Arc Calculator

by

Arc Calculator

Understanding the properties of a circle's arc is essential in geometry, engineering, architecture, and design. Whether you need to measure arc length, chord length, sector area, or arc height (sagitta), the Arc Calculator simplifies these calculations in seconds.

This online tool is ideal for students, engineers, carpenters, and anyone working with curved structures, making complex circular calculations effortless and accurate.

Why Use the Arc Calculator?

Manual calculations for arcs can be complicated, involving trigonometry and formulas. The Arc Calculator offers:

  • Quick Calculations: Instant results for arcs, sectors, segments, chords, and radii.
  • Multiple Input Options: Use radius with central angle, radius with arc length, or chord with arc height.
  • Flexible Units: Metric (cm, m) or imperial (in, ft).
  • Visualized Results: View all related properties like perimeter, segment area, and arc height at once.
  • Accurate and Reliable: Reduces human error in geometry computations.

With this tool, you can save time and ensure precision, especially in projects where measurements are critical.

How to Use the Arc Calculator

  1. Select Calculation Type – Choose what you want to calculate:
    • Arc Length
    • Sector Area
    • Segment Area
    • Chord Length
    • Arc Height (Sagitta)
  2. Choose Input Method – Depending on what information you have:
    • Radius & Central Angle
    • Radius & Arc Length
    • Chord Length & Arc Height
  3. Enter Required Values – Fill in radius, central angle, chord length, or arc height as per your chosen method.
  4. Select Measurement Units – Metric (cm, m) or Imperial (in, ft).
  5. Click Calculate – The calculator instantly provides:
    • Arc Length
    • Sector Area
    • Segment Area
    • Chord Length
    • Arc Height (Sagitta)
    • Radius
    • Central Angle in degrees and radians
    • Perimeter (arc + radii)
  6. Optional Reset – Clear all values to start a new calculation.

Arc Calculator Formulas Used

The calculator uses the following key formulas:

  • Arc Length (L): L = r * θ (θ in radians)
  • Sector Area (A_sector): A = 0.5 * r² * θ
  • Chord Length (c): c = 2 * r * sin(θ / 2)
  • Arc Height (Sagitta, h): h = r - r * cos(θ / 2)
  • Segment Area (A_segment): A_segment = A_sector - 0.5 * r² * sin(θ)
  • Perimeter (P): P = arc length + 2 * radius

These formulas cover all common arc-related measurements, ensuring complete results from minimal input.

Example: Calculating an Arc

Suppose you have a circle radius of 10 cm and a central angle of 60°:

  1. Arc Length = 10 * (60 * π/180) ≈ 10.47 cm
  2. Sector Area = 0.5 * 10² * (60 * π/180) ≈ 52.36 cm²
  3. Chord Length = 2 * 10 * sin(60/2 * π/180) ≈ 10.34 cm
  4. Arc Height (Sagitta) = 10 - 10 * cos(60/2 * π/180) ≈ 1.34 cm
  5. Segment Area = Sector Area - Triangle Area ≈ 49.64 cm²
  6. Perimeter = Arc Length + 2 * radius ≈ 30.47 cm

With just the radius and angle, the Arc Calculator instantly computes all these properties without additional formulas.

Tips for Using the Arc Calculator

  • Choose the Right Input Method: Depending on what you know, pick radius & angle, radius & arc, or chord & height.
  • Check Units: Make sure metric and imperial units match your project requirements.
  • Use for Construction: Perfect for arches, curved beams, circular gardens, or metalwork.
  • Double-Check Angles: Ensure angles are in degrees or radians according to input selection.
  • Visualize Segments: Use the segment area to understand material requirements for partial circular shapes.

Benefits of the Arc Calculator

  • Time-Saving: Avoid lengthy trigonometric calculations.
  • Accurate: Reduces errors common in manual geometry.
  • Comprehensive: Calculates all arc-related properties in one click.
  • User-Friendly: Clear inputs, dynamic display of results.
  • Flexible: Works for students, engineers, designers, and DIY projects.

FAQs

  1. What is an arc in a circle?
    An arc is a portion of the circumference of a circle.
  2. What is a chord?
    A chord is a straight line connecting two points on a circle.
  3. What is a sagitta?
    The sagitta (arc height) is the perpendicular distance from the chord to the arc.
  4. Can I calculate in inches or cm?
    Yes, the calculator supports both metric and imperial units.
  5. Do I need to convert degrees to radians manually?
    No, the calculator handles both degrees and radians automatically.
  6. Can I find segment area directly?
    Yes, the segment area is computed automatically from radius and central angle or chord and height.
  7. Is this suitable for engineering or construction?
    Absolutely, it provides precise measurements needed for arches, beams, and circular designs.
  8. Can it handle large radii?
    Yes, there’s no limit on the radius beyond practical computational values.
  9. What input should I use if I know chord and height?
    Select “Chord Length & Arc Height” input method for direct calculation.
  10. Is it free to use?
    Yes, this online Arc Calculator is completely free and accessible anytime.

The Arc Calculator is a reliable, fast, and accurate tool for all your geometry and design needs. Whether for school assignments, engineering projects, or construction work, it simplifies arc, chord, and segment calculations with precision.

Leave a Comment