What is Arc Length?
Distance between point A to point B along a section of a curve is known as Arc Length. Ensure you don’t misunderstand length of an arc with the associate degree of arc that is the degree size of its central angle.
How to find Arc Length?
Finding arc length is easy as a circle is always equal to 360° and it is consisting of consecutive points lined up in 360 degree; so, if you divide the measured arc’s degree by 360°, you discover the fraction of the circle’s circumference that the arc makes up.
Then, if you multiply that fraction by the circle’s circumference the length all the approach round the circle, you will get the length of the arc. Formula for arc length is
$$\text{arc length}\;= s\;=\;r\;\theta$$
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What is Arc Length Formula (Degree)?
To find the arc length by using length of arc formula:
$$\text{Arc length}\;=\;2πR\;*\;\frac{C}{360}$$
where:
C = central angle of the arc (degree)
R = is the radius of the circle
π = is Pi, which is approximately 3.142
360° = Full angle
Remember that the circumference of the whole circle is 2πR, so the Arc Length Formula above simply reduces this by dividing the arc angle to a full angle (360).
By implementing the above Arc Length Formula, you can solve for the central angle, radius or arc length if you know any two of them. Try Circumference Calculator for your practice regarding circumference.
What is Arc Length Formula (Radians)?
If the central angle is radians, then arc length formula is simpler:
$$\text{arc length}\;= \;R\;*\;C$$
where:
C = is the central angle of the arc(radians)
R =is the radius of the arc
Arc Length Formula (Radians) is the same as the method used in degrees version, but in the degrees, the 2π/360 converts the degrees to radians.
Another way of measuring angles instead of degrees are Radians. One radian is approximately equals to 57.3° . For dispersion or variation of set of values, try Standard Diviation Calculator.
What is Area of Circle?
We can define area of circle in the following ways:
- All the space inside the circumference of a circle is called the area of that circle.
- Total number of square units inside a circle is called area of that circle.
- Area of space inside the circle is called the area of that circle.
How to find the Area of a Circle?
The basic formula to find the area of a circle is:
$$A = π r^2$$
Where:
A=Area of the circle
r=Radius of the circle
π =Mathematical constant whose value is 22/7 or 3.14.
Let we solve an example to find area of circle!
Example: Radius of a circle is 2cm.What is the area of circle?
Solution: As
$$r = 2cm$$
$$A =?$$
We know that,
$$A = π r^2$$
So, putting values in the above formula we get,
$$A = 3.14* (2)^2$$
$$A= 3.14*4 =12.56 cm^2$$
For calculating trapezium or pair of parallel sides, try out Trapezoid Area Calculator.
How to calculate Area of a Circle?
In geometry class, a common problem is to calculate the area of circle depending upon given information. Even though, the formula (A = π r2 )is very simple and we only need to know the radius of circle to find its area. We also need to practice converting some other bits of the given data in the terms that can help us use this formula.
There are various other methods to find the area of a circle. We will discuss these methods one by one. Before that, we should be known about the terminologies which are described below:
- Circumference (C):
Circumference of a circle is the enclosing boundary of that circle.
- Radius (r):
The length of a line from any point on the boundary of the circle to the center of the circle is known as the radius of the circle.
- Diameter (d):
Diameter is the length of the line that passes across the circle through the center of the circle.
- Pi (π):
Pi is a mathematical constant whose value is approximately 3.14
Now we discuss the methods,
- Method 1:
Pi is a mathematical constant whose value is approximately 3.14
Calculating Area from Diameter
If we know the diameter of a circle, the area can be found using the following formula:
$$Area = πD^2/4$$
Where D is the diameter, and Pi =3.14
- Method 2:
Calculating Area from Circumference
If we know the circumference of a circle, then area can be found as:
$$Area= C^2 /4π$$
Where C is the circumference of the circle.
- Method 3:
Calculating Area from a Sector of a Circle
- Sector:
A sector is defined by drawing two radii from the center out to the edge of the circle. The space between these two radii is called sector.
If we know the area of a sector and its central angle measurement, then:
Acir = Asec * 360/C
Where,
Acir = Area of circle.
Asec = Area of sector.
C = Central angle measure.
How to find Curve Length?
The length of a curve or line is curve length. The length of an arc can be found by following formula for any differentiable curve.
These curves are defined by rectangular, polar or parametric equations. See arc of a circle for the length of a circular arc.
Curve Length Calculator Formula:
where a and b represent x, y, t, or θ-values as appropriate, and DX is the small change in X and Y can be found as well. Curve length calculator calculators the same formula as what an length of an arc calculator uses.
$$\text{arc length}\;= s\;=\;r\;\theta$$
For learning limit of a function, equation & formula find our Limit Calculator for free.
How to use Arc Length Calculator?
Calculatored introduce Arc Length Calculator for calculation of Arc length:
Where,
You have to enter central angle and diameter,
After you entered the central angle and diameter then press “CALCULATE” button and Arc Length Calculator will calculate the Arc length.
Here is the example to calculate Arc Length through Arc Length Formula Calculator.
After entering the central angle of arc (30 degree) and diameter of circle 50, Press “CALCULATE” button and Arc Length Calculator will calculate Arc length on the right side of the calculator in the status block.
For the stduents & teachers of math, we also have Integral Calculator & Derivative Calculator. These calculators are free to use and a great asset for learning online.