How do I convert front toe alignment measurements from inches, such as 1/16" toe-out, to degrees?
My alignment shop measures everything in degrees so I need to provide my alignment specs in degrees not inches.

I simplistically thought:
(180deg/Tire Dia) x Toe in Inches = Toe in Degrees
So for a 24" diameter tire:
180 deg / 24" * 1/16" toe = 0.47 deg toe

But I do not think that is correct, seems too large degrees of toe.

What should be the correct degrees for 1/16" front toe?
Is it 0.149 degrees = 1/16"?

Can I think of it as a triangle with the base being the toe (in inches) and the rise being the tire diameter with the top angle being the toe in degrees? If so, then I can use trig to calculate the top angle:
top angle = arctan(base/rise)
Toe Angle = arctan(1/16" toe / 24" tire dia) = 0.1492 degrees (based on 24" tire dia)

If I am thinking correctly, this would give me toe per side. The total toe would be twice the calculated number. In this example, total toe would be 0.2984 deg or 1/8".

Or do I have to think of it as a trapezoid, with the tires being the sides of the trapezoid and the top of the trapezoid being the distance between the front of the two front tires and the bottom of the trapezoid being the distance between the rear of the two front tires?

 

the easiest way to think about it is to convert arc-length into angle, since we are dealing with such a small angle. so use radius of tire (12") as the circle radius. use 1/2 total toe as the arc length around the circle. convert to angle.

for example...

1/8" toe = 0.125" / 2 = 0.0625" = arc length
12" = radius

now find the angle... i just went here and plugged in the numbers.

i got 0.29deg toe in (per wheel)*


*this is wrong, see below

 

btw... i'm hovering over the tire looking straight down through the tire to the ground. the pivot point is the center of the circle, the edge (tread face) of the tire traces the arc length.

 

Thanks. I believe we are both thinking about this the same why. My thought of a triangle is the same as arc length. I could not get to the "here" link in your post to see what math was performed but our numbers come out about the same. I get 0.298 deg and you get 0.29 deg for 1/8".

 

sonichris is getting .298 per wheel ie 1/16".

Here's the complete link to the calculator.

 

I am still thinking that you have to use tire diameter instead of radius in the calculation. My thinking is that you have to use the tire diameter because the alignment measurement is the difference between the left and right side, taken from the front and back of tires, thus the diameter. I realize that the pivot point is the center of the tire, thus it might make sense to use the radius instead of diameter but I am not sure that would match the alignment station calulation. As we see it makes a big difference on whether we use radius or diameter so it would be good to figure this out.

The way I look at it:
If you want 1/8" total toe out (meaning the difference between a measurement taken at the front of the left and right tires and a measurement taken at the rear of the left and right tires) you would want each tire to create a 1/16" arc length (half the total toe) based on the tire diameter. So that the front of the tire would be pointed out 1/16" from the rear of the same tire.

The calculation is:
Angle = arctan x (opposite side / adjacent side)
Toe Angle = arctan x (toe in inches / tire diameter) [Instead of radius]
Toe Angle = arctan x (1/16" / 24") [for 24" diameter tire & 1/16" toe]
Toe Angle of 1/16" = 0.149 degrees
Total Toe Angle would be 1/8" = 0.298 degrees

Can someone confirm whether I should use tire diameter or radius to calculate toe angle.

 

you are correct in you toe definition. i was assuming the toe measurement was the difference between the track (middle of tire) and the front. the actual measurement is difference between front and rear.

so, using 1/8" again on 24" diameter tire...

that would mean both tires were in 1/16" on the front and OUT 1/16" on the rear, for a total of 1/8". notice that is BOTH tires combined. in other words, looking at just the front, 1/16" is the total of both tires' inward movement at the front, meaning each tire contributes to half of that, or 1/32"

using that in the equation i get...

0.03125 as the arc length transcribed by the tread face, using the center of the tire as the center of a circle of 12" radius.

plugging that in i get 0.149deg on each wheel or 0.298deg total toe.



Q.E.D.

 

Thanks sonichris and chuckt for your inputs/discussions on this topic.