Circle Radius Calculator: Diameter, Circumference, Area

Radius of a Circle Calculator

Introduction

Radius ya mduara ni moja ya mali zake za msingi. Ni umbali kutoka katikati ya mduara hadi sehemu yoyote kwenye ukingo wake. Kihesabu hiki kinakuwezesha kubaini radius ya mduara kulingana na vigezo vitatu tofauti:

Kipenyo
Mzunguko
Eneo

Kwa kutoa moja ya hizi thamani, unaweza kuhesabu radius kwa kutumia uhusiano wa kimaadili uliopo katika jiometri ya mduara.

Formula

Radius inaweza kuhesabiwa kutoka kwa kipenyo, mzunguko, au eneo kwa kutumia fomula zifuatazo:

Kutoka Kipenyo ( $d$ ):
$r = \frac{d}{2}$
Kutoka Mzunguko ( $C$ ):
$r = \frac{C}{2\pi}$
Kutoka Eneo ( $A$ ):
$r = \sqrt{\frac{A}{\pi}}$

Fomula hizi zinatokana na mali za kimsingi za mduara:

Kipenyo: Kipenyo ni mara mbili ya radius ( $d = 2r$ ).
Mzunguko: Mzunguko ni umbali wa kuzunguka mduara ( $C = 2\pi r$ ).
Eneo: Eneo lililo ndani ya mduara ( $A = \pi r^2$ ).

Calculation

Hesabu Radius Kutoka Kipenyo

Kutoa kipenyo, radius ni nusu yake tu:

r = \frac{d}{2}

Mfano:

Ikiwa kipenyo ni vitengo 10:

r = \frac{10}{2} = 5 \text{ vitengo}

Hesabu Radius Kutoka Mzunguko

Kuanza na fomula ya mzunguko:

C = 2\pi r

Kutatua kwa $r$ :

r = \frac{C}{2\pi}

Mfano:

Ikiwa mzunguko ni $31.4159$ vitengo:

r = \frac{31.4159}{2\pi} \approx \frac{31.4159}{6.2832} \approx 5 \text{ vitengo}

Hesabu Radius Kutoka Eneo

Kuanza na fomula ya eneo:

A = \pi r^2

Kutatua kwa $r$ :

r = \sqrt{\frac{A}{\pi}}

Mfano:

Ikiwa eneo ni $78.5398$ vitengo vya mraba:

r = \sqrt{\frac{78.5398}{\pi}} = \sqrt{\frac{78.5398}{3.1416}} \approx \sqrt{25} = 5 \text{ vitengo}

Mambo ya Kando na Uthibitishaji wa Ingizo

Ingizo la Sifuri au Mbaya: Mduara hauwezi kuwa na kipenyo, mzunguko, au eneo hasi au sifuri. Ikiwa mojawapo ya hizi thamani ni sifuri au hasi, radius haijafafanuliwa. Kihesabu kitaonyesha ujumbe wa kosa katika hali kama hizo.
Ingizo lisilo la Nambari: Kihesabu kinahitaji ingizo la nambari. Thamani zisizo za nambari (k.m. herufi au alama) hazikubaliki.

Usahihi na Upunguzaji

Kihesabu hiki kinatumia hesabu ya nambari ya floating-point ya double kwa ajili ya mahesabu. Matokeo kwa kawaida yanaonyeshwa yakiwa yamepunguzwa hadi mahali manne ya desimali kwa usahihi zaidi. Wakati wa kutumia vigezo vya kimaadili kama $\pi$ , kihesabu kinatumia usahihi wote unaopatikana katika lugha ya programu au mazingira. Kuwa makini kwamba hesabu ya floating-point inaweza kuleta makosa madogo ya upunguzaji katika baadhi ya matukio.

Matumizi

Kuhesabu radius ya mduara ni muhimu katika nyanja mbalimbali:

Uhandisi na Ujenzi

Kusimamia Vipengele vya Mduara: Wahandisi mara nyingi wanahitaji kubaini radius wanapobuni magurudumu, gia, mabomba, au dome.
Architektura: Wajenzi hutumia radius kubuni arches, dome, na majengo ya mduara.

