of the outline. To do this, you just need to enter the diameter of the circle. The formula will be applied automatically. You can also calculate the circumference of a circle using the radius. Also, if you know the circumference of a circle, the online calculator will calculate the radius and diameter using this formula.