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Our church had to re-do a parking lot. The edge of the parking lot moved, and there are no lines, so it seemed to me like the back of my vehicle stuck out too far. I thought I could compensate for that by parking at an angle. Then someone else parking nearby said that a shallow angle would make the vehicle longer, which got me thinking “what is the angle at which the vehicle starts becoming shorter?”

And now I have an answer : 45 degrees

I took the dimensions of two different vehicles (a PT Cruiser and a minivan (Dodge Grand Caravan) because they seemed like different classes of vehicles and should give some variety.

I drew out some rectangles to scale, and I was surprised how long and narrow they looked. But I double checked and they are correct. Then I drew in some guidelines, copied the rectangle over, rotated the rectangle until it fit within the guidelines, then noted the angle at which that occurred.

The answers were 42 and 43 degrees for the two vehicles, closer than I expected to each other, and a larger angle than I expected.

So if you see angled parking spots and the angle is less than 45 degrees, they angled the spots in order to control traffic flow direction, not to save space.