Astronomiya

Mizunguko ya Sayari: Wanajimu wanahesabu radius ya mizunguko ya sayari kulingana na data za uchunguzi.
Mifumo ya Nyota: Kubaini ukubwa wa sayari, nyota, na vitu vingine vya angani.

Kutatua Matatizo ya Kila Siku

Sanaa na Ubunifu: Wasanii na wabunifu wanahesabu radius ili kuunda mifumo na michoro ya mduara.
Miradi ya DIY: Kuhesabu vifaa vinavyohitajika kwa ajili ya meza za mduara, bustani, au visima.

Hisabati na Elimu

Kujifunza Jiometri: Kuelewa mali za mduara ni muhimu katika elimu ya jiometri.
Kutatua Matatizo: Hesabu za radius ni za kawaida katika matatizo ya hisabati na mashindano.

Mbadala

Ingawa radius ni mali ya msingi, wakati mwingine mali nyingine za mduara zinaweza kuwa rahisi kupima moja kwa moja:

Kupima Urefu wa Chord: Inatumika wakati una alama zilizowekwa kwenye mduara na unahitaji kuhesabu radius.
Kutumia Eneo la Sekta au Urefu wa Arc: Katika hali zinazohusisha sehemu za mduara.

Historia

Utafiti wa mduara umeanzia katika tamaduni za kale:

Jiometri ya Kale: Mduara umekuwa ukisomeka tangu wakati wa Wamisri wa kale na Wababiloni.
Kazi za Euclid: Takriban mwaka 300 KK, Euclid alifafanua mduara na mali zake katika kazi yake maarufu, Elements.
Archimedes: Alitoa mbinu za kukadiria (\pi) na kuhesabu maeneo na volumu zinazohusiana na miduara na mipira.
Maendeleo ya (\pi): Katika karne nyingi, wanahisabati kama Liu Hui, Zu Chongzhi, Aryabhata, na hatimaye John Wallis na Isaac Newton walipunguza thamani na uelewa wa (\pi).

Radius inabaki kuwa dhana muhimu sio tu katika jiometri bali pia katika fizikia, uhandisi, na sayansi mbalimbali za matumizi.

Mifano

Hapa kuna mifano ya msimbo katika lugha mbalimbali za programu ili kuhesabu radius kutoka kipenyo, mzunguko, na eneo.

Kutoka Kipenyo

Python

1## Hesabu radius kutoka kipenyo
2def radius_from_diameter(diameter):
3    if diameter <= 0:
4        raise ValueError("Kipenyo kinapaswa kuwa kikubwa kuliko sifuri.")
5    return diameter / 2
6
7## Mfano wa matumizi
8d = 10
9r = radius_from_diameter(d)
10print(f"The radius is {r} units.")
11

JavaScript

1// Hesabu radius kutoka kipenyo
2function radiusFromDiameter(diameter) {
3    if (diameter <= 0) {
4        throw new Error("Kipenyo kinapaswa kuwa kikubwa kuliko sifuri.");
5    }
6    return diameter / 2;
7}
8
9// Mfano wa matumizi
10let d = 10;
11let r = radiusFromDiameter(d);
12console.log(`The radius is ${r} units.`);
13

Java

1public class CircleRadiusCalculator {
2    public static double radiusFromDiameter(double diameter) {
3        if (diameter <= 0) {
4            throw new IllegalArgumentException("Kipenyo kinapaswa kuwa kikubwa kuliko sifuri.");
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}
15

C++

1// Hesabu radius kutoka kipenyo
2#include <iostream>
3#include <stdexcept>
4
5double radiusFromDiameter(double diameter) {
6    if (diameter <= 0) {
7        throw std::invalid_argument("Kipenyo kinapaswa kuwa kikubwa kuliko sifuri.");
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}
22

