Arc Length Calculator
Calculate the length of a circular arc given the radius and central angle in degrees.
This free online arc length calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
Minimum: 0
The angle subtended by the arc at the center
Results
Arc Length
7.854 units
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Arc Length Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Arc Length Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
When to Use This Calculator
- •Use the Arc Length Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
- •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
- •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
- •Use it to explore the behavior of mathematical functions across a range of inputs.
Related Calculators
Central Angle Calculator
Calculate the central angle of a circle given the arc length and radius using theta = arc/radius. The central angle is the angle at the center subtended by an arc, fundamental to circle geometry, surveying, navigation, and engineering applications.
Chord Length Calculator
Calculate the length of a chord in a circle given the radius and the central angle subtended by the chord. Uses the formula c = 2r*sin(theta/2), essential for geometry, engineering, surveying, and arc-based constructions in architecture and design.
Circular Segment Area Calculator
Calculate the area of a circular segment (the region between a chord and its arc) given the radius and central angle. Uses A = (r^2/2)(theta - sin(theta)), essential for engineering, architecture, tank volume calculations, and curved surface analysis.
Sector Area Calculator
Calculate the area of a circular sector given the radius and central angle.
Annulus Area Calculator
Calculate the area of an annulus (ring shape) using A = PI*(R^2 - r^2), where R is the outer radius and r is the inner radius. Essential for engineering washers, pipe cross-sections, circular tracks, orbital mechanics, and ring-shaped design elements.
Complementary Angles Calculator
Find the complement of an angle (90 minus the given angle). Complementary angles sum to 90 degrees and appear in right triangles, architecture, optics, and navigation. Enter any angle between 0 and 90 degrees to find its complement instantly.
About Arc Length Calculator
An arc is a portion of the circumference of a circle. The arc length is the distance along the curved line between two points on the circle. The formula s = rθ, where θ is in radians, is one of the most elegant in geometry because of its simplicity. This relationship is actually the defining property of radian measure: one radian is the angle that subtends an arc equal in length to the radius. Arc length calculations are essential in engineering for designing curved structures such as roads, bridges, and tracks. They also appear in physics when calculating the distance traveled along circular paths, in cartography for measuring distances along the Earth's surface, and in computer graphics for rendering smooth curves. This calculator converts degrees to radians automatically and computes the arc length for any radius and angle.
The Math Behind It
Formula Reference
Arc Length
s = rθ
Variables: r = radius, θ = central angle in radians
Worked Examples
Example 1: Curved road
A road curves along a 200 m radius circle for 30 degrees.
s ≈ 104.72 meters
Common Mistakes & Tips
- !Forgetting to convert degrees to radians before using s = rθ.
- !Confusing arc length (a distance) with the central angle (a measure of rotation).
- !Using the diameter instead of the radius in the formula.
Related Concepts
Used in These Calculators
Calculators that build on or apply the concepts from this page:
Frequently Asked Questions
What is a radian?
A radian is the angle subtended at the center of a circle by an arc whose length equals the radius. One full revolution = 2π radians = 360°.
How do I convert degrees to radians?
Multiply the degree value by π/180. For example, 90° = 90 × π/180 = π/2 radians.
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