The arc length of a circle is the distance along the curved line that forms part of the circumference of a circle. Imagine stretching out a portion of the circle's edge into a straight line; its length is the arc length.
To calculate the arc length, we need two primary pieces of information:
The Radius (r): This is the distance from the center of the circle to any point on its circumference.
The Central Angle (θ): This is the angle formed at the center of the circle by two radii drawn to the endpoints of the arc. The angle can be measured in degrees or radians.
The Formula
The general formula for arc length (s) is derived from the proportion of the central angle to the full circle's angle (360° or 2π radians).
If the angle θ is in degrees:
s = (θ / 360°) * 2πr
If the angle θ is in radians:
s = rθ
This calculator simplifies the process by allowing you to input the radius and the central angle, specifying the unit of the angle. It then applies the appropriate formula to give you the arc length.
Use Cases
The concept of arc length is fundamental in various fields:
Engineering: Designing curved structures, gears, and circular tracks.
Physics: Analyzing circular motion, trajectories, and rotational dynamics.
Geometry: Calculating properties of sectors and segments of circles.
Navigation: Determining distances along curved paths on maps or celestial bodies.
function calculateArcLength() {
var radius = parseFloat(document.getElementById("radius").value);
var angle = parseFloat(document.getElementById("angle").value);
var angleUnit = document.getElementById("angle_unit").value;
var resultDiv = document.getElementById("result");
var resultText = "";
if (isNaN(radius) || isNaN(angle)) {
resultText = "Please enter valid numbers for radius and angle.";
} else if (radius <= 0) {
resultText = "Radius must be a positive number.";
} else {
var arcLength;
if (angleUnit === "degrees") {
if (angle 360) {
resultText = "Angle in degrees should be between 0 and 360.";
} else {
arcLength = (angle / 360) * 2 * Math.PI * radius;
resultText = "Arc Length = " + arcLength.toFixed(4) + "";
}
} else { // radians
if (angle < 0) {
resultText = "Angle in radians must be non-negative.";
} else {
arcLength = radius * angle;
resultText = "Arc Length = " + arcLength.toFixed(4) + "";
}
}
}
resultDiv.innerHTML = resultText;
}