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103 LearnersLast updated on September 11, 2025
Chord Length Calculator
Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you’re cooking, tracking BMI, or planning a construction project, calculators will make your life easy. In this topic, we are going to talk about chord length calculators.
What is a Chord Length Calculator?
A chord length calculator is a tool used to determine the length of a chord given certain parameters of a circle.
Since the chord is a line segment with both endpoints on the circle, calculating its length can be complex depending on the information available.
This calculator simplifies the process, providing accurate and quick results.
How to Use the Chord Length Calculator?
Given below is a step-by-step process on how to use the calculator:
Step 1: Enter the circle's radius and the central angle (in degrees): Input these values into the given fields.
Step 2: Click on calculate: Click on the calculate button to compute the chord length.
Step 3: View the result: The calculator will display the chord length instantly.
How to Calculate Chord Length?
To calculate the chord length, the calculator uses a simple formula.
For a circle with radius r and a central angle (θ ) in degrees, the chord length c is given by: c = 2rsin(θ/2)
This formula uses the sine function to determine the length of the chord based on the segment of the circle.
Tips and Tricks for Using the Chord Length Calculator
When using a chord length calculator, there are a few tips and tricks to ensure accuracy:
Consider using radians for more precise angle measurements in some contexts.
Double-check the radius and angle inputs for potential errors.
Use the calculator for real-world applications like construction or design projects where precise measurements are crucial.
Common Mistakes and How to Avoid Them When Using the Chord Length Calculator
Even when using a calculator, mistakes can happen. Here are some common errors to watch out for:
Mistake 1
Incorrect angle measurement units.
Ensure you are using degrees if the calculator requires it, or convert to radians if necessary. Mixing up the units can lead to incorrect results.
Mistake 2
Forgetting to halve the angle.
The formula uses half the central angle, so failing to divide the angle by two will result in an incorrect chord length.
Mistake 3
Incorrect input of radius or angle.
A common mistake is entering the wrong values for the radius or angle. Double-check these values before calculation.
Mistake 4
Relying too heavily on default values.
Always verify that the default values in the calculator match the specifics of your problem. Adjust them as necessary to suit your needs.
Mistake 5
Assuming all calculators are the same.
Different calculators may have different features or require different inputs. Be sure to understand the specifics of the calculator you are using.
Chord Length Calculator Examples
Problem 1
What is the chord length of a circle with a radius of 10 cm and a central angle of 60 degrees?
Use the formula: c =2rsin(θ/2)
c = 2 × 10 × sin(60/2)
c = 20 ×sin(30)
Since sin(30) = 0., c = 20 × 0.5 = 10
The chord length is 10 cm.
Explanation
By using a radius of 10 cm and a central angle of 60 degrees, the formula gives us a chord length of 10 cm.
Problem 2
A circle has a radius of 15 meters and a central angle of 90 degrees. What is the chord length?
Use the formula: c = 2rsin(θ/2)
c = 2 ×15 × sin(90 / 2)
c = 30 × sin(45)
Since sin(45) = √2 / 2,
c = 30 × (√2 / 2) = 15√2
The chord length is approximately 21.21 meters.
Explanation
With a radius of 15 meters and a central angle of 90 degrees, the result is a chord length of approximately 21.21 meters.
Problem 3
Find the chord length of a circle with a radius of 8 units and a central angle of 120 degrees.
Use the formula: c =2rsin(θ/2)
c = 2 × 8 × sin(120 / 2 )
c = 16 ×sin(60)
Since sin(60) = √(3 /2),
c = 16 × √(3 / 2) = 8√3
The chord length is approximately 13.86 units.
Explanation
Using a radius of 8 units and a central angle of 120 degrees, we find the chord length to be approximately 13.86 units.
Problem 4
A circle has a radius of 5 cm and a central angle of 150 degrees. Determine the chord length.
Use the formula: c =2rsin(θ/2)
c = 2 × 5 × sin(150/ 2)
c = 10 × sin(75)
Since sin(75) =(√6+√2) / 4 )
c = 10 × ((√6+√2) / 4 )
The chord length is approximately 9.66 cm.
Explanation
With a radius of 5 cm and a central angle of 150 degrees, the chord length is approximately 9.66 cm.
Problem 5
Calculate the chord length for a circle with a radius of 12 meters and a central angle of 45 degrees.
Use the formula: c =2rsin(θ/2)
c = 2 × 12 × sin(45/2)
c = 24 × sin(22.5)
Since sin(22.5) ≈ 0.3827,
c = 24 × 0.3827 ≈ 9.18
The chord length is approximately 9.18 meters.
Explanation
For a radius of 12 meters and a central angle of 45 degrees, the chord length is approximately 9.18 meters.
FAQs on Using the Chord Length Calculator
1.How do you calculate chord length?
2.Is a chord the same as a radius?
3.Can the chord length calculator handle radians?
4.How do I use a chord length calculator?
5.Is the chord length calculator accurate?
Glossary of Terms for the Chord Length Calculator
- Chord: A line segment with both endpoints on the circle.
- Radius: The distance from the center of the circle to any point on the circle.
- Central Angle: The angle subtended at the center by two radii.
- Sine Function: A trigonometric function used in the chord length formula.
- Radians: An alternative unit to degrees for measuring angles.
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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
