Calculate the radius of a circle from diameter, circumference, or area. Free tool with formulas, examples, and instant results for geometry and design projects.
Calculating the radius of a circle is essential for geometry, engineering, and everyday measurements. The circle radius represents the distance from the center point to any point on the circumference, making it a fundamental property in circular calculations. This radius calculator helps you quickly find the radius of a circle using three different input methods:
Whether you're solving geometry problems, designing circular objects, or planning construction projects, this circle radius calculator provides instant, accurate results for all your radius calculations.
The radius of a circle can be calculated from the diameter, circumference, or area using these proven mathematical formulas:
From Diameter ():
From Circumference ():
From Area ():
These circle radius formulas are derived from the fundamental properties of circles:
To calculate radius from diameter, simply divide the diameter by 2. This is the easiest radius calculation method:
Example:
If the diameter is 10 units:
To find the radius from circumference, divide the circumference by 2π. Starting with the circumference formula:
Solving for :
Example:
If the circumference is units:
To calculate radius from area, take the square root of area divided by π. Starting with the area formula:
Solving for :
Example:
If the area is square units:
Zero or Negative Inputs: A circle cannot have a negative or zero diameter, circumference, or area. If any of these values are zero or negative, the radius is undefined. The calculator will display an error message in such cases.
Non-numeric Inputs: The calculator requires numeric inputs. Non-numeric values (e.g., letters or symbols) are invalid.
This calculator uses double-precision floating-point arithmetic for calculations. Results are typically displayed rounded to four decimal places for greater accuracy. When using mathematical constants like , the calculator utilizes the full precision available in the programming language or environment. Be aware that floating-point arithmetic can introduce small rounding errors in some cases.
Knowing how to calculate the radius of a circle is essential across numerous professional and personal applications:
Designing Circular Components: Engineers often need to determine the radius when designing wheels, gears, pipes, or domes.
Architecture: Architects use the radius to design arches, domes, and circular buildings.
Planetary Orbits: Astronomers calculate the radius of planetary orbits based on observational data.
Celestial Bodies: Determining the sizes of planets, stars, and other celestial objects.
Art and Design: Artists and designers calculate the radius to create circular patterns and designs.
DIY Projects: Calculating materials needed for circular tables, gardens, or fountains.
Learning Geometry: Understanding the properties of circles is fundamental in geometry education.
Problem-Solving: Radius calculations are common in mathematical problems and competitions.
While the radius is a primary property, sometimes other circle properties are more convenient to measure directly:
Measuring the Chord Length: Useful when you have fixed points on a circle and need to calculate the radius.
Using Sector Area or Arc Length: In cases involving partial sections of a circle.
The study of circles dates back to ancient civilizations:
Ancient Geometry: The circle has been studied since the time of the ancient Egyptians and Babylonians.
Euclid's Elements: Around 300 BCE, Euclid defined the circle and its properties in his seminal work, Elements.
Archimedes: Provided methods to approximate (\pi) and calculated areas and volumes related to circles and spheres.
Development of (\pi): Over centuries, mathematicians like Liu Hui, Zu Chongzhi, Aryabhata, and ultimately John Wallis and Isaac Newton refined the value and understanding of (\pi).
The radius of a circle remains a fundamental concept not only in geometry but also across physics, engineering, and various applied sciences. Understanding how to find the radius empowers you to solve countless real-world measurement and design challenges.
Here are code examples in multiple programming languages to calculate the radius from diameter, circumference, and area.
1## Calculate radius from diameter
2def radius_from_diameter(diameter):
3 if diameter <= 0:
4 raise ValueError("Diameter must be greater than zero.")
5 return diameter / 2
6
7## Example usage
8d = 10
9r = radius_from_diameter(d)
10print(f"The radius is {r} units.")
111// Calculate radius from diameter
2function radiusFromDiameter(diameter) {
3 if (diameter <= 0) {
4 throw new Error("Diameter must be greater than zero.");
5 }
6 return diameter / 2;
7}
8
9// Example usage
10let d = 10;
11let r = radiusFromDiameter(d);
12console.log(`The radius is ${r} units.`);
131public class CircleRadiusCalculator {
2 public static double radiusFromDiameter(double diameter) {
3 if (diameter <= 0) {
4 throw new IllegalArgumentException("Diameter must be greater than zero.");
5 }
6 return diameter / 2;
7 }
8
9 public static void main(String[] args) {
10 double d = 10;
11 double r = radiusFromDiameter(d);
12 System.out.printf("The radius is %.2f units.%n", r);
13 }
14}
151// Calculate radius from diameter
2#include <iostream>
3#include <stdexcept>
4
5double radiusFromDiameter(double diameter) {
6 if (diameter <= 0) {
7 throw std::invalid_argument("Diameter must be greater than zero.");
8 }
9 return diameter / 2.0;
10}
11
12int main() {
13 double d = 10.0;
14 try {
15 double r = radiusFromDiameter(d);
16 std::cout << "The radius is " << r << " units." << std::endl;
17 } catch (const std::exception& e) {
18 std::cerr << e.what() << std::endl;
19 }
20 return 0;
21}
221## Calculate radius from diameter
2radius_from_diameter <- function(diameter) {
3 if (diameter <= 0) {
4 stop("Diameter must be greater than zero.")
