Arc Length Calculator

This Arc Length Calculator helps you find the length of an arc when the radius and central angle are known. It first converts the angle from degrees to radians, then uses the formula s = rθ, where r is the radius and θ is the angle in radians. Multiply the radius by the angle in radians to get the arc length. It is a simple way to check answers, understand arc length formulas, and practise basic trigonometry step by step.

Step-by-step method

1. Identify what is given.
2. Convert the angle from degrees to radians.
3. Use the arc length formula and calculate.

Formulas:

Formula: Degrees to radians

Formula: Arc length

Example 1: r = 5, θ = 60°

Step 1 - Identify what is given.

In this problem: The given values are r = 5 and θ = 60°.

Step 2 - Convert the angle from degrees to radians.

In this problem: Convert degrees to radians using θ(rad) = (θ×π)/180, then substitute the angle.

Step 3 - Use the arc length formula and calculate.

In this problem: Use L = r × θ(rad), then substitute and multiply.

Final answer: L = 5.23598776

Example 2: r = 10, θ = 90°

Step 1 - Identify what is given.

In this problem: The given values are r = 10 and θ = 90°.

Step 2 - Convert the angle from degrees to radians.

In this problem: Convert degrees to radians using θ(rad) = (θ×π)/180, then substitute the angle.

Step 3 - Use the arc length formula and calculate.

In this problem: Use L = r × θ(rad), then substitute and multiply.

Final answer: L = 15.70796327