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), the area of a circle and a ball, and the volume of a ball.
Calculate radius
The task 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 not at all more complex 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 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 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 and get 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.
A circle is a closed curve, all points of which are at the same distance from the center. This figure is flat. Therefore, the solution to the problem, the question of which is how to find the circumference, is quite simple. We will look at all available methods in today's article.
Figure descriptions
In addition to a fairly simple descriptive definition, there are three more mathematical characteristics of a circle, which in themselves contain the answer to the question of how to find the circumference:
- Consists of points A and B and all others from which AB can be seen at right angles. The diameter of this figure is equal to the length of the segment under consideration.
- Includes only those points X such that the ratio AX/BX is constant and not equal to one. If this condition is not met, then it is not a circle.
- It consists of points, for each of which the following equality holds: the sum of the squares of the distances to the other two is a given value, which is always more than half the length of the segment between them.
Terminology
Not everyone at school had a good math teacher. Therefore, the answer to the question of how to find the circumference is further complicated by the fact that not everyone knows the basic geometric concepts. Radius is a segment that connects the center of a figure to a point on a curve. A special case in trigonometry is the unit circle. A chord is a segment that connects two points on a curve. For example, the already discussed AB falls under this definition. The diameter is the chord passing through the center. The number π is equal to the length of a unit semicircle.
Basic formulas
The definitions directly follow geometric formulas that allow you to calculate the main characteristics of a circle:
- The length is equal to the product of the number π and the diameter. The formula is usually written as follows: C = π*D.
- The radius is equal to half the diameter. It can also be calculated by calculating the quotient of dividing the circumference by twice the number π. The formula looks like this: R = C/(2* π) = D/2.
- The diameter is equal to the quotient of the circumference divided by π or twice the radius. The formula is quite simple and looks like this: D = C/π = 2*R.
- The area of a circle is equal to the product of π and the square of the radius. Similarly, diameter can be used in this formula. In this case, the area will be equal to the quotient of the product of π and the square of the diameter divided by four. The formula can be written as follows: S = π*R 2 = π*D 2 /4.
How to find the circumference of a circle by diameter
For simplicity of explanation, let us denote by letters the characteristics of the figure necessary for the calculation. Let C be the desired length, D its diameter, and π approximately equal to 3.14. If we have only one known quantity, then the problem can be considered solved. Why is this necessary in life? Suppose we decide to surround a round pool with a fence. How to calculate the required number of columns? And here the ability to calculate the circumference comes to the rescue. The formula is as follows: C = π D. In our example, the diameter is determined based on the radius of the pool and the required distance from the fence. For example, suppose that our home artificial pond is 20 meters wide, and we are going to place the posts at a ten-meter distance from it. The diameter of the resulting circle is 20 + 10*2 = 40 m. Length is 3.14*40 = 125.6 meters. We will need 25 posts if the gap between them is about 5 m.
Length through radius
As always, let's start by assigning letters to the characteristics of the circle. In fact, they are universal, so mathematicians from different countries It is not at all necessary to know each other's language. Let's assume that C is the circumference of the circle, r is its radius, and π is approximately equal to 3.14. The formula in this case looks like this: C = 2*π*r. Obviously, this is an absolutely correct equation. As we have already figured out, the diameter of a circle is equal to twice its radius, so this formula looks like this. In life, this method can also often come in handy. For example, we bake a cake in a special sliding form. To prevent it from getting dirty, we need a decorative wrapper. But how to cut a circle of the required size. This is where mathematics comes to the rescue. Those who know how to find out the circumference of a circle will immediately say that you need to multiply the number π by twice the radius of the shape. If its radius is 25 cm, then the length will be 157 centimeters.
Sample problems
We have already looked at several practical cases of the knowledge gained on how to find out the circumference of a circle. But often we are not concerned about them, but about the real mathematical problems contained in the textbook. After all, the teacher gives points for them! So let's look at a more complex problem. Let's assume that the circumference of the circle is 26 cm. How to find the radius of such a figure?
Example solution
First, let's write down what we are given: C = 26 cm, π = 3.14. Also remember the formula: C = 2* π*R. From it you can extract the radius of the circle. Thus, R= C/2/π. Now let's proceed to the actual calculation. First, divide the length by two. We get 13. Now we need to divide by the value of the number π: 13/3.14 = 4.14 cm. It is important not to forget to write the answer correctly, that is, with units of measurement, otherwise the entire practical meaning of such problems is lost. In addition, for such inattention you can receive a grade one point lower. And no matter how annoying it may be, you will have to put up with this state of affairs.
The beast is not as scary as it is painted
So we have dealt with such a difficult task at first glance. As it turns out, you just need to understand the meaning of the terms and remember a few simple formulas. Math is not that scary, you just need to put in a little effort. So geometry is waiting for you!
A circle is a curved line that encloses a circle. In geometry, shapes are flat, so the definition refers to a two-dimensional image. It is assumed that all points of this curve are located at an equal distance from the center of the circle.
The circle has several characteristics on the basis of which calculations related to this geometric figure are made. These include: diameter, radius, area and circumference. These characteristics are interrelated, that is, to calculate them, information about at least one of the components is sufficient. For example, knowing only the radius of a geometric figure, you can use the formula to find the circumference, diameter, and area.
