Arc Length Calculator

Calculate the arc length of a circle segment given the radius and central angle. Supports degrees and radians.

Radius

Central Angle

Angle Unit

Result

Please check your inputs.

Choose the unit for your central angle — either degrees (°) or radians (rad) using the dropdown menu. Enter the radius of the circle in the first input field (e.g., 5). Enter the central angle value in the second input field (e.g., 60 for degrees or π/3 for radians). Click the 'Calculate' button to instantly compute the arc length. Read the result displayed below, with the option to copy or recalculate with new values.

📖 How to Use This Tool

Choose the unit for your central angle — either degrees (°) or radians (rad) using the dropdown menu.

Enter the radius of the circle in the first input field (e.g., 5).

Enter the central angle value in the second input field (e.g., 60 for degrees or π/3 for radians).

Click the 'Calculate' button to instantly compute the arc length.

Read the result displayed below, with the option to copy or recalculate with new values.

📝 What Is Arc Length Calculator?

An arc length is the distance along the curved line that makes up a portion of a circle’s circumference. Instead of measuring the whole circle, you measure only the part corresponding to a given central angle. This concept is fundamental in geometry, trigonometry, and real‑world fields like engineering, architecture, and navigation — wherever you need to design curved roads, circular arches, or compute distances along a curved path.

Using an arc length calculator saves time and eliminates manual formula errors. Whether you are a student solving homework problems or a professional laying out a circular race track, this tool delivers accurate results in seconds. It supports both degrees and radians, so you never have to worry about unit conversion mistakes. Simply input your radius and angle, and the tool does the rest — making complex circle geometry accessible to everyone.

🧮 Formula

Arc Length (s) = r × θ (when θ is in radians)

If the angle is given in degrees, the formula becomes: Arc Length (s) = (π / 180) × r × θ - r = radius of the circle - θ = central angle (in radians or degrees) - π ≈ 3.14159 In plain English: multiply the radius by the central angle (converted to radians if needed) to get the length of the curved segment.

💡 Tips for Best Results

✨📐 Always use radians for the simplest calculation — the formula s = r × θ is direct and avoids extra steps.

✨🔄 If you have an angle in degrees, remember to convert it to radians by multiplying by π/180, or let this tool handle it for you.

✨📏 Double‑check your radius unit (e.g., cm, m, inches) to ensure the arc length result is in the same unit — consistency is key.

✨🧮 For partial circles (e.g., a 90° turn), make sure your angle correctly represents the portion — a semicircle uses 180° or π radians.

❓ Frequently Asked Questions

What if my central angle is given in degrees?

No problem — just select “degrees” from the unit dropdown before entering your angle. The calculator will automatically convert it to radians using the formula (π/180) × angle and apply the arc length formula correctly.

Can I use this tool for a full circle (angle = 360°)?

Yes, entering 360° (or 2π radians) gives the full circumference, which is 2πr. The arc length formula works for any angle from 0° to 360° (or 0 to 2π radians).

What happens if I enter a radius of zero?

If the radius is zero, the arc length will always be zero regardless of the angle, because there is no curved path. The calculator will still compute it, but the result will be 0 — great for sanity‑checking your inputs.