R

1## Hesabu radius kutoka kipenyo
2radius_from_diameter <- function(diameter) {
3  if (diameter <= 0) {
4    stop("Kipenyo kinapaswa kuwa kikubwa kuliko sifuri.")
5  }
6  return(diameter / 2)
7}
8
9## Mfano wa matumizi
10d <- 10
11r <- radius_from_diameter(d)
12cat(sprintf("The radius is %.2f units.\n", r))
13

Ruby

1## Hesabu radius kutoka kipenyo
2def radius_from_diameter(diameter)
3  raise ArgumentError, "Kipenyo kinapaswa kuwa kikubwa kuliko sifuri." if diameter <= 0
4  diameter / 2.0
5end
6
7## Mfano wa matumizi
8d = 10
9r = radius_from_diameter(d)
10puts "The radius is #{r} units."
11

PHP

1<?php
2// Hesabu radius kutoka kipenyo
3function radiusFromDiameter($diameter) {
4    if ($diameter <= 0) {
5        throw new Exception('Kipenyo kinapaswa kuwa kikubwa kuliko sifuri.');
6    }
7    return $diameter / 2;
8}
9
10// Mfano wa matumizi
11$d = 10;
12$r = radiusFromDiameter($d);
13echo "The radius is {$r} units.";
14?>
15

Rust

1// Hesabu radius kutoka kipenyo
2fn radius_from_diameter(diameter: f64) -> Result<f64, &'static str> {
3    if diameter <= 0.0 {
4        return Err("Kipenyo kinapaswa kuwa kikubwa kuliko sifuri.");
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}
16

Swift

1import Foundation
2
3// Hesabu radius kutoka kipenyo
4func radiusFromDiameter(_ diameter: Double) throws -> Double {
5    if diameter <= 0 {
6        throw NSError(domain: "InvalidInput", code: 0, userInfo: [NSLocalizedDescriptionKey: "Kipenyo kinapaswa kuwa kikubwa kuliko sifuri."])
7    }
8    return diameter / 2.0
9}
10
11// Mfano wa matumizi
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}
19

Kutoka Mzunguko

Python

1import math
2
3## Hesabu radius kutoka mzunguko
4def radius_from_circumference(circumference):
5    if circumference <= 0:
6        raise ValueError("Mzunguko unapaswa kuwa mkubwa kuliko sifuri.")
7    return circumference / (2 * math.pi)
8
9## Mfano wa matumizi
10C = 31.4159
11r = radius_from_circumference(C)
12print(f"The radius is {r:.2f} units.")
13

JavaScript

1// Hesabu radius kutoka mzunguko
2function radiusFromCircumference(circumference) {
3    if (circumference <= 0) {
4        throw new Error("Mzunguko unapaswa kuwa mkubwa kuliko sifuri.");
5    }
6    return circumference / (2 * Math.PI);
7}
8
9// Mfano wa matumizi
10let C = 31.4159;
11let r = radiusFromCircumference(C);
12console.log(`The radius is ${r.toFixed(2)} units.`);
13

Java

1public class CircleRadiusCalculator {
2    public static double radiusFromCircumference(double circumference) {
3        if (circumference <= 0) {
4            throw new IllegalArgumentException("Mzunguko unapaswa kuwa mkubwa kuliko sifuri.");
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}
15

C++

1// Hesabu radius kutoka mzunguko
2#include <iostream>
3#include <cmath>
4#include <stdexcept>
5
6double radiusFromCircumference(double circumference) {
7    if (circumference <= 0) {
8        throw std::invalid_argument("Mzunguko unapaswa kuwa mkubwa kuliko sifuri.");
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}
23

R

1## Hesabu radius kutoka mzunguko
2radius_from_circumference <- function(circumference) {
3  if (circumference <= 0) {
4    stop("Mzunguko unapaswa kuwa mkubwa kuliko sifuri.")
5  }
6  return(circumference / (2 * pi))
7}
8
9## Mfano wa matumizi
10C <- 31.4159
11r <- radius_from_circumference(C)
12cat(sprintf("The radius is %.2f units.\n", r))
13

