Radius Calculator

Category: Geometry
- June 01, 2025
| |

Calculate radius, diameter, circumference, and area of circles using various input methods. Essential for geometry, engineering, construction, and mathematical applications.

Input Method

Input Values

m
Distance across circle through center

Display Options

1 decimal 8 decimals
3 decimal places

Understanding Radius and Circle Measurements

The radius is the fundamental measurement of a circle - the distance from the center to any point on the circumference. All other circle properties can be derived from the radius using mathematical relationships.

Key Circle Properties
  • Radius (r): The distance from the center to any point on the circle
  • Diameter (d): The straight line distance across the circle through its center (d = 2r)
  • Circumference (C): The distance around the circle (C = 2πr)
  • Area (A): The space enclosed by the circle (A = πr²)
  • Pi (π): Mathematical constant approximately equal to 3.14159
Advanced Circle Elements
  • Chord: A straight line connecting two points on the circle
  • Sagitta: The perpendicular distance from a chord to the arc
  • Arc: A portion of the circumference between two points
  • Sector: A region bounded by two radii and an arc (like a pie slice)
  • Central Angle: The angle formed by two radii from the center
Common Applications
  • Engineering: Bearing design, wheel specifications, pipe calculations
  • Construction: Circular structures, arches, foundation design
  • Manufacturing: Machining operations, quality control, tooling
  • Architecture: Circular elements, decorative features, space planning
  • Mathematics: Geometric calculations, trigonometry, calculus applications

Disclaimer: This calculator provides mathematical results based on standard geometric formulas. For critical applications, verify calculations independently and consider manufacturing tolerances and real-world constraints.

What Is the Radius Calculator?

The Radius Calculator is an easy-to-use tool that helps you find the radius of a circle using various types of input. Whether you're working with a known diameter, circumference, area, chord, arc, sector, or inscribed polygon, this tool quickly delivers accurate results. It's a valuable resource for anyone involved in Geometry, engineering, design, or education.

Common Circle Formulas Used:
  • From Diameter: r = d ÷ 2
  • From Circumference: r = C ÷ (2π)
  • From Area: r = √(A ÷ π)
  • From Chord & Height: r = (c² ÷ 8h) + (h ÷ 2)
  • From Arc & Angle: r = s ÷ θ (θ in radians)
  • From Sector & Angle: r = √(2A ÷ θ) (θ in radians)
  • From Polygon: r = s ÷ (2 × sin(π ÷ n))

How to Use the Calculator

Follow these steps to get the most accurate radius calculation:

  • Select your input method (e.g., Diameter, Area, Chord Length).
  • Enter your known measurement(s) into the appropriate fields.
  • Choose the desired unit of measurement (mm, cm, m, in, ft, yd).
  • Set the decimal precision using the slider.
  • Click the “Calculate Radius” button to get results.
  • Optionally, view the formulas used, unit conversions, and practical applications.

Key Features

  • Supports multiple input types for versatile calculations.
  • Displays related measurements: diameter, area, and circumference.
  • Includes visual diagrams for better understanding.
  • Converts results across various metric and imperial units.
  • Provides real-world examples and use cases based on the size of the radius.

Why This Calculator Is Useful

Accurate radius measurements are important in many fields. This calculator saves time and ensures precision whether you're:

  • Designing mechanical parts
  • Planning architectural curves
  • Measuring circular areas for construction or landscaping
  • Teaching or learning geometry concepts

It also complements Other tools like the Circle Calculator, Area Calculator, Volume Calculator, and Circumference Calculator. You might also explore triangle-based tools such as the Triangle Area Tool, Right Triangle Solver, or Pythagorean Theorem Tool for broader geometry problem-solving.

Frequently Asked Questions (FAQ)

1. What is the radius of a circle?

The radius is the distance from the center of the circle to any point on its edge.

2. Can I calculate the radius if I only know the area?

Yes. The formula is r = √(A ÷ π). Just enter the area into the calculator and select "Area" as your input method.

3. How does the calculator handle angles?

When using arc or sector inputs, you can choose between degrees and radians. The calculator automatically converts angles as needed.

4. What if I’m working with polygons inside circles?

You can use the “Inscribed Polygon” option by specifying the number of sides and the side length. The tool handles calculations using trigonometric formulas.

5. Are results accurate for all units?

Yes. You can select your unit and see the results converted to other units if desired. Precision can be adjusted using the slider.

Related Calculators You May Find Helpful

  • Triangle Geometry Solver – Solve triangle side and angle problems
  • Volume Formula Tool – Calculate the volume of common 3D shapes
  • Right Triangle Solver – Find hypotenuse and angles using right triangle rules
  • Chord Finder – Calculate chords and arcs within circles
  • Surface Area Tool – Measure surface areas of spheres, cones, and more
  • Distance Measurement – Measure distance between two points or along a route

Whether you’re solving classroom problems, designing parts, or analyzing geometry in the field, this tool simplifies the process of understanding and working with circles. It's an excellent companion to your triangle solvers, area measurement tools, and other geometric calculators.