Arc length calculator
Before moving straight to what’s and how’s of the Arc length
calculator (calc), let us recall what an arc is? An arch is a curve
formed in a crescent shape, which gets generally found in a circle.
Arcs could get found anywhere around you as well like the moon. But
the question arises how one could find the length of an arc? We’ll
find out soon.
The Arch length calculator is a tool, which could help you find
out the length of the crescent shape arc and also, the area of a
circle sector. Now, let us move ahead with the details about the
arc length formula and its calculations.
How to use the arc length formula calculator?
Firstly, the length of an arch revolves around the radius and the
central angle, theta, of the circle. With the necessary knowledge,
we know that the central intersection is equal to 360 degrees,
which is further equivalent to 2π. So, now the length of the arch
is similar to the circumference. Hence it is proved that the
proportion is constant between the arch length and the central
intersection.Now, the arc length formula is derived by:
S / Θ = C / 2π
Where the S= Arc length; Θ= central angle; C= circumference; 2π=
As the circumference gets derived as C = 2πr,
Then, S / Θ = 2πr / 2π S /
Θ = r
Now, calc* arc length formula by multiplying theta to the radius,
which results as,
S = r * Θ
The result will get calculated in radians.
How to find the area of a sector of a circle
Similarly, as above operations, we could find out the area of a
sector of a circle. So, as we all know that the area of a circle is
equal to πr². Now, let us see what proportions could lead us to.
- A / Θ = πr² / 2π
- A / Θ = r² / 2
The area of a sector of a circle’s formula is: A = r² * Θ
How to calculate the arc length and the area of a sector: An
The following points would tell you how to find the length of the
arch by an example:
- Let us think about the radius first. Let the radius be 15 cm,
or you could choose the diameter as well for the area of a sector
in the calculator itself.
- Now, consider the angle between the ends of given curve as 45
degrees or π/4.
- Then, obtain the result by putting values to the arc length
formula in terms of Pi mentioned above L = r * Θ = 15 * π/4 =
- After that, put the values to the area of sector formula, which
further results into A = r² * Θ / 2 = 15² * π/4 / 2 = 88.36 cm².
- Also, you can use the arc measure calculator to find the
central angle and the radius of a circle. All you need is to put
any two values in the formula and solve the equation.
Equation forming by the length of curve calculator without
The following points would suggest some of certain ways to find
the arc length calc without radius:
With the central angle and sector area
- First of all, you must start with multiplying the area by 2 and
then divide the result with the angle at the centre formed, which
is theta. The answer turns out to be radians.
- Now, please take out the square root of the given outcome,
which was obtained after dividing it.
- In order to get the arch length, multiply the square root with
the central intersection again.
- Then the units will turn out to be the square root of a given
area of the sector angle.
With the central angle and the chord length
- Firstly, divide the angle at the centre by 2 in radians and
then apply the sin function to the equation.
- Secondly, you must divide the chord length by the double of the
result obtained in the point above. The answer you get is the
value of the radius.
- Last but not least, you must multiply the central intersection
with the radius in order to obtain the arch length.
The circle arc calc using radians:
The answer to this query is as simple as a multiplication. All
you need to do is take the central intersection in radians and
multiply it to the radius of the circle.
The central angle calculator
The following points would suggest you find the arch length without the angle at the centre:
With radius and sector area
- First of all, you must multiply the area by 2.
- Then all you have to do is divide the result obtained through
the point above to the squared radius. Also, make sure they have
the same units.
- Following the steps above would help you get the central
With the radius and the chord length
- Firstly, double the radius and then divide the chord length to
- Then, you must find the inverse sin of the result obtained in
the point above.
- Now, double the result formed by the inverse sin. This
operation will be your central edge in radians.
- So, now you have your central edge and radius to find the arch
- Also, note that the S=r theta calc becomes more comfortable
when the central edge is in radians, albeit you can use any unit
of angles. Radians make the calculations more straightforward and
effective like multiplication. Also, as the arch length is a
distance measurement and hence cannot be in radians.