5 }
6 return(diameter / 2)
7}
8
9## Example usage
10d <- 10
11r <- radius_from_diameter(d)
12cat(sprintf("The radius is %.2f units.\n", r))
131## Calculate radius from diameter
2def radius_from_diameter(diameter)
3 raise ArgumentError, "Diameter must be greater than zero." if diameter <= 0
4 diameter / 2.0
5end
6
7## Example usage
8d = 10
9r = radius_from_diameter(d)
10puts "The radius is #{r} units."
111<?php
2// Calculate radius from diameter
3function radiusFromDiameter($diameter) {
4 if ($diameter <= 0) {
5 throw new Exception('Diameter must be greater than zero.');
6 }
7 return $diameter / 2;
8}
9
10// Example usage
11$d = 10;
12$r = radiusFromDiameter($d);
13echo "The radius is {$r} units.";
14?>
151// Calculate radius from diameter
2fn radius_from_diameter(diameter: f64) -> Result<f64, &'static str> {
3 if diameter <= 0.0 {
4 return Err("Diameter must be greater than zero.");
5 }
6 Ok(diameter / 2.0)
7}
8
9fn main() {
10 let d = 10.0;
11 match radius_from_diameter(d) {
12 Ok(r) => println!("The radius is {:.2} units.", r),
13 Err(e) => println!("{}", e),
14 }
15}
161import Foundation
2
3// Calculate radius from diameter
4func radiusFromDiameter(_ diameter: Double) throws -> Double {
5 if diameter <= 0 {
6 throw NSError(domain: "InvalidInput", code: 0, userInfo: [NSLocalizedDescriptionKey: "Diameter must be greater than zero."])
7 }
8 return diameter / 2.0
9}
10
11// Example usage
12do {
13 let d = 10.0
14 let r = try radiusFromDiameter(d)
15 print("The radius is \(r) units.")
16} catch {
17 print(error.localizedDescription)
18}
191import math
2
3## Calculate radius from circumference
4def radius_from_circumference(circumference):
5 if circumference <= 0:
6 raise ValueError("Circumference must be greater than zero.")
7 return circumference / (2 * math.pi)
8
9## Example usage
10C = 31.4159
11r = radius_from_circumference(C)
12print(f"The radius is {r:.2f} units.")
131// Calculate radius from circumference
2function radiusFromCircumference(circumference) {
3 if (circumference <= 0) {
4 throw new Error("Circumference must be greater than zero.");
5 }
6 return circumference / (2 * Math.PI);
7}
8
9// Example usage
10let C = 31.4159;
11let r = radiusFromCircumference(C);
12console.log(`The radius is ${r.toFixed(2)} units.`);
131public class CircleRadiusCalculator {
2 public static double radiusFromCircumference(double circumference) {
3 if (circumference <= 0) {
4 throw new IllegalArgumentException("Circumference must be greater than zero.");
5 }
6 return circumference / (2 * Math.PI);
7 }
8
9 public static void main(String[] args) {
10 double C = 31.4159;
11 double r = radiusFromCircumference(C);
12 System.out.printf("The radius is %.2f units.%n", r);
13 }
14}
151// Calculate radius from circumference
2#include <iostream>
3#include <cmath>
4#include <stdexcept>
5
6double radiusFromCircumference(double circumference) {
7 if (circumference <= 0) {
8 throw std::invalid_argument("Circumference must be greater than zero.");
9 }
10 return circumference / (2.0 * M_PI);
11}
12
13int main() {
14 double C = 31.4159;
15 try {
16 double r = radiusFromCircumference(C);
17 std::cout << "The radius is " << r << " units." << std::endl;
18 } catch (const std::exception& e) {
19 std::cerr << e.what() << std::endl;
20 }
21 return 0;
22}
231## Calculate radius from circumference
2radius_from_circumference <- function(circumference) {
3 if (circumference <= 0) {
4 stop("Circumference must be greater than zero.")
