Arc Length Calculator – Calculate Arc Length Using Radius & Angle

Arc Length Calculator

Calculate the arc length using radius and angle.

Radius (units) Angle (degrees)

 

Arc Length Calculator – Find the Length of an Arc Instantly

Understanding the arc length of a circle is essential in geometry, engineering, construction, design, and trigonometry. Whether you’re a student solving math problems or a professional working on circular structures, our Arc Length Calculator makes the process simple, fast, and accurate.

Just enter the radius and angle in degrees, and the calculator automatically converts the angle to radians and applies the arc length formula. It gives an instant and error-free answer.

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⭐ What Is Arc Length?

Arc length is the distance measured along the curved edge of a circle. It represents a portion of the circle’s circumference.

If you imagine cutting a slice of pizza or marking a curved portion of a wheel, the arc is the length of that curved boundary.

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⭐ Arc Length Formula

The standard formula for calculating arc length is:

$$L = r \times \theta$$

Where:

• L = arc length

• r = radius of the circle

• θ = angle in radians

Most angles are given in degrees, so the calculator converts them using:

$$\theta = \frac{\pi}{180} \times \text{(degrees)}$$

This ensures accurate arc length calculations.

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⭐ How the Arc Length Calculator Works

The calculator requires two inputs:

✔ Radius (units)

Distance from the center of the circle to any point on its circumference.

✔ Angle (degrees)

The central angle that subtends the arc.

Once entered, the calculator computes:

🔹 Arc Length (units)

Accurate to four decimal places.

It also displays the formula used for transparency.

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⭐ Why Use an Online Arc Length Calculator?

✔ Saves time
✔ Eliminates manual conversion errors
✔ Perfect for geometry students
✔ Useful for architects & engineers
✔ Helps in construction & design planning
✔ Easy to use, mobile-friendly, and free

This tool removes the confusion of converting degrees to radians manually.

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⭐ Example Arc Length Calculation

Given:

• Radius = 10 units

• Angle = 45°

Step 1: Convert angle to radians

$$\theta = 45 \times \frac{\pi}{180} = 0.7854$$

Step 2: Apply arc length formula

$$L = 10 \times 0.7854 = 7.854 \text{ units}$$

Our calculator instantly produces this result.

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⭐ Where Arc Length Is Used

Arc length comes up in many practical applications, such as:

• Circle geometry problems

• Construction of curved structures

• Road and railway design

• Gear and wheel measurements

• Robotics and mechanical engineering

• Circular gardens, tracks, and boundaries

• Graphic design and CAD modeling

Knowing arc length helps improve precision and engineering accuracy.

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⭐ Benefits of This Arc Length Calculator

✨ Clean and simple interface
✨ Instant calculation
✨ Accurate conversion to radians
✨ Works on all devices
✨ Ideal for students and professionals
✨ Free to use anytime

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⭐ Conclusion: Calculate Arc Length Quickly & Accurately

Our Arc Length Calculator offers a fast and reliable solution for calculating the length of a circular arc. Instead of manually converting degrees to radians or applying formulas, you can enter your values and get perfect results instantly.

Whether you're studying geometry, working in construction, or designing curved structures, this tool helps you save time and avoid errors.