How accurate is this?
Two different questions get answered as one, and separating them is the whole point of this page. The bearing is arithmetic and it is exact. The direction your phone points is a measurement, and measurements have error bars.
The calculation: better than you need
The great-circle bearing to the Kaaba is a closed-form formula. Given your coordinates it returns the same answer every time, to as many decimal places as you care to print. There is no approximation in it to be sceptical of.
Two smaller things sit underneath it. We model the Earth as a sphere rather than the slightly flattened ellipsoid it really is, which moves the answer by around a tenth of a degree from the UK. And your position comes from GPS, which is typically good to a few metres in the open — over a distance of nearly five thousand kilometres, ten metres of position error changes the bearing by well under a thousandth of a degree.
Both are far below anything that could affect where you stand. If the only thing between you and Makkah were arithmetic, this would be a solved problem.
The compass: the part that is actually uncertain
Your phone finds direction with a magnetometer — a sensor measuring a field of about fifty microtesla, which is weak enough that a laptop, a radiator, a car dashboard, a steel-framed building or a magnetic phone case will visibly bend it. A well-calibrated phone in the open is usually within a few degrees. A phone indoors, near metal, that has not been calibrated recently can be tens of degrees out, and it will not necessarily tell you.
The one systematic part of that error is magnetic declination: the gap between magnetic and true north, currently around a degree either side of zero across Britain. It is the only component that is predictable, so it is the only one that can be corrected — and correcting it is what this tool does. The rest can only be reported, which is why an accuracy warning appears instead of a confident arrow when the device says its compass is unreliable.
How much error actually matters
More than most people fear. The classical position for anyone not in sight of the Kaaba is that the obligation is to face its direction rather than its exact point, and the majority of jurists treat a deviation of roughly the width of the qibla arc — a margin usually put somewhere between about 24 and 45 degrees — as leaving the prayer valid.
That is not an argument for carelessness; it is an argument against anxiety. A few degrees of compass error does not invalidate anything. Being ninety degrees out, which is what happens when a tool corrects in the wrong direction or a phone case reverses the needle, is a different matter — and it is exactly the kind of error that a stated bearing lets you catch by eye.
How to check us
Compare the degrees, not the arrows. If another source gives a bearing for the same spot and it differs by a degree or two, one of you has probably not corrected for declination. If it differs by more than about five, something is genuinely wrong and it is worth finding out which of us it is.
The most independent check needs no electronics at all: use the sun. It cannot be thrown off by a radiator.