5 }
6 return(circumference / (2 * pi))
7}
8
9## Example usage
10C <- 31.4159
11r <- radius_from_circumference(C)
12cat(sprintf("The radius is %.2f units.\n", r))
131## Calculate radius from circumference
2def radius_from_circumference(circumference)
3 raise ArgumentError, "Circumference must be greater than zero." if circumference <= 0
4 circumference / (2 * Math::PI)
5end
6
7## Example usage
8C = 31.4159
9r = radius_from_circumference(C)
10puts "The radius is #{format('%.2f', r)} units."
111<?php
2// Calculate radius from circumference
3function radiusFromCircumference($circumference) {
4 if ($circumference <= 0) {
5 throw new Exception('Circumference must be greater than zero.');
6 }
7 return $circumference / (2 * M_PI);
8}
9
10// Example usage
11$C = 31.4159;
12$r = radiusFromCircumference($C);
13echo "The radius is " . round($r, 2) . " units.";
14?>
151use std::f64::consts::PI;
2
3// Calculate radius from circumference
4fn radius_from_circumference(circumference: f64) -> Result<f64, &'static str> {
5 if circumference <= 0.0 {
6 return Err("Circumference must be greater than zero.");
7 }
8 Ok(circumference / (2.0 * PI))
9}
10
11fn main() {
12 let C = 31.4159;
13 match radius_from_circumference(C) {
14 Ok(r) => println!("The radius is {:.2} units.", r),
15 Err(e) => println!("{}", e),
16 }
17}
181import Foundation
2
3// Calculate radius from circumference
4func radiusFromCircumference(_ circumference: Double) throws -> Double {
5 if circumference <= 0 {
6 throw NSError(domain: "InvalidInput", code: 0, userInfo: [NSLocalizedDescriptionKey: "Circumference must be greater than zero."])
7 }
8 return circumference / (2 * Double.pi)
9}
10
11// Example usage
12do {
13 let C = 31.4159
14 let r = try radiusFromCircumference(C)
15 print(String(format: "The radius is %.2f units.", r))
16} catch {
17 print(error.localizedDescription)
18}
191import math
2
3## Calculate radius from area
4def radius_from_area(area):
5 if area <= 0:
6 raise ValueError("Area must be greater than zero.")
7 return math.sqrt(area / math.pi)
8
9## Example usage
10A = 78.5398
11r = radius_from_area(A)
12print(f"The radius is {r:.2f} units.")
131// Calculate radius from area
2function radiusFromArea(area) {
3 if (area <= 0) {
4 throw new Error("Area must be greater than zero.");
5 }
6 return Math.sqrt(area / Math.PI);
7}
8
9// Example usage
10let A = 78.5398;
11let r = radiusFromArea(A);
12console.log(`The radius is ${r.toFixed(2)} units.`);
131public class CircleRadiusCalculator {
2 public static double radiusFromArea(double area) {
3 if (area <= 0) {
4 throw new IllegalArgumentException("Area must be greater than zero.");
5 }
6 return Math.sqrt(area / Math.PI);
7 }
8
9 public static void main(String[] args) {
10 double A = 78.5398;
11 double r = radiusFromArea(A);
12 System.out.printf("The radius is %.2f units.%n", r);
13 }
14}
151// Calculate radius from area
2#include <iostream>
3#include <cmath>
4#include <stdexcept>
5
6double radiusFromArea(double area) {
7 if (area <= 0) {
8 throw std::invalid_argument("Area must be greater than zero.");
9 }
10 return std::sqrt(area / M_PI);
11}
12
13int main() {
14 double A = 78.5398;
15 try {
16 double r = radiusFromArea(A);
17 std::cout << "The radius is " << r << " units." << std::endl;
18 } catch (const std::exception& e) {
19 std::cerr << e.what() << std::endl;
20 }
21 return 0;
22}
231## Calculate radius from area
2radius_from_area <- function(area) {
3 if (area <= 0) {
4 stop("Area must be greater than zero.")
5 }
6 return(sqrt(area / pi))
7}
8
9## Example usage
10A <- 78.5398
11r <- radius_from_area(A)
12cat(sprintf("The radius is %.2f units.\n", r))
131% Calculate radius from area
2function r = radius_from_area(area)
3 if area <= 0
4 error('Area must be greater than zero.');
5 end
6 r = sqrt(area / pi);
7end
8
9% Example usage
10A = 78.5398;
11r = radius_from_area(A);
12fprintf('The radius is %.2f units.\n', r);
131using System;
2
3class CircleRadiusCalculator
4{
5 public static double RadiusFromArea(double area)
6 {
7 if (area <= 0)
8 throw new ArgumentException("Area must be greater than zero.");
9 return Math.Sqrt(area / Math.PI);
10 }
11
12 static void Main()
13 {
14 double A = 78.5398;
15 double r = RadiusFromArea(A);
16 Console.WriteLine("The radius is {0:F2} units.", r);
17 }
18}
191package main
2
3import (
4 "fmt"
5 "math"
6)
7
8func radiusFromArea(area float64) (float64, error) {
9 if area <= 0 {
10 return 0, fmt.Errorf("Area must be greater than zero.")
