Arc length from given Angle?

Here we will see how to calculate the arc length from a given angle. When a circle with radius r is given and we know the angle x in degrees, we can find the arc length using a simple formula.

Here r is the radius and x is the angle in degrees. We need to find the value of L (arc length). The formula is −

Syntax

L = 2?r × (x/360)

Where L is arc length, r is radius, x is angle in degrees, and ? ? 3.14159.

Example

Let's implement a C program to calculate arc length using the given formula −

#include <stdio.h>

float getArcLength(float r, float x) {
    return (2 * 3.14159f * r) * (x / 360.0f);
}

int main() {
    float rad = 12.0f;
    float angle = 45.0f;
    
    printf("Radius: %.2f<br>", rad);
    printf("Angle: %.2f degrees<br>", angle);
    printf("Arc Length: %.4f<br>", getArcLength(rad, angle));
    
    return 0;
}

Radius: 12.00
Angle: 45.00 degrees
Arc Length: 9.4248

How It Works

• The complete circumference of a circle is 2?r
• For 360°, the arc length equals the full circumference
• For any angle x°, the arc length is the proportional part: (x/360) × 2?r
• A 45° arc is 1/8th of the complete circle (45/360 = 1/8)

Conclusion

Arc length calculation is straightforward using the formula L = 2?r × (x/360), where the angle portion (x/360) gives us the fraction of the complete circumference. This method works for any angle in degrees.