The pitch of your hand railings is also known as the slope. This is how steep the hand railing is. The basic formula for calculating pitch is rise divided by run. The rise is how high the hand railing goes and the run is how far the hand railing lasts. Since the formula for pitch is a trigonometric formula, the rise and run are two sides of a triangle, with the actual railing being the hypotenuse.
Place the tape measure anywhere along the hand railing. The best place to put it is about halfway down the railing. Then, measure from that point to the other end of the hand railing. For example, assume the railing measures 4 feet. This is your run.
Measure from the end of the railing where you previously measured upward to the top of the railing. In the example, assume this measures 2 feet. This is your rise.
Divide the rise by the run to calculate the pitch of the hand railing. In the example, 2 divided by 4 equals a pitch of 0.5. You can then compare this pitch to the pitch of your stairs. You want each one to be roughly the same. In order to calculate the pitch of the stairs, you can use the same formula, but use the stairwell for your measurements.