Ruby

1## Hesabu radius kutoka mzunguko
2def radius_from_circumference(circumference)
3  raise ArgumentError, "Mzunguko unapaswa kuwa mkubwa kuliko sifuri." if circumference <= 0
4  circumference / (2 * Math::PI)
5end
6
7## Mfano wa matumizi
8C = 31.4159
9r = radius_from_circumference(C)
10puts "The radius is #{format('%.2f', r)} units."
11

PHP

1<?php
2// Hesabu radius kutoka mzunguko
3function radiusFromCircumference($circumference) {
4    if ($circumference <= 0) {
5        throw new Exception('Mzunguko unapaswa kuwa mkubwa kuliko sifuri.');
6    }
7    return $circumference / (2 * M_PI);
8}
9
10// Mfano wa matumizi
11$C = 31.4159;
12$r = radiusFromCircumference($C);
13echo "The radius is " . round($r, 2) . " units.";
14?>
15

Rust

1use std::f64::consts::PI;
2
3// Hesabu radius kutoka mzunguko
4fn radius_from_circumference(circumference: f64) -> Result<f64, &'static str> {
5    if circumference <= 0.0 {
6        return Err("Mzunguko unapaswa kuwa mkubwa kuliko sifuri.");
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}
18

Swift

1import Foundation
2
3// Hesabu radius kutoka mzunguko
4func radiusFromCircumference(_ circumference: Double) throws -> Double {
5    if circumference <= 0 {
6        throw NSError(domain: "InvalidInput", code: 0, userInfo: [NSLocalizedDescriptionKey: "Mzunguko unapaswa kuwa mkubwa kuliko sifuri."])
7    }
8    return circumference / (2 * Double.pi)
9}
10
11// Mfano wa matumizi
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}
19

Kutoka Eneo

Python

1import math
2
3## Hesabu radius kutoka eneo
4def radius_from_area(area):
5    if area <= 0:
6        raise ValueError("Eneo linapaswa kuwa kubwa kuliko sifuri.")
7    return math.sqrt(area / math.pi)
8
9## Mfano wa matumizi
10A = 78.5398
11r = radius_from_area(A)
12print(f"The radius is {r:.2f} units.")
13

JavaScript

1// Hesabu radius kutoka eneo
2function radiusFromArea(area) {
3    if (area <= 0) {
4        throw new Error("Eneo linapaswa kuwa kubwa kuliko sifuri.");
5    }
6    return Math.sqrt(area / Math.PI);
7}
8
9// Mfano wa matumizi
10let A = 78.5398;
11let r = radiusFromArea(A);
12console.log(`The radius is ${r.toFixed(2)} units.`);
13

Java

1public class CircleRadiusCalculator {
2    public static double radiusFromArea(double area) {
3        if (area <= 0) {
4            throw new IllegalArgumentException("Eneo linapaswa kuwa kubwa kuliko sifuri.");
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}
15

C++

1// Hesabu radius kutoka eneo
2#include <iostream>
3#include <cmath>
4#include <stdexcept>
5
6double radiusFromArea(double area) {
7    if (area <= 0) {
8        throw std::invalid_argument("Eneo linapaswa kuwa kubwa kuliko sifuri.");
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}
23

R

1## Hesabu radius kutoka eneo
2radius_from_area <- function(area) {
3  if (area <= 0) {
4    stop("Eneo linapaswa kuwa kubwa kuliko sifuri.")
5  }
6  return(sqrt(area / pi))
7}
8
9## Mfano wa matumizi
10A <- 78.5398
11r <- radius_from_area(A)
12cat(sprintf("The radius is %.2f units.\n", r))
13

MATLAB

1% Hesabu radius kutoka eneo
2function r = radius_from_area(area)
3    if area <= 0
4        error('Eneo linapaswa kuwa kubwa kuliko sifuri.');
5    end
6    r = sqrt(area / pi);
7end
8
9% Mfano wa matumizi
10A = 78.5398;
11r = radius_from_area(A);
12fprintf('The radius is %.2f units.\n', r);
13

