# How to draw a protractor in Mathematica

I would like to draw a protractor with Mathematica. I hope this is a fun question. Here is some start codes I tried:

r1 = 0.95; r2 = 0.98; r3 = 0.9; R = 1;
Show[{ParametricPlot[{{Cos[x], Sin[x]}, {2 x/Pi - 1, 0}}, {x, 0, Pi},
PlotStyle -> Black],
Table[ParametricPlot[{{Cos[i Degree] x, x Sin[i Degree]}}, {x, r2,
R}, PlotRange -> {-R, R}], {i, 0, 180}],
Table[ParametricPlot[{{Cos[i Degree] x, x Sin[i Degree]}}, {x, r1,
R}, PlotRange -> {-R, R}], {i, 0, 180, 5}],
Table[ParametricPlot[{{Cos[i Degree] x, x Sin[i Degree]}}, {x, r3,
R}, PlotRange -> {-R, R}], {i, 0, 180, 10}]}, Axes -> False]


I draw this protractor just for fun. I hope someone may be interested in this question. As advice from @shrx, the skeleton of the protractor is drawn. However, the labels are not easy for me to add, the alignment and direction are not easy task to do. Any suggestion on this part?

Here are some protractor designs from wiki:

The correct way to draw this kind object is directly draw each part, not as in the question using parametric equations to draw. I slightly modified @george2079's answer based on @wxffles's suggestion.

Graphics[{{Thickness[.003], Circle[{0, 0}, 1, {0, Pi}],
Circle[{0, 0}, .03],
Line[{{1, 0}, {1, -.1}, {-1, -.1}, {-1, 0}}]},
{Thickness[.001], Line[{{-0.015, 0}, {0.015, 0}}],
Line[{{0, -0.015}, {0, 0.015}}]},
Rotate[{Thickness[.003], Line[{{.03, 0}, {.6, 0}}]}, #, {0,
0}] & /@ {0, Pi/2, Pi},
GeometricTransformation[
Piecewise[{{{Red, Line[{{.8, 0}, {1, 0}}], Black,
Line[{{.2, 0}, {.5, 0}}],
Rotate[{Red,
Text[Style[#, FontSize -> Scaled[0.028],
FontFamily -> "Times"], {.75, 0}, {0, 0}]}, -Pi/2],
Rotate[{Black,
Text[Style[180 - #, FontSize -> Scaled[0.026],
FontFamily -> "Times"], {.65, 0}, {0, 0}]}, -Pi/2]},
Mod[#, 10] == 0}, {{Blue, Line[{{.85, 0}, {1, 0}}]},
Mod[#, 5] == 0}, {Line[{{.9, 0}, {1, 0}}], True}}],
RotationTransform[# Degree]] & /@ (Range[0, 180])}]


• Please edit your post in the form of a question. Right now it is unclear what you're asking. You have clearly managed to draw a protractor, it's just missing some finishing details.
– shrx
Jun 16, 2015 at 13:49
• @shrx texts alignment and direction are quite tough question for me. Jun 16, 2015 at 14:02
• Thank you for the clarification.
– shrx
Jun 16, 2015 at 14:08
• Related to your text rotation issue mathematica.stackexchange.com/q/5719/193 Jun 16, 2015 at 14:30

Graphics[{Circle[{0, 0}, 1, {0, Pi}], Circle[{0, 0}, .03],
Line[{{1, 0}, {1, -.1}, {-1, -.1}, {-1, 0}}],
Rotate[ Line[{{.03, 0}, {.6, 0}}] , #, {0, 0}] & /@ {0, Pi/2, Pi},
GeometricTransformation[
Piecewise[{
{{Red, Line[{{.8, 0}, {1, 0}}], Black,
Line[{{.2, 0}, {.5, 0}}],
Rotate[{Red, Text[#, {.75, 0}, {0, 0}]}, -Pi/2],
Rotate[{Black,
Text[Style[180 - #, Larger], {.65, 0}, {0, 0}]}, -Pi/2]},
Mod[#, 10] == 0},
{{Blue, Line[{{.85, 0}, {1, 0}}]},
Mod[#, 5] == 0},
{Line[{{.9, 0}, {1, 0}}], True}}],
RotationTransform[# Degree]] & /@ (Range[0, 180])}]


the mathematicians version...

