My sat-nav consistently reports that my car is going 4-5 mph slower than my car’s speedometer. This is not the case when the car is stationary (both then reliably report that it is not moving), but as soon as I’m going 20mph+ the car says it’s going (say) 25mph, while the sat-nav says 21mph. This discrepancy is the same regardless of the speed I’m going - so if the sat-nav says 70mph then the speedometer will say 74mpg.
Why is this? And which one is correct?
Thanks in advance 
the speedometer is greatly effected by the tire size. As tires wear, the accuracy of the speedometer will vary. That said, if the car is new, the tires are not worn, the speedometer should be accurate within one mph or so.
The GPS on my car, for example, consistently says I’m going slower than my speedometer, the opposite of your situation.
I would be inclined to believe the GPS for the most part. I imagine the local state police would be happy give you their opinion, and, if they had the time, check your speed with one of their radar guns as you go down the road at what seems a steady 65 mph, for example, so you can make sure not to go more than 5 actual mph faster than the posted limit, an excess all police seem to allow.
The most likely answer is ‘neither’, but I tend to trust my sat-nav over my speedo. In the winter I put snow tires on my truck and my speedo is then off by 8 mph. The best way to tell is to find a town with a speed sign to slow down drivers that directly measures your speed and displays it. I find those to be pretty accurate, based on my sat nav anyway…
A good GPS should be accurate to a few percent, at most. (With a 4-bird lock, I think speed error is <1%.) Whether your nav system is accurate to that degree is not certain. You might borrow a Garmin or similar to check it.
The chances are your GPS is giving the accurate speed. A speedo is allowed a certain amount of error but it is not allowed to under-read. This means manufacturers will err on the side of caution and intentionally calibrate the speedo to over-read (it also makes your mileage look better). The GPS will just give the most accurate information it can.
Does this depend on how the GPS is measuring speed? I thought there were at least a couple different ways:
Using the actual satellites. Wouldn’t this be an average over time instead of your instantaneous speed? Like it might triangulate your position every X seconds and time how long it took you to get there from the last update. But then this would be dependent on the sampling rate and GPS’s inherit precision limitations, no?
Using an internal accelerometer, like the kind that performs dead reckonings? (So that they can still measure forward momentum while you’re going through a tunnel or heavily wooded area). Is this any more or less accurate that the tire-based speedometer?
Both of you have a point. GPS is very accurate… but vehicle nav systems don’t necessarily mirror that accuracy or reliability. A lot of them have “vamp til ready” modes that meet most driver demands but aren’t truly accurate. That’s why I suggest the OP borrow a “real” GPS for a calibration check.
Richard Pearse has it right. Speedometers are never allowed to read lower than actual and are often calibrated to to still be at or higher than actual for the most common incorrect tire sizes that might be mounted. In the GPS age, I’ve never owned a car or motorcycle that didn’t read 4-7% high. Interestingly enough, the odometers have always been dead on.
Motorcycle magazines used to report speedo error, and it was almost always the maximum that could be gotten away with.
GPS by far. GPS uses moving averages to calculate speed, which tends to factor out position error. GPS systems in cars are generally accurate to less than 1 mph, and often as good as .1 mph.
The speedometer in your car is subject to a number of potential inaccuracies. The biggest one is tire size. If your speedo was calibrated with factory tires but you put on a set of low-profile tires, your speedo will change significantly. You don’t even have to change rims - just the profile of the tire.
For example, a 255mm tire with a 60 aspect ratio on a 17" rim (255/60R17) will have a circumference of 91.254". Change that tire out for a 50 series aspect ratio, and the circumference drops to 85 inches. If your car speedo was calibrated to think a single revolution of the wheel will move the car 91.25 inches, your speedometer will now over-read by about 7%.
Even if you have the same tires, as they wear and your tread is worn down the circumference will get smaller, again causing the speedo to over-read.
Other errors could come from
GPS results should be within 0.5 mph. Close enough for government work.
You are correct here that there is some error introduced due to sampling and GPS precision, but there would be no bias to that error, so it should average out over long distances. I.e. the measured instantaneous velocity might be off all the time, but the measured average speed over a significant period should match your actual average speed much more closely.
If the GPS speed is consistently slower than the speedo, then the speedo has a biased error to it.
