Arc Length Calculator

In case you must want to determine the length of an arc in a circular sector. Our ARC calculator is able to help to calculate your values. You just only have to provide the rotation degrees or the central angle, and the radius as inputs. You can find the length that you want.

Arc Length Calculator

Enter two values to calculate the third.

Enter the radius of the circle in the chosen unit.



Enter the central angle or angle of rotation in degrees or radians.



The arc length will be calculated here.



Enter the total radius and angle to calculate the total arc length.







With the help of this Calculator, you can determine the length of an arc from various parameters such as radius, angle or the radius of the whole curve. Alongside that, you can also use basic or advanced calculations as per your requirements. This tool is beneficial for students, architects, and engineers.

How to calculate arc length

Using the Arc Length Calculator

1. Basic Mode

Step Guide
Radius Enter the radius value (e.g., 5 meters).
Units (Radius) Choose unit for radius (meters, inches, etc.).
Central Angle Input the angle (in degrees or radians).
Units (Angle) Select angle unit (degrees or radians).
Arc Length Leave blank if calculating, or enter if known.

Advanced Mode

Step Guide
Total Radius Enter total radius for combined curves (e.g., 10 m).
Units (Radius) Choose unit for radius.
Total Angle Enter combined angle (degrees or radians).
Units (Angle) Select unit (degrees or radians).
Arc Length Will calculate based on inputs.

Formula for Arc Length

To find the arc length:

 
Arc Length=θ×r

Where

  • θ is the angle in radians
  • r is the radius of the circle

If the angle is in degrees:

Arc Length=θ360×2πr\text{Arc Length} = \frac{\theta}{360} \times 2\pi
Variable Description
Radius Distance from the center to a point on the circle.
Central Angle Angle subtended by the arc at the center (degrees/radians)
Arc Length Length of curve/arc between two points on the circle.
Total Radius Sum of multiple radii for advanced calculations.
Total Angle Sum of multiple angles for advanced calculations.

Calculation Example

1. Basic Arc Calculation Example

Step Calculation
Radius 5 meters
Angle 90 degrees
Arc Length Calculation 90360×2π×5=7.85\frac{90}{360} \times 2\pi \times 5 = 7.85 meters

Answer: The arc length is 7.85 meters.

2. Advanced Calculation Example

Step Calculation
Total Radius 10 meters
Total Angle 180 degrees
Arc Length Calculation 180360×2π×10=31.42\frac{180}{360} \times 2\pi \times 10 = 31.42meters

Answer: The arc length is 31.42 meters.

Additional Guide

  • Arc Length in Terms of π: Using Arc Length=θ360×2πr\text{Arc Length} = \frac{\theta}{360} \times 2\pi r, with a radius of 4 and angle of 180 degrees, the arc length is 4π4\pi.

  • Arc Length vs Sector Area: Arc length is the curve distance, while sector area is the space enclosed by the arc and two radii.

  • For Semicircles: For an angle of 180° or π radians, Arc Length=πr\text{Arc Length} = \pi r. For a radius of 3, the arc length is 3π3\pi, or approximately 9.42 units.

  • Finding Arc Length Without Radius: Use r=Arc Lengthθr = \frac{\text{Arc Length}}{\theta} if the arc length and angle (in radians) are known.

 

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