Arc Length Calculator
Arc Length = (θ / 360°) × 2πr
Or in radians:
Arc Length = θ × r
Where:
• θ = central angle
• r = radius
• π ≈ 3.14159
Central angle: 60°
Arc length = (60/360) × 2π × 10
= (1/6) × 62.83
= 10.47 cm
If angle in radians (π/3):
Arc length = (π/3) × 10 = 10.47 cm
🔗 Related Calculators
📐 Formula
Arc Length = (θ / 360°) × 2πr
Or in radians:
Arc Length = θ × r
Where:
• θ = central angle
• r = radius
• π ≈ 3.14159
📝 Example Calculation
Central angle: 60°
Arc length = (60/360) × 2π × 10
= (1/6) × 62.83
= 10.47 cm
If angle in radians (π/3):
Arc length = (π/3) × 10 = 10.47 cm
About Arc Length
An arc is a portion of the circumference of a circle. The arc length is the distance measured along this curved path between two points on the circle. This calculator helps you determine the arc length when you know the radius of the circle and the central angle.
Arc Length Formula
The formula for calculating arc length is:
- s = r * θ (where θ is in radians)
- s = r * (θdeg * PI/180) (where θdeg is in degrees)
Where:
- s = arc length
- r = radius of the circle
- θ = central angle in radians
- θdeg = central angle in degrees
How to Use This Calculator
- Enter the radius of the circle
- Enter the central angle in degrees
- Click "Calculate" to get the arc length
- View detailed results including the angle in radians and percentage of the full circle
Understanding Arc Length
The arc length is directly proportional to both the radius and the central angle. A larger radius or a larger angle will result in a longer arc. When the central angle is 360deg, the arc length equals the full circumference of the circle (2PIr).
Frequently Asked Questions
What is arc length?
Arc length is the distance along the curved line of a portion of a circle. It represents the measurement of the curve between two points on the circle's circumference.
What is the formula for arc length?
The arc length formula is s = r * θ, where s is the arc length, r is the radius, and θ is the central angle in radians. If the angle is in degrees, first convert to radians by multiplying by PI/180.
How do you convert degrees to radians?
To convert degrees to radians, multiply the angle in degrees by PI/180. For example, 90deg = 90 * PI/180 = PI/2 radians ≈ 1.5708 radians.
What is the relationship between arc length and circumference?
Arc length is a portion of the full circumference. If the central angle is 360deg, the arc length equals the full circumference (2PIr). For any other angle, the arc length is proportional to the fraction of 360deg that the angle represents.
What are practical applications of arc length?
Arc length calculations are used in engineering for designing curved roads and railway tracks, in architecture for arches and domes, in astronomy for measuring angular distances, and in manufacturing for cutting curved materials like pipes and sheet metal.
Can arc length be greater than the circumference?
No, arc length cannot exceed the circumference for a single arc. If the angle is 360deg or less, the arc length will be at most equal to the circumference. Angles greater than 360deg would represent multiple rotations around the circle.