Chord Calculator

- May 10, 2025
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Calculate various properties of a chord in a circle including chord length, arc length, chord height, and more. This calculator supports multiple calculation methods and provides visualisations with step-by-step explanations.

Select Calculation Method

Advanced Options

About Chords in Geometry

A chord is a line segment whose endpoints both lie on a circle. Chords are important in geometry and have numerous applications in mathematics, physics, engineering, and more.

Key Properties and Formulas
  • Chord Length: c = 2r × sin(θ/2) [where r is radius and θ is central angle]
  • Chord Height: h = r - d = r(1 - cos(θ/2)) [where d is distance from chord to centre]
  • Arc Length: s = r × θ [where θ is in radians]
  • Distance from Centre: d = r × cos(θ/2)
  • Segment Area: A = (r²/2) × (θ - sin(θ)) [where θ is in radians]
Important Relationships
  • The perpendicular bisector of a chord passes through the centre of the circle.
  • Equal chords are equidistant from the centre.
  • Chords equidistant from the centre are equal in length.
  • If two chords intersect, the product of the segments of one chord equals the product of the segments of the other.
  • The chord length relates to the chord height by the formula: c² = 4r × h - 4h².
Applications

Chords have many practical applications:

  • Construction: Laying out circular arcs and curves
  • Engineering: Designing circular components and curves
  • Physics: Analysing circular motion and wave propagation
  • Music Theory: The term "chord" in music originates from geometry
  • Architecture: Planning arches and curved structures
  • Astronomy: Calculating distances and angles in celestial observations

Understanding the Chord Calculator

The Chord Calculator is a handy tool designed to help you calculate key properties of a chord within a circle. This includes finding the chord length, arc length, chord height, and more. Whether you're a student, teacher, or just curious about Geometry, this calculator makes complex calculations straightforward and visual. With its simple interface and various calculation methods, it’s easy to see why so many people find it so useful.

Different Ways to Calculate

This calculator offers several methods for calculation, allowing you to choose the one that suits you best. Here are the available options:

  • Radius and Chord Length
  • Radius and Central Angle
  • Chord Length and Height
  • Diameter and Chord Length
  • Arc Length and Central Angle

These options let you apply different parameters depending on what information you have and what you need to find.

Inputting Your Data

Once you've selected your calculation method, you will need to enter specific measurements. For example, if you're calculating using the radius and chord length, you’ll input the radius of the circle and the length of the chord. The calculator supports various units like millimetres, centimetres, and metres, ensuring you can work in the units you're most comfortable with.

Results at Your Fingertips

After entering your data, the calculator provides immediate results. You can see values like the chord length, chord height, central angle, arc length, and more. This instant feedback helps you understand the relationships between the values and can be very helpful for study or practical applications.

Visual Learning Made Easy

The Chord Calculator also includes visualisation options to help you see the results in a graphical form. This feature is perfect for visual learners who benefit from seeing concepts in action. The diagram shows how the chord interacts with the circle, making it easier to grasp geometric relationships.

Learn with Calculation Steps

This tool doesn't just give you answers; it also explains how those answers were reached. Each calculation comes with detailed steps so you can follow along and learn the process. This educational aspect can be particularly valuable for students or anyone trying to strengthen their understanding of geometry.

Explore Geometry Concepts

Understanding chords isn’t just about calculations; it's also about grasping their properties and applications. Here are some important concepts related to chords:

  • A chord is a line segment within a circle connecting two points on the circumference.
  • The longest chord in a circle is the diameter.
  • Chords that are the same length are equidistant from the centre of the circle.

These concepts are fundamental in geometry and relate to various fields like Physics and engineering.

Applications of the Chord Calculator

The Chord Calculator can be used in different scenarios, making it a versatile tool. This includes applications in construction, engineering, and even Music theory. Whether you're laying out circular arcs for a project or analysing wave patterns in physics, knowing how to work with chords is beneficial.