C#

1using System;
2
3class CircleRadiusCalculator
4{
5    public static double RadiusFromArea(double area)
6    {
7        if (area <= 0)
8            throw new ArgumentException("Eneo linapaswa kuwa kubwa kuliko sifuri.");
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}
19

Go

1package main
2
3import (
4	"fmt"
5	"math"
6)
7
8func radiusFromArea(area float64) (float64, error) {
9	if area <= 0 {
10		return 0, fmt.Errorf("Eneo linapaswa kuwa kubwa kuliko sifuri.")
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}
24

Ruby

1## Hesabu radius kutoka eneo
2def radius_from_area(area)
3  raise ArgumentError, "Eneo linapaswa kuwa kubwa kuliko sifuri." if area <= 0
4  Math.sqrt(area / Math::PI)
5end
6
7## Mfano wa matumizi
8A = 78.5398
9r = radius_from_area(A)
10puts "The radius is #{format('%.2f', r)} units."
11

PHP

1<?php
2// Hesabu radius kutoka eneo
3function radiusFromArea($area) {
4    if ($area <= 0) {
5        throw new Exception('Eneo linapaswa kuwa kubwa kuliko sifuri.');
6    }
7    return sqrt($area / M_PI);
8}
9
10// Mfano wa matumizi
11$A = 78.5398;
12$r = radiusFromArea($A);
13echo "The radius is " . round($r, 2) . " units.";
14?>
15

Rust

1use std::f64::consts::PI;
2
3// Hesabu radius kutoka eneo
4fn radius_from_area(area: f64) -> Result<f64, &'static str> {
5    if area <= 0.0 {
6        return Err("Eneo linapaswa kuwa kubwa kuliko sifuri.");
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}
18

Swift

1import Foundation
2
3// Hesabu radius kutoka eneo
4func radiusFromArea(_ area: Double) throws -> Double {
5    if area <= 0 {
6        throw NSError(domain: "InvalidInput", code: 0, userInfo: [NSLocalizedDescriptionKey: "Eneo linapaswa kuwa kubwa kuliko sifuri."])
7    }
8    return sqrt(area / Double.pi)
9}
10
11// Mfano wa matumizi
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}
19

Excel

1## Hesabu radius kutoka kipenyo kwenye seli B1
2=IF(B1>0, B1/2, "Ingizo batili")
3
4## Hesabu radius kutoka mzunguko kwenye seli B2
5=IF(B2>0, B2/(2*PI()), "Ingizo batili")
6
7## Hesabu radius kutoka eneo kwenye seli B3
8=IF(B3>0, SQRT(B3/PI()), "Ingizo batili")
9

Visualization

Mchoro wa SVG unaoonyesha uhusiano kati ya radius, kipenyo, na mzunguko:

References

Mduara - Wikipedia
Mzunguko - Math Is Fun
Eneo la Mduara - Khan Academy
Historia ya (\pi) - Wikipedia

Circle Radius Calculator: Diameter, Circumference, Area

Kihesabu Kipenyo cha Duara

Nyaraka

Radius of a Circle Calculator

Introduction

Formula

Calculation

Hesabu Radius Kutoka Kipenyo

Hesabu Radius Kutoka Mzunguko

Hesabu Radius Kutoka Eneo

Mambo ya Kando na Uthibitishaji wa Ingizo

Usahihi na Upunguzaji

Matumizi

Uhandisi na Ujenzi

Astronomiya

Kutatua Matatizo ya Kila Siku

Hisabati na Elimu

Mbadala

Historia

Mifano

Kutoka Kipenyo

Python

JavaScript

Java

C++

R

Ruby

PHP

Rust

Swift

Kutoka Mzunguko

Python

JavaScript

Java

C++

R

Ruby

PHP

Rust

Swift

Kutoka Eneo

Python

JavaScript

Java

C++

R

MATLAB

C#

Go

Ruby

PHP

Rust

Swift

Excel

Visualization

References

Maoni

Zana Zinazohusiana

Right Circular Cone Area and Volume Calculator Tool

Kikokotoo cha Kipenyo cha Mkonoo kwa Urefu na Mduara

Circle Measurements Calculator for Radius and Area