- The radius of a circle is the segment inside the circle connected to its center.
- A diameter is a segment inside a circle connecting its points and passing through the center. Essentially, the diameter is two radii. This is exactly what the formula for calculating it looks like: D=2r.
- There is one more component of a circle - a chord. This is a straight line that connects two points on a circle, but does not always pass through the center. So the chord that passes through it is also called the diameter.
How to find out the circumference? Let's find out now.
Circumference: formula
The Latin letter p was chosen to denote this characteristic. Archimedes also proved that the ratio of the circumference of a circle to its diameter is the same number for all circles: this is the number π, which is approximately equal to 3.14159. The formula for calculating π is: π = p/d. According to this formula, the value of p is equal to πd, that is, the circumference: p= πd. Since d (diameter) is equal to two radii, the same formula for the circumference can be written as p=2πr. Let's consider the application of the formula using simple problems as an example:
Problem 1
At the base of the Tsar Bell the diameter is 6.6 meters. What is the circumference of the base of the bell?
- So, the formula for calculating the circle is p= πd
- Substitute the existing value into the formula: p=3.14*6.6= 20.724
Answer: The circumference of the bell base is 20.7 meters.
Problem 2
The artificial satellite of the Earth rotates at a distance of 320 km from the planet. The radius of the Earth is 6370 km. What is the length of the satellite's circular orbit?
- 1. Calculate the radius of the circular orbit of the Earth satellite: 6370+320=6690 (km)
- 2.Calculate the length of the satellite’s circular orbit using the formula: P=2πr
- 3.P=2*3.14*6690=42013.2
Answer: the length of the circular orbit of the Earth satellite is 42013.2 km.
Methods for measuring circumference
Calculating the circumference of a circle is not often used in practice. The reason for this is the approximate value of the number π. In everyday life, to find the length of a circle, a special device is used - a curvimeter. An arbitrary starting point is marked on the circle and the device is led from it strictly along the line until they reach this point again.
How to find the circumference of a circle? You just need to keep simple calculation formulas in your head.
The circumference of a circle is indicated by the letter C and is calculated by the formula:
C = 2πR,
Where R - radius of the circle.
Derivation of the formula expressing the circumference
Path C and C’ are the lengths of circles of radii R and R’. Let us inscribe a regular n-gon into each of them and denote their perimeters by P n and P" n, and their sides by a n and a" n. Using the formula for calculating the side of a regular n-gon a n = 2R sin (180°/n) we get:
P n = n a n = n 2R sin (180°/n),
P" n = n · a" n = n · 2R" sin (180°/n).
Hence,
P n / P" n = 2R / 2R". (1)
This equality is valid for any value of n. We will now increase the number n without limit. Since P n → C, P" n → C", n → ∞, then the limit of the ratio P n / P" n is equal to C / C". On the other hand, by virtue of equality (1), this limit is equal to 2R/2R". Thus, C/C" = 2R/2R". From this equality it follows that C/2R = C"/2R", i.e. . The ratio of the circumference of a circle to its diameter is the same number for all circles. This number is usually denoted by the Greek letter π (“pi”).
From the equality C / 2R = π we obtain the formula for calculating the circumference of a circle of radius R:
C = 2πR.
Circular arc length
Since the length of the entire circle is 2πR, then the length l of an arc of 1° is equal to 2πR / 360 = πR / 180.
That's why length l of an arc of a circle with degree measure α expressed by the formula
l = (πR / 180) α.
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 the distance of 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 and is denoted by the Greek letter π .
Determining the circumference
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
Task:
Calculate circumference, having a radius of 10 centimeters.
Solution:Formula for calculating the circumference of a circle has the form:
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 length of a circle having a radius of 10 centimeters is:
L = 2 × 3.14 × 5 = 31.4 centimeters
Circle is a geometric figure, which is a collection of all points on a plane removed from a given point, which is called its center, by a certain distance not equal to zero and called the radius. Scientists were able 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 was compiled around 1900 BC in ancient Babylon.
We encounter geometric shapes such as circles every day and everywhere. It is its shape that has the outer surface of the wheels that are equipped with various vehicles. This detail, despite its apparent simplicity and unpretentiousness, is considered one of the greatest inventions of mankind, and it is interesting that the Australian aborigines and 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 was improved, their design became more and more complex, and their manufacture required the use of 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 cover it with metal strips. In order to determine the lengths of these elements, it is necessary to use a formula for calculating the circumference (although in practice, most likely, the craftsmen did this “by eye” or simply by encircling the wheel with a strip and cutting off the required section).
It should be noted that wheel It is not only used in vehicles. For example, its shape is shaped like a potter's wheel, as well as elements of gears of gears, widely used in technology. Wheels have long 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, which were used to make threads from animal wool and plant fibers.
Circles can often be found in construction. Their shape is shaped by fairly 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 of special tools. One of the varieties of round windows are portholes installed in ships and aircraft.
Thus, design engineers who develop various machines, mechanisms and units, as well as architects and designers, often have to solve the problem of determining the circumference of a circle. Since the number π , necessary for this, is infinite, it is not possible to determine this parameter with absolute accuracy, and therefore the calculations take into account the degree of it that in a particular case is necessary and sufficient.