formpi[v_] := Module[ { frac = v/Pi,num,den },
num = If[Numerator[frac] == 1, Unevaluated[Sequence[]],
Numerator[frac]];
den = If[Denominator[frac] == 1, Unevaluated[Sequence[]],
{"/", Denominator[frac]}];
Switch[
frac, 1, Pi , 0, 0,
x_Integer, Row[{frac, Pi}],
x_Rational, Row[{num, Pi}~Join~den], __, Row[ {v/Pi, Pi}  ] ]]
Graphics[{Circle[{0, 0}, 1, {0, Pi}], Circle[{0, 0}, .03],
Line[{{1, 0}, {1, -.1}, {-1, -.1}, {-1, 0}}],
Rotate[Line[{{.03, 0}, {.6, 0}}], #, {0, 0}] & /@ {0, Pi/2, Pi},
GeometricTransformation[Piecewise[{
{{Red, Line[{{.8, 0}, {1, 0}}], Black,
Line[{{.2, 0}, {.5, 0}}],
Rotate[{Red, Text[Style[formpi[#]], {.75, 0}, {0, 0}]}, -Pi/2],
Rotate[{Black,
Text[Style[formpi[Pi - #]], {.65, 0}, {0, 0}]}, -Pi/2]},
Mod[#, Pi/4 ] == 0},
{{Blue, Line[{{.85, 0}, {1, 0}}], Black,
Line[{{.2, 0}, {.5, 0}}],
Rotate[{Red, Text[Style[formpi[#]], {.75, 0}, {0, 0}]}, -Pi/2],
Rotate[{Black,
Text[Style[formpi[Pi - #]], {.65, 0}, {0, 0}]}, -Pi/2]},
Mod[#, Pi/12] == 0}, {Line[{{.9, 0}, {1, 0}}], True}}],
RotationTransform[# ]] & /@ (Range[0, Pi  , Pi/180])}]


• May I suggest using a relative font size? Instead of something like Style[#, Larger], I like to use Style[#, FontSize->Scaled[0.02]. It makes it easier when resizing and exporting graphics. Jun 16, 2015 at 22:47
• This one is great! Jun 17, 2015 at 2:48
• Very nice - I feel like a cro-magnon cave artist when I see results like this, +1
– ciao
Jun 17, 2015 at 6:33
• @wxffles good point, I didn't realize you could do specify a Scaled FontSize. Jun 17, 2015 at 14:27

This is not a protractor, but it is a related application that that serves as an example of rotated text which is the only thing missing in the protractor shown in the question.

I did it a while a go and keep it near the kitchen oven:

c[f_]:=5/9 (-32+f)

f[c_]:=1/5 (160+9 c)

cToAngle[c_]:=(c+40)/300*(2\[Pi]-5Degree)

fToAngle[f_]:=(f+40)/540*(2\[Pi]-5Degree)

Module[{k1=0.86,k2=1.128},
Graphics[
{Style[Text["\[Degree]C\[LeftRightArrow]\[Degree]F",{0,0}],FontSize->50],
Style[Text["C[F_] := 5/9(F-32)",{0,.3}],FontFamily->"Courier"],
Style[Text["F[C_] := (160+9 C)/5",{0,-.3}],FontFamily->"Courier"],
Table[{Line[{k1{Sin[cToAngle@c],Cos[cToAngle@c]},{Sin[cToAngle@c],Cos[cToAngle@c]}}],
Text[ToString[c]<>"\[Degree]C",k1{Sin[cToAngle@c],Cos[cToAngle@c]},{1,0},{Sin[cToAngle@c],Cos[cToAngle@c]}]},
{c,-40,260,10}],
Table[{Line[{{Sin[fToAngle@f],Cos[fToAngle@f]},k2*{Sin[fToAngle@f],Cos[fToAngle@f]}}],
Text[ToString[f]<>"\[Degree]F",(k2+0.125){Sin[fToAngle@f],Cos[fToAngle@f]},{1,0},{Sin[fToAngle@f],Cos[fToAngle@f]}]},
{f,-40,500,20}],
AbsoluteThickness[0.1],
Table[{Line[{{Sin[fToAngle@f],Cos[fToAngle@f]},(1.1)*{Sin[fToAngle@f],Cos[fToAngle@f]}}]},
{f,-40,500,2}],
White,Point[{0,0}]},BaseStyle->{FontSize->Larger}
]
]


• This is very interesting. Jun 17, 2015 at 3:38
• This doesn't make a good protractor because this circle weirdly has 540 degrees, and not 360 ;-P +1 Jun 17, 2015 at 15:47