DuckieDai Arc Solver Python Program

trigonometry · MIT License

Overview

Find the arc length of a circle from its radius and an angle in degrees, a fraction of pi, or radians, or work back to the angle or the radius from an arc length.

Owner-tested on a TI calculator
Version 1.0.0
2160 bytes
Uses math

Download ARCSOLV.py Read the source How to install

Before you run it

TI-84 Plus CE Python · No calculator OS or Python App version has been verified.
TI Connect CE .py transfer to the Python App; the owner's transfer details were not recorded
The arc and the radius use the same length unit, such as centimeters for both.
The angle is the central angle of the arc, the angle at the center of the circle.
Numbers may be typed as decimals or fractions such as 1/3; inf and nan are asked for again.

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Follow the program's prompts and result flow before downloading.

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Simulation boundary: This preview uses a reviewed browser adapter. It does not execute the downloaded Python and does not prove TI-Python or calculator compatibility.

Learn the math

How to find arc length, angle, and radius

The idea

An arc is a piece of a circle's edge. How long it is depends on two things: the size of the circle, given by its radius, and how much of the circle you take, given by the central angle at the middle.

With the angle in radians the link is as simple as it gets: arc length is radius times angle. That is the reason radians exist. An angle in degrees or as a fraction of pi just needs turning into radians first.

The formula

s = r*theta (theta in radians)

theta = s/r

r = s/theta

radians = degrees*pi/180

s: arc length, in the same unit as the radius
r: the radius of the circle
theta: the central angle in radians
pi: about 3.141593; a full turn is 2pi radians, which is 360 degrees

Using the program

Choose 1 to find arc length, 2 to find the angle, or 3 to find the radius.
For arc length, choose how you will give the angle: 1 for degrees, 2 for a fraction of pi such as 3/4 for 3pi/4, or 3 for radians. Then enter the radius.
When the degrees or the pi fraction and the radius are whole numbers, the program first shows the EXACT answer in terms of pi, then DEC, the decimal to six places, and ROUND 2, the same answer to two places.
To find the angle, enter the arc length and the radius. The answer is in radians.
To find the radius, enter the arc length, then the angle in degrees, as a multiple of pi, or in radians.
Numbers can be decimals or fractions such as 1/3.

Worked example

A circle has radius 3. How long is the arc cut off by a 90 degree angle? Choose 1, then 1 for degrees, and enter 90 and 3.

s = 3 x 90pi/180 = 3pi/2

The program shows EXACT: 3/2pi, then DEC: 4.712389 and ROUND 2: 4.71.

An arc 10 long on a circle of radius 4 spans what angle? Choose 2 and enter 10 and 4. The program shows Angle rad: 2.5.

An arc 10 long comes from a 90 degree angle. What is the radius? Choose 3, enter 10, then 1 for degrees and 90. The program shows Radius: 6.366198, which is 20/pi.

Tips and common mistakes

Use the same unit for the arc and the radius. If the radius is in meters, the arc comes out in meters.
Check the answer against the whole circumference, 2*pi*r: a 90 degree arc is a quarter of it and a 180 degree arc is half.
The angle answer is in radians. Multiply by 180/pi to get degrees: 2.5 radians is about 143.2 degrees.
For an angle like 5pi/6, choose the pi option and type 5/6. Typing 0.8333 in degrees or radians would be a different angle.

Where this comes up

Arc length and radian measure come up in geometry and at the start of the trigonometry unit in precalculus, and again in physics for circular motion.

Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

# DUCKIEDAI TM - TRIG LITE
# TI-84 CE PYTHON
from math import pi

def n(p):
 while 1:
  try:
   s=input(p)
   if '/' in s:
    a,b=s.split('/')
    v=float(a)/float(b)
   else:v=float(s)
   if v-v:raise ValueError
   return v
  except:
   print('Try again')

def f(a,b):
 a=int(a);b=int(b)
 x=abs(a);y=abs(b)
 while y:x,y=y,x%y
 if x:a//=x;b//=x
 if b==1:return str(a)
 return str(a)+'/'+str(b)

def pause():
 input("ENTER to continue")

def intro():
 print('DUCKIEDAI(TM)')
 print('ARC SOLVER')
 print('      __')
 print('  ___(o )> quack!')
 print('  \\ <_. )')
 print("   `---'")
 print('by DuckieDai')
 print('hiddenwordscanner.com')
 input('Press Enter ')
 print('\n'*7)

def bye():
 print('DUCKIEDAI (TM)')
 print('hiddenwordscanner.com')
 input('ENTER to exit')

def menu():
 while 1:
  print('\n'*7)
  print('DUCKIEDAI ARC')
  print('1 Arc 2 Angle 3 Radius')
  print('0 Exit')
  q=input('Find: ')
  if q=='0':break
  if q=='1':
    print('1 Deg 2 Pi 3 Rad')
    z=input('Angle type: ')
    if z=='1':
     d=n('Degrees: ')
     r=n('Radius: ')
     t=d*pi/180
     if d==int(d) and r==int(r):
      print('EXACT:',f(int(d)*int(r),180)+'pi')
    elif z=='2':
     try:
      s=input('Pi fraction: ')
      if '/' in s:
       x,y=s.split('/')
       a=int(x);b=int(y)
      else:a=int(s);b=1
      if b==0:raise ValueError
      r=n('Radius: ')
      t=a*pi/b
      if r==int(r):
       print('EXACT:',f(a*int(r),b)+'pi')
     except:
      print('Invalid pi input')
      pause()
      continue
    elif z=='3':
     t=n('Radians: ')
     r=n('Radius: ')
    else:
     print('Invalid type')
     pause()
     continue
    v=r*t
    print('DEC:',round(v,6))
    print('ROUND 2:',round(v,2))
  elif q=='2':
    s=n('Arc length: ')
    r=n('Radius: ')
    if r==0:print('Invalid radius')
    else:print('Angle rad:',round(s/r,6))
  elif q=='3':
    s=n('Arc length: ')
    print('1 Deg 2 pi 3 Rad')
    z=input('Angle type: ')
    if z=='1':t=n('Degrees: ')*pi/180
    elif z=='2':t=n('pi x: ')*pi
    elif z=='3':t=n('Radians: ')
    else:continue
    if t==0:print('Invalid angle')
    else:print('Radius:',round(s/t,6))
  pause()
intro()
menu()
bye()