Ah, neat. The power of statistics!
Why not test your speedometer?
Drive on an interstate with cruise control set to 60 MPH for say 15 minutes and note the miles driven base on the mile markers. Multiply that distance by 4 to get actual MPH. (15 x 4 = 60min)
Or, 60MPH = 1 mile per minute. Drive a known distance at 60. Actual speed is distance/time.
I time mine with a stopwatch and a Canadian Automobile Association 10-kilometre measured distance with signs each kilometre on the Trans-Canada Highway, driving at 100 km/h. The time does indeed change, but very slightly, as the tires wear, but when they’re new the speedo is accurate. I also checked it against the speed registered by a Garmin unit’s satellite readout, so I’m golden.
There are railway tracks that run for miles parallel to a couple of highways nearish to me, and I’ve switched the speedometer/odometer to miles and checked it at 60 mph against the railway signs that occur each mile — the railways didn’t switch to metric because the locomotives work in the States and U.S. locos in Canada.
But I resist the urge to honk at W(histle) signs.
Actually, there is bias to the error, but this makes the GPS even more accurate. The ionosphere is a major source of GPS error (temperature/density/electron variations cause radio wave refraction). However, it changes slowly and causes a consistent deviation. So even if your GPS unit is, say, 10 meters off, a few seconds from now it’ll still be 10 meters off in the same direction. The difference between these two position reports will thus cancel out the error and so the velocity calculation will be very accurate.
On the cars I own, the speedometers are graduated in 5 mph increments, so I’m only guessing at readings that fall between the markings on my speedometer. So if the needle is between 60 and 65, how fast am I going? 62? 63? Hell if I know for sure. I tend to use a speedometer app on my phone to check my speed.
GPS systems can measure speed in two different ways. Either by taking positions and time over distance, or by doppler. Over short distances location and time won’t work - you won’t get a near instantaneous readout, nor will it be very accurate. Doppler however can give both, a reasonably accurate and instantaneous value. Long term, location and distance will win for accuracy, but not in real time. Car based units will display doppler.
Where GPS runs into trouble is with the layout of satellites in the sky. You need four for a fix, and more adds accuracy. If, for some reason, the layout of satellites is not a nice widely spaced set, but are concentrated in one part of the sky, or in a line, you will have major issues with accuracy. This can happen when not all of the sky is visible - say in a city, on one side of a hill, or the constellation is not full or fully operational. If you can only see a set of satellites that are currently forming a line, your position and thus speed at right angles to that line can be wildly out, even though the GPS unit will give a fix.
In-built car GPS systems can have access to the car’s own speedometer, and in the face of loss of signal (in a tunnel for instance) can use that to dead recon until signal is re-acquired. My car unit can lose all signal, and display some utterly insane ideas about where I am based on this. When I first got it, it woke up after a cross continent journey on the back of a truck, and for the period when it was cold starting it displayed the position as driving in the ocean some thousand odd miles away. In-car systems will use the heuristic that you are probably driving on a road, and if they are not getting a good fix, will try to keep the location on a road, even if you have actually driven off, or are on a nearby road - and you can see the location flick across when it gets proper fix again.
Here I was hoping you’d blow the correct signal at intersections. I sometimes do when there’s nobody right nearby to get confused. 
Are you serious? If it’s 2/5 of the way between 60 and 65, you are doing 62, if it is 3/5 you are doing 63, 1/5 is 61, etc.
In a brand-new car with brand-new tires, I would expect the speedometer to read 4-5 mph higher than your actual speed. That’s normal. They calibrate the speedometers high on purpose, for a variety of reasons. GPS will tell you the truth about how fast you are going. As the tires wear, the circumference gets smaller by 1% or 2% and then your speedometer will only read 3-4 mph higher than your actual speed.
The beauty of this situation is that most drivers are unaware of these facts and assume that their speedometer is accurate, so when they think to themselves “Speed limit 60? HA! Only suckers drive the speed limit! I’ll go FASTER than the speed limit… but not too much because I don’t want a ticket. I’ll go… 64. Yeah, that’s it, 64 is perfect! Four miles over the speed limit.”, what actually happens is they end up going 60. So there are millions of people out there who THINK they are speeding but really they aren’t.