I'm working on modernizing Rosetta Code's infrastructure. Starting with communications. Please accept this time-limited open invite to RC's Slack.. --Michael Mol (talk) 20:59, 30 May 2020 (UTC)

# Length of an arc between two angles

Length of an arc between two angles is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Write a method (function, procedure etc.) in your language which calculates the length of the major arc of a circle of given radius between two angles.

In this diagram the major arc is colored green   (note: this website leaves cookies).

Illustrate the use of your method by calculating the length of the major arc of a circle of radius 10 units, between angles of 10 and 120 degrees.

## 11l

Translation of: Python
`F arc_length(r, angleA, angleB)   R (360.0 - abs(angleB - angleA)) * math:pi * r / 180.0 print(arc_length(10, 10, 120))`
Output:
```43.6332
```

## Action!

`INCLUDE "H6:REALMATH.ACT" PROC ArcLength(REAL POINTER r,a1,a2,len)  REAL tmp1,tmp2,r180,r360,pi   IntToReal(360,r360)  IntToReal(180,r180)  ValR("3.14159265",pi)  RealAbsDiff(a1,a2,tmp1)     ;tmp1=abs(a1-a2)  RealSub(r360,tmp1,tmp2) ;tmp2=360-abs(a1-a2)  RealMult(tmp2,pi,tmp1)  ;tmp1=(360-abs(a1-a2))*pi  RealMult(tmp1,r,tmp2)   ;tmp2=(360-abs(a1-a2))*pi*r  RealDiv(tmp2,r180,len)  ;len=(360-abs(a1-a2))*pi*r/180RETURN PROC Main()  REAL r,a1,a2,len   Put(125) PutE() ;clear screen  Print("Length of arc: ")  IntToReal(10,r)  IntToReal(10,a1)  IntToReal(120,a2)  ArcLength(r,a1,a2,len)  PrintR(len)RETURN`
Output:
```Length of arc: 43.63323122
```

`with Ada.Text_Io;with Ada.Numerics; procedure Calculate_Arc_Length is   use Ada.Text_Io;    type Angle_Type is new Float range 0.0 .. 360.0;       -- In degrees   type Distance   is new Float range 0.0 .. Float'Last;  -- In units    function Major_Arc_Length (Angle_1, Angle_2 : Angle_Type;                              Radius           : Distance)                             return Distance   is      Pi            : constant := Ada.Numerics.Pi;      Circumference : constant Distance   := 2.0 * Pi * Radius;      Major_Angle   : constant Angle_Type := 360.0 - abs (Angle_2 - Angle_1);      Arc_Length    : constant Distance   :=        Distance (Major_Angle) / 360.0 * Circumference;   begin      return Arc_Length;   end Major_Arc_Length;    package Distance_Io is new Ada.Text_Io.Float_Io (Distance);    Arc_Length : constant Distance := Major_Arc_Length (Angle_1 =>  10.0,                                                       Angle_2 => 120.0,                                                       Radius  =>  10.0);begin   Put ("Arc length : ");   Distance_Io.Put (Arc_Length, Exp => 0, Aft => 4);   New_Line;end Calculate_Arc_Length;`
Output:
```Arc length : 43.6332
```

## ALGOL W

Follows the Fortran interpretation of the task and finds the length of the major arc.

`begin    % returns the length of the arc between the angles a and b on a circle of radius r %    % the angles should  be specified in degrees                                       %    real procedure majorArcLength( real value a, b, r ) ;    begin        real angle;        angle := abs( a - b );        while angle > 360 do angle := angle - 360;        if angle < 180 then angle := 360 - angle;        ( r * angle * PI ) / 180    end majorArcLength ;    % task test case                                                                   %    write( r_w := 10, r_d := 4, r_format := "A", majorArcLength( 10, 120, 10 ) )end.`
Output:
```   43.6332
```

