Arc Length Calculator: Your Guide to Finding a Circle's Curve
ByMuhammad Ali•Founder of KruskalCode
22:41
6 min read
Ever wondered how to measure just a part of a circle's edge? That's what arc length is all about! Whether you're working on geometry homework or just curious, understanding arc length is a fundamental skill. This guide will walk you through the concept, the formula, and how to use our free Arc Length Calculator to make your calculations a breeze.
Explanation
An arc is simply a segment of the circumference of a circle. The arc length is the distance along this curved line. To find it, you need two key pieces of information: the circle's radius (the distance from the center to any point on the circle) and the central angle (the angle formed by two radii connecting the center to the endpoints of the arc). The central angle tells you what fraction of the entire circle's circumference the arc represents.
Formula
The formula for arc length depends on whether your central angle is measured in degrees or radians. **If the angle (θ) is in degrees:** Arc Length (L) = (θ / 360°) × 2πr **If the angle (θ) is in radians:** Arc Length (L) = θ × r Where: * L = Arc Length * θ = Central Angle * r = Radius of the circle * π (Pi) ≈ 3.14159
Example
Let's say you have a circle with a radius of 8 inches, and the central angle of the arc you're interested in is 45 degrees. Using the formula for degrees: L = (45 / 360) × 2 × π × 8 L = (1/8) × 16π L = 2π L ≈ 6.28 inches So, the arc length is approximately 6.28 inches.
How to use the related calculator
Using our Arc Length Calculator is straightforward. Simply enter the 'Radius' of your circle into the first input field. Then, input the 'Central Angle' in degrees into the second field. The calculator will instantly display the arc length, helping you verify your homework or quickly solve problems. Remember, if your angle is in radians, you'll need to convert it to degrees first (multiply radians by 180/π) before entering it into the calculator.
Try the related calculator
Open toolFAQ
What is the difference between arc length and circumference?
Circumference is the total distance around the entire circle, while arc length is the distance along just a portion of that circle's edge.
Can this calculator work with radians?
Our calculator currently takes the angle in degrees. If you have an angle in radians, multiply it by 180/π to convert it to degrees first before entering it into the tool.
Why is Pi (π) used in the arc length formula?
Pi is a fundamental constant in circle geometry, representing the ratio of a circle's circumference to its diameter. Since arc length is a part of the circumference, Pi naturally appears in its formula.
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About the author
Muhammad Ali. Muhammad Ali is a full-stack developer and founder of KruskalCode. He builds SaaS platforms and automation systems with React and Laravel, and helps teams ship fast, scalable tools.
Need a custom calculator, dashboard, or automation workflow? Reach out to KruskalCode.
