In mathematics and physics, the right-hand rule is a common mnemonic for understanding the orientation of axes in three-dimensional space. It is also a convenient method for quickly finding the direction of a cross-product of 2 vectors.

Most of the various left-hand and right-hand rules arise from the fact that the three axes of three-dimensional space have two possible orientations. One can see this by holding one's hands outward and together, palms up, with the thumbs out-stretched to the right and left, and the fingers making a curling motion from straight outward to pointing upward. (Note the picture to right is not an illustration of this.) The curling motion of the fingers represents a movement from the first (x-axis) to the second (y-axis); the third (z-axis) can point along either thumb. Left-hand and right-hand rules arise when dealing with coordinate axes. The rule can be used to find the direction of the magnetic field, rotation, spirals, electromagnetic fields, mirror images, and enantiomers in mathematics and chemistry.

The sequence is often: index finger, middle finger, thumb. Two other sequences also work because they preserve the cycle:

• Middle finger, thumb, index finger.
• Thumb, index finger, middle finger (e.g., see the ninth series of the Swiss 200-francs banknote).