Length Of An Arc Calculator

Understanding the geometry of a circle can be useful in everything from construction to design, math homework to engineering. One of the most common and practical geometric calculations involving circles is arc length — the distance along the curved portion of a circle. Whether you’re a student, teacher, engineer, or DIY enthusiast, calculating arc length doesn’t have to be complicated.

That’s why we’ve built the Arc Length Calculator — a fast, accurate, and simple-to-use tool that lets you calculate the curved length of a circle segment by just inputting the radius and central angle.

What Is Arc Length?

Arc length refers to the distance between two points along a circle’s edge or circumference. It represents a “slice” of the circle, determined by a central angle measured in degrees.

The formula for arc length is: Arc Length=(θ360)×2πr\text{Arc Length} = \left(\frac{θ}{360}\right) × 2πrArc Length=(360θ​)×2πr

Where:

  • θ = central angle in degrees
  • r = radius of the circle
  • π = mathematical constant (~3.14159)

Rather than doing manual calculations, our tool simplifies the process and reduces the chance of error — providing instant and accurate results.

How to Use the Arc Length Calculator

Using our calculator is incredibly straightforward. Just follow these steps:

  1. Enter the Radius of the Circle:
    Input the radius (r) in any unit you prefer — inches, meters, centimeters, etc. Just be consistent.
  2. Enter the Central Angle (Degrees):
    Provide the central angle of the arc in degrees (θ), between 0 and 360.
  3. Click “Calculate”:
    Hit the button and get your arc length instantly, calculated using the standard circle arc formula.
  4. View the Result:
    The arc length will be displayed in the same unit as your input for radius. You can reset the form to try different values.

Example: Real-World Use of Arc Length Calculation

Example 1:
You’re designing a curved garden edge and want to know how much fencing material you’ll need for the arc.

  • Radius of the curve: 10 feet
  • Central angle: 90 degrees

Using the formula: Arc Length=(90360)×2π×10=14×2π×10=14×62.83≈15.71 feet\text{Arc Length} = \left(\frac{90}{360}\right) × 2π × 10 = \frac{1}{4} × 2π × 10 = \frac{1}{4} × 62.83 ≈ 15.71 \text{ feet}Arc Length=(36090​)×2π×10=41​×2π×10=41​×62.83≈15.71 feet

So, you’ll need about 15.71 feet of material to cover the arc.

Example 2:
A student working on a geometry problem is asked to find the arc length of a circle with a radius of 7 cm and an angle of 60 degrees. Arc Length=(60360)×2π×7≈7.33 cm\text{Arc Length} = \left(\frac{60}{360}\right) × 2π × 7 ≈ 7.33 \text{ cm}Arc Length=(36060​)×2π×7≈7.33 cm

Practical Use Cases

Here are some scenarios where calculating arc length is essential:

  • Construction & Landscaping: Estimating curved paths, archways, or circular segments.
  • Mechanical Engineering: Calculating belt lengths around pulleys or gear circumferences.
  • Architecture: Designing rounded balconies, domes, or curved facades.
  • Graphic Design: Creating circular text or designs that fit precisely along a curve.
  • Education: Assisting students with geometry and trigonometry problems.

Extra Tips When Using the Calculator

  • Units Matter: The output uses the same unit you use for the radius. So, if the radius is in meters, arc length is in meters.
  • Decimal Friendly: You can input decimal numbers (e.g., 12.75) for more precise calculations.
  • 360° Cap: The angle must be between 0 and 360 degrees. If you go over 360, it’s no longer a single circle arc.

Frequently Asked Questions (FAQs)

1. What is arc length?
Arc length is the measurement of the curved segment of a circle, determined by a central angle and the radius.

2. What units are used in the calculator?
The calculator is unit-agnostic. Input your radius in any unit, and the arc length will be in the same unit.

3. How do I find the arc length manually?
Use the formula: Arc Length = (θ / 360) × 2πr. Just plug in the radius and central angle in degrees.

4. Can I use this for semi-circles or full circles?
Yes. For a semi-circle, use 180°; for a full circle, use 360°. The calculator supports both.

5. What if the angle is 0 or 360 degrees?
At 0°, arc length is 0. At 360°, the arc length equals the full circumference of the circle.

6. Why is the angle input limited to 360 degrees?
A central angle greater than 360° doesn’t exist within a single circle. 360° covers the entire circumference.

7. Can I enter decimals for radius or angle?
Yes, both fields accept decimal values for precise measurements.

8. Is arc length the same as chord length?
No. Arc length follows the circle’s curve; chord length is the straight line connecting two points on the circle.

9. Can I calculate arc length without degrees?
This calculator uses degrees only. If you have radians, convert to degrees by multiplying by 180/π.

10. Does this calculator work on mobile?
Yes, it’s fully responsive and works on smartphones, tablets, and desktops.

11. What’s the difference between arc length and circumference?
Arc length is a portion of the circle’s circumference, defined by a specific central angle.

12. Is this tool accurate for real-world construction?
Yes, as long as you input correct values and remain consistent with your units.

13. Can I use this for sectors or pies?
Yes. Arc length is part of the information needed to calculate the area of a sector (pie slice).

14. What’s the formula if the angle is in radians?
Arc Length = r × θ (if θ is in radians). This calculator uses degrees, but you can convert radians to degrees.

15. How do I convert between radians and degrees?
Degrees = Radians × (180/π), or Radians = Degrees × (π/180)

16. Can I use this for partial curves in roads or tracks?
Absolutely. It’s ideal for calculating curved road lengths or track segments.

17. Is the tool free to use?
Yes! The Arc Length Calculator is completely free and requires no registration.

18. What browsers support the tool?
All modern browsers (Chrome, Firefox, Safari, Edge) fully support the tool.

19. Does it work offline?
Yes, once the page is loaded, the calculator functions without an internet connection.

20. Can I embed this calculator on my own site?
You’d need the underlying code (HTML/JS) and permission, but technically, yes.

Final Thoughts

Whether you’re tackling a geometry problem, designing a curved feature, or working through a physics challenge, calculating arc length accurately is essential. Our Arc Length Calculator provides a quick, error-free solution that anyone can use — from students and educators to engineers and DIYers.

Don’t waste time with manual math — use the Arc Length Calculator to save time, increase accuracy, and get the results you need in seconds.

👉 Try it now and take the guesswork out of circular calculations!