This post is more about how to use a tool than it is a description of a new tool. Knowledge is arguably our most important tool so I think posts like this belong in the tools section of the forum.
In his book, Home Machinist's Bedside Reader #1 (pg. 11), Guy Lautard describes a technique for measuring a large bore when you don't have a set of calipers large enough to span the diameter.
Basically, you cut a "stick" to a length slightly less than the diameter of the bore and provide it with rounded or pointed ends. Inserted in the bore, this stick will "rattle" back and forth a (hopefully) small amount. You measure the peak-to-peak rattle and then use a formula to calculate the actual diameter. Lautard gives a formula but it looks like an approximation to me, although I haven't examined it closely.
If the rattle distance is small compared to the diameter of the bore, the stick length itself is a very good approximation of the bore diameter.
I wrote RATTLE.EXE to compute the diameter given the stick and rattle lengths in order to evaluate this procedure. You can use it to calculate the diameter if you need to use this procedure. You can download the program from my webpage.
This is the way I was taught to use internal, spring type calipers. If you try to set the calipers to the actual diameter, you're very likely to spring them slightly. When withdrawn from the bore to be measured, they will unspring slightly thus affecting the reading. Better to set them so they "rattle" slightly in the hole and then measure them. RATTLE will prove to you that, if you make the rattle very small, the difference between the measured caliper distance and the actual diameter will be very small indeed.
For an example, I used the values Lautard used in his book...
S = 3.998
R = 13/32 = 0.40625
and the program yielded a calculated diameter of 4.003197. Lautard's approximation yields a value of 4.0033; thus, agreement to one ten thousandth.
For a rattle distance of 0.40625/4.003197 = 10% of the bore diameter, the stick yielded the bore diameter with an error of only 100*(3.998-4.0032)/4.0032 = 1.3%. Decreasing the rattle distance will decrease that error still further.