Arc Length Of Quarter Circle Given Chord Length Calculator

Formula Used:

\[ l_{Arc} = \frac{\pi \times l_{Chord}}{\sqrt{8}} \]

Arc Length of Quarter Circle:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Arc Length of Quarter Circle?

The Arc Length of Quarter Circle is the length of the curved edge of a quarter circle, which represents one-fourth of the circumference of a full circle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{Arc} = \frac{\pi \times l_{Chord}}{\sqrt{8}} \]

Where:

\( l_{Arc} \) — Arc Length of Quarter Circle (m)
\( l_{Chord} \) — Chord Length of Quarter Circle (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \sqrt{8} \) — Square root of 8 (approximately 2.82843)

3. Formula Explanation

Details: This formula derives from the geometric relationship between the chord length and arc length of a quarter circle. The chord length connects the two endpoints of the arc, and the formula provides the exact arc length calculation based on this chord measurement.

4. Using the Calculator

Tips: Enter the chord length of the quarter circle in meters. The value must be positive and greater than zero. The calculator will compute the corresponding arc length.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between chord length and arc length?
A: For a quarter circle, the arc length can be calculated from the chord length using the formula \( l_{Arc} = \frac{\pi \times l_{Chord}}{\sqrt{8}} \), which accounts for the geometric properties of a quarter circle.

Q2: Can this formula be used for other circular segments?
A: No, this specific formula applies only to quarter circles. Other circular segments require different formulas based on their specific geometry.

Q3: What are typical applications of this calculation?
A: This calculation is useful in architecture, engineering, and design where quarter circular elements are used, such as in arches, curved structures, and decorative elements.

Q4: How accurate is this formula?
A: The formula is mathematically exact for perfect quarter circles and provides precise results when accurate input values are provided.

Q5: What units should be used for the calculation?
A: The calculator uses meters as the default unit, but the formula works with any consistent unit system (inches, centimeters, etc.) as long as both input and output use the same units.