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.
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.
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:
Where
- θ is the angle in radians
- r is the radius of the circle
If the angle is in degrees:
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 |
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 |
meters |
Answer: The arc length is 31.42 meters.
Additional Guide
-
Arc Length in Terms of π: Using , with a radius of 4 and angle of 180 degrees, the arc length is .
-
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, . For a radius of 3, the arc length is , or approximately 9.42 units.
-
Finding Arc Length Without Radius: Use if the arc length and angle (in radians) are known.