You’re in the middle of a calculus problem, and you suddenly find that you need to find the value of an arc length. Do you remember off the top of your head how to do this?
Rather than search high and low how to determine the value, why not use a simple arc length calculator? This will save you the time and energy you need to devote to other portions of your work and let you continue on to other problems.
Let’s get to finding the value of your arc length!
USING AN ARC LENGTH CALCULATOR
If you’re planning on finding arc lengths with no arc length calculator, or if you simply need a refresher on how to do this by hand, let’s review how to figure out the length of an arc inside a circle.
Pretend you’re back in high school or college and visualize the blackboard in front of you.
The length of an arc means the exact same thing it has always meant. If, for example, you measure the length of a sliced green pepper inside a pizza, you would get the arc of the pepper piece if it was slightly angled… which it should be, if it was baked properly.
Now, remember – arc length is not the same term as the measure of an arc. This isn’t a redundancy so much as a fundamental difference in math terms.
The arc would be the measure of the green pepper piece. The measure of an arc would be the degree size of the central angle created by the shape of the pepper piece, or the space occupied by the chunk of pizza inside that given pepper piece.
INSIDE THE CIRCLE
You know that a circle is a total of 360 degrees. When you take the arc degree measure and divide it by 360 degrees, you will wind up with a fraction.
The fraction gives you the circumference of the circle that the arc contains – a decent chunk of pizza, depending on the size of the pepper.
From here, you multiply the length around the entire circle (the whole circumference) by the fraction that you got from your division. This is going to give you the length of that arc.
To summarize, this is the formula you want to use as an arc length calculator: The circumference of the circle, times the fraction of the circle represented by the arc measure.
ADJUSTING THE ARC LENGTH CALCULATOR
There’s another way you can find out values with an arc length calculator. This involves measuring not in degrees, but in radians.
You will need a formula of Theta times r. Theta is the measurement of the central angle in radians (not degrees, remember this part), and r is the length of a given circle’s radius. If you’re still thinking in terms of pizza, just remember half of the size that you ordered.
Now, you can insert the length of the radius into the formula.
Did you indulge and order an extra-large? Keep your sizes in mind as you substitute values in formulas, as one tiny miscalculation can doom your entire problem. Also, don’t make the mistake of inserting diameter. You need to remember that the radius is only half of the circle’s length, not the entirety of it.
Next, take the measure of the arc’s central angle, and substitute it in for the Theta value. We’re going to repeat ourselves because it’s important: make sure you have done any necessary conversions from degrees into angles.
If you’re using a calculator and the value comes back “Huh?”, you’ve probably made a mistake somewhere.
Now that you have the values you need, you can perform some basic multiplication. Take that theta value, multiply it by the measure of the radius, and voila! You have yourself the length of an arc inside a circle with a given radius.
REVIEWING SECTORS AND AREAS
If the arc length calculator isn’t on your mind right now and you’re having some trouble with the fundamentals, let’s take a step back and review some other concepts in geometry.
You can find the area of a circle with a simple formula: Pi times the square of the radius. Pi will be a constant value, represented by the Greek letter on your calculator. For the circumference, you need to determine that with 2 times the product of Pi and the radius.
Going back to the pizza angle (because it’s pizza and why not?), we can remove a section of the circle by turning the entire circle and marking off a section.
The angle of the marked-off section becomes out Theta angle, used in the formula for an arc length calculator. Each line that contains the section will be the same length, as the center of a circle extends to the same length when you get to the end of the circle.
This angle is referred to as the central angle, but sometimes you’ll see it labeled as the subtended angle. It’s not a common term outside of deeper math, and you shouldn’t have to worry about seeing the word much in the future unless you’re winning a trivia game.
FINDING AN ARC LENGTH CALCULATOR ONLINE
If you want to skip the formula work for now and just skip to getting an arc length calculator, we can jump to some links for your browsing convince.
Listed below are some website resources that will have you finding arc lengths as fast as your mouser-clicking ability will allow.
The Wolfram Alpha website contains an arc length calculator that is free of charge and available to anyone who needs to use it.
To get the arc length, you’ll input the values to compute through coordinate systems and a number of different dimensions.
Wolfram Alpha allows you to find several different types of arc lengths, depending on where exactly you wish to find them. If you’re computing the arc length of common curves, you will be able to find the arc length of a circle. You can also input values and snag the cardioid length.
Cardioids are heart-shaped curves that you can trace by finding a point on the circumference of a circle which rolls around another circle that looks just like the first one. WolframAlpha also allows you to specify a curve in polar coordinates, compute the length of an arc from a given curve, or give parametric specifications of a curve.
The website for eMathHelp is simple and to the point, if you need to use the arc length calculator. Detailed instructions are available on the calculator page, explaining that you have the option to skip some multiplication signs and parentheses.
You need to be careful when inputting certain signs, as one small step will obliterate your end result. They also give tips on where to properly include parentheses in the calculator, which might differ from what you are used to on a hand held graphing calculator.
The table on the website gives you the text necessary to input for constants, such as absolute values, square roots, and cube roots. You can take advantage of abbreviations for hyperbolic functions and inverse trigonometric functions as well.
Once you have your values, you’ll need to choose a type, a function, and enter your upper and lower limits. It’s up to you if you want the arc length calculator to display the steps through the problem.
If reading text is starting to drag for you, YouTube is a fantastic resource for help in finding an arc length calculator. Rather than just explain through lines of text that you could find in a book, content producers make the learning process a more engaging experience.
Video tutorials are available on how to find the arc length yourself, or how to ask the proper questions when you discuss the subject with your instructor.
There are also videos for how to work problems on paper, as well as how to properly input values into your own calculator(Check our 10 Best Financial Calculators to Buy in 2018).
Once you have the formula down, you can search deeper and find some example problems. Sometimes, math professors will upload their own courses for archiving purposes, and you can take advantage of their content without being enrolled in a course.
CHOOSING AN ARC LENGTH CALCULATOR
Finding the right arc length calculator involves examining yourself and determining what your learning style is. If visuals aren’t your thing, you might want to find a video that is heavy on narration.
Using an arc length calculator instead of working out the problem on its own might not give you the practice you need if you’re rusty on the execution.
Once you find the arc length calculator that works for you, be sure to keep an eye on the website so that it doesn’t drop off the face of the earth. Some of the web pages look a bit dated, despite their functionality. It might work out in your favor to learn the formula just in case you lose access to the calculator you typically use! Choosing the right calculator for your work? Here are some of our suggested calculator you should check, TI-92 Graphing Calculator, Canon LS-100TS Calculator, or the Sharp EL233SB Standard.
Featured Image: CC by SA, Jrheller1, via Wikimedia Commons.