11 }
12 return math.Sqrt(area / math.Pi), nil
13}
14
15func main() {
16 A := 78.5398
17 r, err := radiusFromArea(A)
18 if err != nil {
19 fmt.Println(err)
20 return
21 }
22 fmt.Printf("The radius is %.2f units.\n", r)
23}
241## Calculate radius from area
2def radius_from_area(area)
3 raise ArgumentError, "Area must be greater than zero." if area <= 0
4 Math.sqrt(area / Math::PI)
5end
6
7## Example usage
8A = 78.5398
9r = radius_from_area(A)
10puts "The radius is #{format('%.2f', r)} units."
111<?php
2// Calculate radius from area
3function radiusFromArea($area) {
4 if ($area <= 0) {
5 throw new Exception('Area must be greater than zero.');
6 }
7 return sqrt($area / M_PI);
8}
9
10// Example usage
11$A = 78.5398;
12$r = radiusFromArea($A);
13echo "The radius is " . round($r, 2) . " units.";
14?>
151use std::f64::consts::PI;
2
3// Calculate radius from area
4fn radius_from_area(area: f64) -> Result<f64, &'static str> {
5 if area <= 0.0 {
6 return Err("Area must be greater than zero.");
7 }
8 Ok((area / PI).sqrt())
9}
10
11fn main() {
12 let A = 78.5398;
13 match radius_from_area(A) {
14 Ok(r) => println!("The radius is {:.2} units.", r),
15 Err(e) => println!("{}", e),
16 }
17}
181import Foundation
2
3// Calculate radius from area
4func radiusFromArea(_ area: Double) throws -> Double {
5 if area <= 0 {
6 throw NSError(domain: "InvalidInput", code: 0, userInfo: [NSLocalizedDescriptionKey: "Area must be greater than zero."])
7 }
8 return sqrt(area / Double.pi)
9}
10
11// Example usage
12do {
13 let A = 78.5398
14 let r = try radiusFromArea(A)
15 print(String(format: "The radius is %.2f units.", r))
16} catch {
17 print(error.localizedDescription)
18}
191## Calculate radius from diameter in cell B1
2=IF(B1>0, B1/2, "Invalid input")
3
4## Calculate radius from circumference in cell B2
5=IF(B2>0, B2/(2*PI()), "Invalid input")
6
7## Calculate radius from area in cell B3
8=IF(B3>0, SQRT(B3/PI()), "Invalid input")
9An SVG diagram illustrating the relationship between the radius, diameter, and circumference:
The radius of a circle is the distance from the center of the circle to any point on its edge (circumference). It's one of the most fundamental measurements in circular geometry and is exactly half the diameter.
To calculate radius from diameter, simply divide the diameter by 2. The formula is: r = d/2. For example, if a circle has a diameter of 10 units, the radius is 5 units.
The radius from circumference formula is: r = C/(2π). Divide the circumference by 2π (approximately 6.2832) to get the radius. This formula comes from rearranging the circumference equation C = 2πr.
To find radius from area, use the formula: r = √(A/π). Take the area, divide it by π (approximately 3.1416), then take the square root of the result. This derives from the area formula A = πr².
The diameter is always twice the radius (d = 2r), or conversely, the radius is half the diameter (r = d/2). They are directly proportional, making radius-to-diameter conversion straightforward.
Yes! You can easily calculate the circle radius from circumference using the formula r = C/(2π). The circumference measurement alone is sufficient to determine the radius precisely.
The radius is the fundamental measurement for circles because all other circle properties (diameter, circumference, area) can be derived from it. It appears in virtually every circle formula and represents the defining characteristic of a circle's size.
The radius uses the same units as your input measurement. If you enter diameter in centimeters, your radius will be in centimeters. If you use inches, feet, meters, or any other length unit, the radius maintains that same unit.
Meta Title: Calculate Circle Radius from Diameter, Area & Circumference
Meta Description: Free circle radius calculator. Instantly find the radius of a circle using diameter, circumference, or area. Simple formulas, step-by-step examples, and code snippets included.
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