## APL

Works with: Dyalog APL
`arc ← (○÷180)×⊣×360-(|(-/⊢))`
Output:
```      10 arc 10 120
43.6332313```

## AutoHotkey

`MsgBox % result := arcLength(10, 10, 120)return arcLength(radius, angle1, angle2){    return (360 - Abs(angle2-angle1)) * (π := 3.141592653589793) * radius / 180}`
Output:
`43.633231`

## AWK

` # syntax: GAWK -f LENGTH_OF_AN_ARC_BETWEEN_TWO_ANGLES.AWK# converted from PHIXBEGIN {    printf("%.7f\n",arc_length(10,10,120))    exit(0)}function arc_length(radius,angle1,angle2) {    return (360 - abs(angle2-angle1)) * 3.14159265 / 180 * radius}function abs(x) { if (x >= 0) { return x } else { return -x } } `
Output:
```43.6332313
```

## BASIC

`10 DATA 10, 10, 12020 READ R, A1, A230 GOSUB 10040 PRINT A50 END100 REM Calculate length of arc of radius R, angles A1 and A2110 A = ATN(1)*R*(360-ABS(A1-A2))/45120 RETURN`
Output:
` 43.6332`

## C

Translation of: AWK
` #define PI 3.14159265358979323846#define ABS(x)  (x<0?-x:x) double arc_length(double radius, double angle1, double angle2) {    return (360 - ABS(angle2 - angle1)) * PI / 180 * radius;} void main(){    printf("%.7f\n",arc_length(10, 10, 120));} `
Output:
```43.6332313
```

## C++

Translation of: Kotlin
`#include <iostream> #define _USE_MATH_DEFINES#include <math.h> double arcLength(double radius, double angle1, double angle2) {    return (360.0 - abs(angle2 - angle1)) * M_PI * radius / 180.0;} int main() {    auto al = arcLength(10.0, 10.0, 120.0);    std::cout << "arc length: " << al << '\n';    return 0;}`
Output:
`arc length: 43.6332`

## D

Translation of: C++
`import std.math;import std.stdio; double arcLength(double radius, double angle1, double angle2) {    return (360.0 - abs(angle2 - angle1)) * PI * radius / 180.0;} void main() {    writeln("arc length: ", arcLength(10.0, 10.0, 120.0));}`
Output:
`arc length: 43.6332`

## Delphi

Translation of: AWK
` program Length_of_an_arc; {\$APPTYPE CONSOLE}{\$R *.res} uses  System.SysUtils; function arc_length(radius, angle1, angle2: Double): Double;begin  Result := (360 - abs(angle2 - angle1)) * PI / 180 * radius;end; begin  Writeln(Format('%.7f', [arc_length(10, 10, 120)]));  Readln;end. `
Output:
```43.6332313
```

## Factor

`USING: kernel math math.constants math.trig prettyprint ; : arc-length ( radius angle angle -- x )    - abs deg>rad 2pi swap - * ; 10 10 120 arc-length .`
Output:
```43.63323129985824
```

## FOCAL

`01.10 S A1=10        ;C SET PARAMETERS01.20 S A2=12001.30 S R=1001.40 D 2            ;C CALL SUBROUTINE 201.50 T %6.4,A,!     ;C DISPLAY RESULT01.60 Q 02.01 C CALCULATE LENGTH OF ARC OF RADIUS R, ANGLES A1 AND A202.10 S A=(360 - FABS(A2-A1)) * (3.14159 / 180) * R`
Output:
`= 43.6332`

## Fortran

The Fortran subroutine contains the MAX(DIF, 360. - DIF) operation. Other solutions presented here correspond to different interpretations of the problem. This subroutine computes the length of the major arc, which is not necessarily equal to distance traveling counter-clockwise.

