After swapping in a new drivetrain in my project 1969 Barracuda, I needed to get the right speedometer pinion gear in the transmission. With a 2.76 gear and 25.5 inch diameter tires, the charts call for a 29 or 30 tooth gear. I installed a 30 tooth gear I had and went for a drive. The speedometer is reading 26% high! I can get a different gear to correct the speed, but I can't believe the charts did not get me closer. Is there some other issue that would explain the error? The speedo needle is steady and quiet.

I would get a rear tire valve stem at 6 0'clock in a parking lot & roll the car straight forward till the stem is back at 6 0'clock (~8 ft) & tape measure that "rollout" distance then divide Pi (3.1416) into that # to get your exact tire diameter. I'm sure you know if those gears are 2.76's or not. you might also go out on the interstate & go past 4 or 5 mile markers & see if your ODO is correct cuz if the axle gears/speedo pinion teeth are correct then the odo must read correct & the prob is in the magnetic speedo head gismo & it needs to be sent to a specialty shop to be recalibrated but my gut tells me something else is wonky here. post how it goes. GPS would solve this or if you see a portable lighted digital roadside sign or if you see a cop parkedon the side of the road ask him if he will clock you! have it a steady easy to read MPH when you pass him such as 40 or 50 etc. post how it goes/what it ends up being.

Mopar Action had an article about this some time back.
R.E.s recommendation was also to check the odometer first.
By checking it against mile markers as Rapid suggests.
Normally if speed is some percentage off, number of pinion teeth will be off a like percentage.
On your car I would have started with 27 teeth, which normally would have you pretty close.
So I'd think yours would be reading low, not high!
Sounds like your speedo is off.
There used to be shops that could calibrate mechanical speedos, not sure if they exist today.
If you could borrow a speedo from someone that would be my next move.
Let us know.

Or else use someone's GPS to give you a speed number to compare to your in dash speedo. I've had some success disassembling a speedo, cleaning with a small paint brush and lubing the pivot points with a drop of wd-40 on a toothpick. No need to break rivets on the face, just wear gloves as the paint on an old speedo face can easily pick up oils from your skin or get smudged. Clean and lube the pivot points for the needle and the rotator mechanism driven off the cable, plus any dirt or dust from the weight assembly attached to the needle. Work carefully here to keep from messing up your dial face as wd 40 can ruin or stain the face paint.

I used a GPS app to get true speed on a straight level road where I could hold speed. Speedo said 60; GPS said 47. I have repeated this test at different speeds, always getting the same percentage error. I know the differential ratio because it is stamped on the ring gear. I could get a more accurate tire diameter by using the rollout method, but I am off by a lot more than measurement error of the tire diameter. Taking the speedometer out of my restored IP would be a real pain and would probably scratch up some new paint. I will drive it for a while and if it is stable, I will probably get a 38 tooth gear.

gear ratio good. tire dia good (& putting a piece of stock across the top of the tire then measureing underneath it down to the ground will get you real close, & will for sure tell you that that part is OK & as you said I'm sure it is). GPS dont lie. all that is left is a misprint in the tooth selection chart. we need 26% more teeth (37.8) so the 38 you mentioned would be very near dead on. Just me I would do rollout while you're at it as it might bump you to 37 or tell you 38 would be dead on. I jack the left side up higher than needed to minimize fluid loss. EDIT tho going to the low side (37) might save you a ticket from an overzealous cop.