Angle calculation

[[Cl...]]

The part is an OD cylinder 0.1760 Ø (R.088, long leg of the triangle). It has a laser etched line parallel and on the same axis to a plane (AO connector if you are familiar with that)

The etched line must be within ± 2° to center of the plane. I did the math and got 0.003 (short leg), but because it's a round surface I'm not sure the short leg of

the triangle isn't slightly different than 0.003?

Edited August 19, 2025

[[Cl...]]

Addendum.

Imagine looking at a pie, sliced in 2° segments. I need to know the width of the fat end of one slice.

[[Ma...]]

I think you need to find the chord length based on the radial distance
 

Chord Length Formula

There are two basic formulas to find the length of the chord of a circle which are:

Formula to Calculate Length of a Chord
Chord Length Using Perpendicular Distance from the Center	Chord Length = 2 × √(r2 − d2)
Chord Length Using Trigonometry	Chord Length = 2 × r × sin(c/2)

 

Where,

• r is the radius of the circle
• c is the angle subtended at the center by the chord
• d is the perpendicular distance from the chord to the circle center

Example Question Using Chord Length Formula

Question: Find the length of the chord of a circle where the radius is 7 cm and perpendicular distance from the chord to the center is 4 cm.

Solution:

Given radius, r = 7 cm

and distance, d = 4 cm

Chord length = 2√(r²−d²)

⇒ Chord length = 2√(7²−4²)

⇒ Chord length = 2√(49−16)

⇒ Chord length = 2√33

⇒ Chord length = 2×5.744

Or , chord length = 11.48 cm

[[Ri...]]

The arc length is just the radius multiplied by the angle (in radians). 

https://www.ajdesigner.com/phpcircle/circle_arc_length_s.php

You can also derive this using Curve - Curve Length. 

[[Cl...]]

Thanks Richard. I forgot all about curve length!

[[Cl...]]

Ok. It turns out that 2° is 0.00307". Which I doubled to use as a bi-lateral true position of 0.00614.

I need the position deviation converted to degrees. I have the calculator that you sent me, but I need

a formula to enter into a result Element. Any help is greatly appreciated.

[[Ha...]]

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If I'm reading the thread correctly, the formula for converting the position deviation to an angle in degrees would look something like this: angle in degrees = (position deviation / radius) * (180 degrees / PI radians)

[[Cl...]]

Yes, thank you!