`*-----------------------------------------------------------------------* given:  polar coordinates of two points on a circle of known radius* find:  length of the major arc between these points**___Name_____Type___I/O___Description___________________________________*   RAD      Real   In    Radius of circle, any unit of measure*   ANG1     Real   In    Angle of first point, degrees*   ANG2     Real   In    Angle of second point, degrees*   MAJARC   Real   Out   Length of major arc, same units as RAD*-----------------------------------------------------------------------      FUNCTION MAJARC (RAD, ANG1, ANG2)       IMPLICIT NONE       REAL RAD, ANG1, ANG2, MAJARC        REAL FACT                          ! degrees to radians       PARAMETER (FACT = 3.1415926536 / 180.)       REAL DIF *       Begin       MAJARC = 0.       IF (RAD .LE. 0.) RETURN       DIF = MOD(ABS(ANG1 - ANG2), 360.)   ! cyclic difference       DIF = MAX(DIF, 360. - DIF)          ! choose the longer path       MAJARC = RAD * DIF * FACT           ! L = r theta       RETURN      END  ! of majarc *-----------------------------------------------------------------------      PROGRAM TMA       IMPLICIT NONE       INTEGER J       REAL ANG1, ANG2, RAD, MAJARC, ALENG       REAL DATARR(3,3)            DATA DATARR / 120.,  10., 10.,     \$                10., 120., 10.,     \$               180., 270., 10. /        DO J = 1, 3         ANG1 = DATARR(1,J)         ANG2 = DATARR(2,J)         RAD = DATARR(3,J)         ALENG = MAJARC (RAD, ANG1, ANG2)                 PRINT *, 'first angle: ', ANG1, ' second angle: ', ANG2,      \$     ' radius: ', RAD, ' Length of major arc: ', ALENG       END DO      END  `
Output:
``` first angle:    120.000000      second angle:    10.0000000      radius:    10.0000000      Length of major arc:    43.6332321
first angle:    10.0000000      second angle:    120.000000      radius:    10.0000000      Length of major arc:    43.6332321
first angle:    180.000000      second angle:    270.000000      radius:    10.0000000      Length of major arc:    47.1238899
```

## FreeBASIC

` #define DEG 0.017453292519943295769236907684886127134 function arclength( r as double, a1 as double, a2 as double ) as double    return (360 - abs(a2 - a1)) * DEG * rend function print arclength(10, 10, 120) `
Output:
``` 43.63323129985824
```

## Go

Translation of: Julia
`package main import (    "fmt"    "math") func arcLength(radius, angle1, angle2 float64) float64 {    return (360 - math.Abs(angle2-angle1)) * math.Pi * radius / 180} func main() {    fmt.Println(arcLength(10, 10, 120))}`
Output:
```43.63323129985823
```

Translation of: Julia
`arcLength radius angle1 angle2 = (360.0 - (abs \$ angle1 - angle2)) * pi * radius / 180.0 main = putStrLn \$ "arcLength 10.0 10.0 120.0 = " ++ show (arcLength 10.0 10.0 120.0)`
Output:
`arcLength 10.0 10.0 120.0 = 43.63323129985823`

## Java

`public static double arcLength(double r, double a1, double a2){    return (360.0 - Math.abs(a2-a1))*Math.PI/180.0 * r;}`

## JavaScript

Translation of: AWK
