104 LearnersLast updated on June 20th, 2025
Arc Length Calculator
A calculator is a tool designed to perform both basic arithmetic operations and advanced calculations, such as those involving trigonometry. It is especially helpful for completing mathematical school projects or exploring complex mathematical concepts. In this topic, we will discuss the Arc Length Calculator.
What is the Arc Length Calculator
The Arc Length Calculator is a tool designed for calculating the arc length of a circle.
An arc is a portion of the circumference of a circle. The arc length can be determined if you know the radius of the circle and the measure of the central angle that subtends the arc.
The word "arc" comes from the Latin word "arcus," meaning "bow" or "curve."
How to Use the Arc Length Calculator
For calculating the arc length, using the calculator, we need to follow the steps below -
Step 1: Input: Enter the radius and the angle in degrees.
Step 2: Click: Calculate Arc Length. By doing so, the values we have given as input will get processed.
Step 3: You will see the length of the arc in the output column.
Tips and Tricks for Using the Arc Length Calculator
Mentioned below are some tips to help you get the right answer using the Arc Length Calculator.
Know the formula: The formula for the arc length is ‘(θ/360) × 2πr’, where ‘θ’ is the central angle in degrees and ‘r’ is the radius.
Use the Right Units: Make sure the radius is in the right units, like centimeters or meters.
The answer will be in linear units (like centimeters or meters), so it’s important to match them.
Enter correct Numbers: When entering the radius and angle, make sure the numbers are accurate.
Small mistakes can lead to big differences, especially with larger numbers.
Common Mistakes and How to Avoid Them When Using the Arc Length Calculator
Calculators mostly help us with quick solutions.
For calculating complex math questions, students must know the intricate features of a calculator.
Given below are some common mistakes and solutions to tackle these mistakes.
Mistake 1
Rounding off too soon
Rounding the decimal number too soon can lead to wrong results.
For example, if the arc length is 15.67 cm, don’t round it to 16 right away. Finish the calculation first.
Mistake 2
Entering the wrong number as the radius
Make sure to double-check the number you are going to enter as the radius.
If you enter the radius as ‘6’ instead of 7, the result will be incorrect.
Mistake 3
Mixing up the formula terms
Ensure you use the correct formula for arc length, ‘(θ/360) × 2πr’.
Using incorrect formulas will give the wrong result. The arc length formula is not merely πr2 or πr3.
Mistake 4
Relying too much on the calculator
The calculator gives an estimate.
Real objects may not be perfect, so the answer might be slightly different.
Keep in mind that it's an approximation.
Mistake 5
Mixing up the positive and negative signs
Always check that you’ve entered the correct positive (+) or negative (–) signs.
A small mistake, like using the wrong sign for the radius, can completely change the result.
Make sure the signs are correct before finishing your calculation.
For example, if the radius is 29 cm, entering -29 cm instead of +29 cm could give you an incorrect arc length.
Arc Length Calculator Examples
Problem 1
Help Sarah find the arc length of a circular garden path if its radius is 9 m and the central angle is 60 degrees.
We find the arc length of the garden path to be 9.42 m.
Explanation
To find the arc length, we use the formula: Arc Length = (θ/360) × 2πr Here, the value of ‘r’ is given as 9, and ‘θ’ is 60 degrees.
Now, we substitute the values in the formula: Arc Length = (60/360) × 2 × 3.14 × 9 = 0.1667 × 2 × 3.14 × 9 = 9.42 m
Problem 2
The radius of a circular track is 12 m, and the central angle is 90 degrees. What will be its arc length?
The arc length is 18.84 m.
Explanation
To find the arc length, we use the formula: Arc Length = (θ/360) × 2πr Since the radius is 12 and the angle is 90 degrees, we find the arc length as Arc Length = (90/360) × 2 × 3.14 × 12 = 0.25 × 2 × 3.14 × 12 = 18.84 m
Problem 3
Find the arc length of a circular race track with a radius of 15 m and a central angle of 45 degrees. Then, compare it to the arc length of another track with a radius of 20 m and a central angle of 30 degrees.
The arc lengths are 11.78 m and 10.47 m, respectively.
Explanation
For the first track, the arc length is calculated using ‘(θ/360) × 2πr’.
Arc Length = (45/360) × 2 × 3.14 × 15 = 0.125 × 2 × 3.14 × 15 = 11.78 m
For the second track: Arc Length = (30/360) × 2 × 3.14 × 20 = 0.0833 × 2 × 3.14 × 20 = 10.47 m
Problem 4
The radius of a circular fountain is 25 m, with a central angle of 120 degrees. Find its arc length.
We find the arc length of the fountain to be 52.36 m.
Explanation
Arc Length = (θ/360) × 2πr = (120/360) × 2 × 3.14 × 25 = 0.3333 × 2 × 3.14 × 25 = 52.36 m
Problem 5
Lucas wants to design a semicircular patio. If the radius of the patio is 30 m, help Lucas find the arc length for the semicircle.
The arc length of the semicircular patio is 94.2 m.
Explanation
Arc Length for a semicircle = (180/360) × 2πr = 0.5 × 2 × 3.14 × 30 = 94.2 m
FAQs on Using the Arc Length Calculator
1.What is the arc length?
2.What is the value of ‘r’ that gets entered as ‘0’?
3.What will be the arc length if the radius is given as 3 and the angle as 45 degrees?
4.What units are used to represent the arc length?
5.Can we use this calculator to find the circumference of a full circle?
Important Glossary for the Arc Length Calculator
- Arc Length: The distance along the curved line forming part of the circumference of a circle.
- Radius: The distance from the center of a circle to any point on its edge.
- Central Angle: The angle subtended at the center of the circle by the arc. Pi (π): A mathematical constant representing the ratio of a circle's circumference to its diameter, approximately equal to 3.14159.
- Linear Units: Units used to measure length, such as meters (m) and centimeters (cm).
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