# DUCKIEDAI TM - TRIG LITE
# TI-84 CE PYTHON
from math import pi
def n(p):
while 1:
try:
s=input(p)
if '/' in s:
a,b=s.split('/')
v=float(a)/float(b)
else:v=float(s)
if v-v:raise ValueError
return v
except:
print('Try again')
def f(a,b):
a=int(a);b=int(b)
x=abs(a);y=abs(b)
while y:x,y=y,x%y
if x:a//=x;b//=x
if b==1:return str(a)
return str(a)+'/'+str(b)
def pause():
input("ENTER to continue")
def intro():
print('DUCKIEDAI(TM)')
print('ARC SOLVER')
print(' __')
print(' ___(o )> quack!')
print(' \\ <_. )')
print(" `---'")
print('by DuckieDai')
print('hiddenwordscanner.com')
input('Press Enter ')
print('\n'*7)
def bye():
print('DUCKIEDAI (TM)')
print('hiddenwordscanner.com')
input('ENTER to exit')
def menu():
while 1:
print('\n'*7)
print('DUCKIEDAI ARC')
print('1 Arc 2 Angle 3 Radius')
print('0 Exit')
q=input('Find: ')
if q=='0':break
if q=='1':
print('1 Deg 2 Pi 3 Rad')
z=input('Angle type: ')
if z=='1':
d=n('Degrees: ')
r=n('Radius: ')
t=d*pi/180
if d==int(d) and r==int(r):
print('EXACT:',f(int(d)*int(r),180)+'pi')
elif z=='2':
try:
s=input('Pi fraction: ')
if '/' in s:
x,y=s.split('/')
a=int(x);b=int(y)
else:a=int(s);b=1
if b==0:raise ValueError
r=n('Radius: ')
t=a*pi/b
if r==int(r):
print('EXACT:',f(a*int(r),b)+'pi')
except:
print('Invalid pi input')
pause()
continue
elif z=='3':
t=n('Radians: ')
r=n('Radius: ')
else:
print('Invalid type')
pause()
continue
v=r*t
print('DEC:',round(v,6))
print('ROUND 2:',round(v,2))
elif q=='2':
s=n('Arc length: ')
r=n('Radius: ')
if r==0:print('Invalid radius')
else:print('Angle rad:',round(s/r,6))
elif q=='3':
s=n('Arc length: ')
print('1 Deg 2 pi 3 Rad')
z=input('Angle type: ')
if z=='1':t=n('Degrees: ')*pi/180
elif z=='2':t=n('pi x: ')*pi
elif z=='3':t=n('Radians: ')
else:continue
if t==0:print('Invalid angle')
else:print('Radius:',round(s/t,6))
pause()
intro()
menu()
bye()

Filename: ARCSOLV.py
Size: 2160 bytes
SHA-256: 21ab891ebf4df2486a1228c89989ff1f657bd02db0b643a856e39a9281b17730

Usage

Inputs

What to find: 1 arc length, 2 angle, or 3 radius
The angle as degrees, a fraction of pi, or radians
The radius or the arc length

Outputs

Arc length exactly in terms of pi when the inputs allow, plus the decimal to 6 places and to 2 places
The angle in radians, or the radius, to 6 decimal places

Units: The arc and the radius share one length unit; angles in degrees, multiples of pi, or radians.

Assumptions and limitations

Assumptions

The arc and the radius use the same length unit, such as centimeters for both.
The angle is the central angle of the arc, the angle at the center of the circle.

Constraints

Numbers may be typed as decimals or fractions such as 1/3; inf and nan are asked for again.
A pi fraction must be whole numbers, such as 3/4 for 3pi/4.
The exact answer in terms of pi appears only when the degrees or pi fraction and the radius are whole numbers.

Known failures

Angles are not reduced to one turn: 450 degrees gives the arc for one and a quarter turns.
A negative angle or radius is not rejected and gives a negative answer.

Compatibility and review

Review status: Owner-tested on a TI calculator
Tested on: Owner reports personally running this program on a TI-84 Plus CE Python calculator; the test date, OS version, and Python App version were not recorded
What happened: Owner reported pass on the calculator before the number prompt was changed to ask again when inf or nan is typed, where the original stopped with an error. Every other step is unchanged; this exact file has not yet been rerun on a calculator.
Dependencies: math
Suggested calculator name: ARCSOLV — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Transfer and launch

Download the .py file, send it to your calculator with TI Connect CE as ARCSOLV or another name, then open the Python App and try the worked example on this page first. This release has no verified calculator OS or Python App version; treat transfer and execution as unverified until independently tested.

Full installation and troubleshooting guide. Check your teacher's or exam's rules before using any program.

Version history

1.0.0 — current version, published 2026-10-13. Download this reviewed version

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