` function arc_length(radius, angle1, angle2) {    return (360 - Math.abs(angle2 - angle1)) * Math.PI / 180 * radius;} console.log(arc_length(10, 10, 120).toFixed(7)); `
Output:
```43.6332313
```

## jq

Translation of: Julia
Works with: jq

Works with gojq, the Go implementation of jq

As noted in the entry for Julia, the function defined here does not correspond to the arc subtended by an angle.

In case you're wondering why `length` appears below where you might expect `abs`, rest assured that jq's `length` applied to a number yields its absolute value.

`# Output is in the same units as radius; angles are in degrees.def arclength(radius; angle1; angle2):  def pi: 1 | atan * 4;  (360 - ((angle2 - angle1)|length)) * (pi/180) * radius; # The task:arclength(10; 10; 120)`
Output:
```43.63323129985824
```

## Julia

The task seems to be to find the distance along the circumference of the circle which is NOT swept out between the two angles.

` arclength(r, angle1, angle2) =  (360 - abs(angle2 - angle1)) * π/180 * r@show arclength(10, 10, 120)   # -->  arclength(10, 10, 120) = 43.63323129985823 `

## Kotlin

Translation of: Go
`import kotlin.math.PIimport kotlin.math.abs fun arcLength(radius: Double, angle1: Double, angle2: Double): Double {    return (360.0 - abs(angle2 - angle1)) * PI * radius / 180.0} fun main() {    val al = arcLength(10.0, 10.0, 120.0)    println("arc length: \$al")}`
Output:
`arc length: 43.63323129985823`

## Lua

Translation of: D
`function arcLength(radius, angle1, angle2)    return (360.0 - math.abs(angle2 - angle1)) * math.pi * radius / 180.0end function main()    print("arc length: " .. arcLength(10.0, 10.0, 120.0))end main()`
Output:
`arc length: 43.633231299858`

## Nim

`import math, strformat const TwoPi = 2 * Pi func arcLength(r, a, b: float): float =  ## Return the length of the major arc in a circle of radius "r"  ## between angles "a" and "b" expressed in radians.  let d = abs(a - b) mod TwoPi  result = r * (if d >= Pi: d else: TwoPi - d) echo &"Arc length: {arcLength(10, degToRad(10.0), degToRad(120.0)):.5f}"`
Output:
`Arc length: 43.63323`

## Perl

Translation of: Raku
`use strict;use warnings;use utf8;binmode STDOUT, ":utf8";use POSIX 'fmod'; use constant π => 2 * atan2(1, 0);use constant τ => 2 * π; sub d2r { \$_[0] * τ / 360 } sub arc {    my(\$a1, \$a2, \$r) = (d2r(\$_[0]), d2r(\$_[1]), \$_[2]);    my @a = map { fmod( (\$_ + τ), τ) } (\$a1, \$a2);    printf "Arc length: %8.5f  Parameters: (%9.7f, %10.7f, %10.7f)\n",       (fmod((\$a[0]-\$a[1] + τ), τ) * \$r), \$a2, \$a1, \$r;} arc(@\$_) for    [ 10, 120,   10],    [ 10, 120,    1],    [120,  10,    1],    [-90, 180, 10/π],    [-90,   0, 10/π],    [ 90,   0, 10/π];`
Output:
```Arc length: 43.63323  Parameters: (2.0943951, 0.1745329, 10.0000000)
Arc length: 43.63323  Parameters: (2.0943951,  0.1745329, 10.0000000)
Arc length:  4.36332  Parameters: (2.0943951,  0.1745329,  1.0000000)
Arc length:  1.91986  Parameters: (0.1745329,  2.0943951,  1.0000000)
Arc length: 15.00000  Parameters: (0.0000000, -1.5707963,  3.1830989)
Arc length:  5.00000  Parameters: (0.0000000,  1.5707963,  3.1830989)```

## Phix

Translation of: Julia
`function arclength(atom r, angle1, angle2)    return (360 - abs(angle2 - angle1)) * PI/180 * rend function?arclength(10, 10, 120) -- 43.6332313`

## Python

`import math def arc_length(r, angleA, angleB):    return (360.0 - abs(angleB - angleA)) * math.pi * r / 180.0   `
```radius = 10
angleA = 10
angleB = 120

print(result)

Output:
43.63323129985823
```

## Raku

Works with: Rakudo version 2020.02

Taking a slightly different approach. Rather than the simplest thing that could possibly work, implements a reusable arc-length routine. Standard notation for angles has the zero to the right along an 'x' axis with a counter-clockwise rotation for increasing angles. This version follows convention and assumes the first given angle is "before" the second when rotating counter-clockwise. In order to return the major swept angle in the task example, you need to supply the "second" angle first. (The measurement will be from the first given angle counter-clockwise to the second.)

If you don't supply a radius, returns the radian arc angle which may then be multiplied by the radius to get actual circumferential length.

Works in radian angles by default but provides a postfix ° operator to convert degrees to radians and a postfix ᵍ to convert gradians to radians.

`sub arc ( Real \a1, Real \a2, :r(:\$radius) = 1 ) {    ( ([-] (a2, a1).map((* + τ) % τ)) + τ ) % τ × \$radius} sub postfix:<°> (\d) { d × τ / 360 }sub postfix:<ᵍ> (\g) { g × τ / 400 } say 'Task example: from 120° counter-clockwise to 10° with 10 unit radius';say arc(:10radius, 120°, 10°), ' engineering units'; say "\nSome test examples:";for \(120°, 10°), # radian magnitude (unit radius)    \(10°, 120°), # radian magnitude (unit radius)    \(:radius(10/π), 180°, -90°), # 20 unit circumference for ease of comparison    \(0°, -90°, :r(10/π),),       #  ↓  ↓  ↓  ↓  ↓  ↓  ↓    \(:radius(10/π), 0°, 90°),    \(π/4, 7*π/4, :r(10/π)),    \(175ᵍ, -45ᵍ, :r(10/π)) {  # test gradian parameters    printf "Arc length: %8s  Parameters: %s\n", arc(|\$_).round(.000001), \$_.raku}`
Output:
```Task example: from 120° counter-clockwise to 10° with 10 unit radius
43.63323129985824 engineering units

Some test examples:
Arc length: 4.363323  Parameters: \(2.0943951023931953e0, 0.17453292519943295e0)
Arc length: 1.919862  Parameters: \(0.17453292519943295e0, 2.0943951023931953e0)
Arc length:        5  Parameters: \(3.141592653589793e0, -1.5707963267948966e0, :radius(3.183098861837907e0))
Arc length:       15  Parameters: \(0e0, -1.5707963267948966e0, :r(3.183098861837907e0))
Arc length:        5  Parameters: \(0e0, 1.5707963267948966e0, :radius(3.183098861837907e0))
Arc length:       15  Parameters: \(0.7853981633974483e0, 5.497787143782138e0, :r(3.183098861837907e0))
Arc length:        9  Parameters: \(2.7488935718910685e0, -0.7068583470577035e0, :r(3.183098861837907e0))```

## REXX

Translation of: Julia

This REXX version handles angles (in degrees) that may be   >   360º.

`/*REXX program calculates the  length of an arc  between two angles (stated in degrees).*/parse arg radius angle1 angle2 .                 /*obtain optional arguments from the CL*/if radius=='' | radius==","  then radius=  10    /*Not specified?  Then use the default.*/if angle1=='' | angle1==","  then angle1=  10    /* "      "         "   "   "     "    */if angle2=='' | angle2==","  then angle2= 120    /* "      "         "   "   "     "    */ say '     circle radius = '   radiussay '           angle 1 = '   angle1"º"          /*angles may be  negative  or  >  360º.*/say '           angle 2 = '   angle2"º"          /*   "    "   "      "      "  "   "   */saysay '        arc length = '   arcLength(radius, angle1, angle2)exit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/arcLength: procedure; parse arg r,a1,a2; #=360; return (#-abs(a1//#-a2//#)) * pi()/180 * r/*──────────────────────────────────────────────────────────────────────────────────────*/pi:        pi= 3.1415926535897932384626433832795;  return pi   /*use 32 digs (overkill).*/`
output   when using the default inputs:
```     circle radius =  10
angle 1 =  10º
angle 2 =  120º

arc length =  43.6332313
```

## Ring

` decimals(7)pi = 3.14159265 see "Length of an arc between two angles:" + nlsee arcLength(10,10,120) + nl func arcLength(radius,angle1,angle2)     x = (360 - fabs(angle2-angle1)) * pi / 180 * radius     return x `
Output:
```Length of an arc between two angles:
43.6332313
```

## Ruby

Translation of: C
`def arc_length(radius, angle1, angle2)    return (360.0 - (angle2 - angle1).abs) * Math::PI / 180.0 * radiusend print "%.7f\n" % [arc_length(10, 10, 120)]`
Output:
`43.6332313`

## Wren

Translation of: Julia
`var arcLength = Fn.new { |r, angle1, angle2| (360 - (angle2 - angle1).abs) * Num.pi / 180 * r } System.print(arcLength.call(10, 10, 120))`
Output:
```43.633231299858
```

## XPL0

`def  Pi = 3.14159265358979323846; func real ArcLen(Radius, Angle1, Angle2); \Length of major arc of circlereal Radius, Angle1, Angle2;real Diff;[Diff:= abs(Angle1 - Angle2);Diff:= 360. - Diff;return Pi * Radius / 180. * Diff;]; RlOut(0, ArcLen(10., 10., 120.)); `
Output:
```   43.63323
```

## zkl

Translation of: Julia
`fcn arcLength(radius, angle1, angle2){   (360.0 - (angle2 - angle1).abs()).toRad()*radius}println(arcLength(10,10,120));`
Output:
```43.6332
```