What this calculator does
Anything moving across the rotating Earth is deflected sideways, to the right in the Northern Hemisphere and to the left in the Southern. The force is small but relentless, and over long distances it dominates the shape of weather systems and ocean currents.
It vanishes completely at the equator and is strongest at the poles. That latitude dependence is why cyclones never form within a few degrees of the equator, however warm the water is.
The formula
Coriolis acceleration is twice Earth's rotation rate times the speed times the sine of the latitude. Multiplying by mass gives the force, and the sine term is what drives it to zero at the equator.
| Term | Meaning |
|---|---|
| Coriolis acceleration | The apparent sideways acceleration seen in Earth's rotating frame. |
| Latitude dependence | The sine of latitude, which is zero at the equator and one at the poles. |
| Fictitious force | A force that appears only because the frame of reference is rotating. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass (kg) | The mass of the moving object, in kilograms. |
| Speed (m/s) | Its speed in metres per second. |
| Latitude (φ) (°) | Latitude in degrees. Negative values indicate the Southern Hemisphere. |
When to use it
Understanding cyclone rotation
Coriolis deflection is what makes air circulate around a low rather than flowing straight into it.
Long-range ballistics
Over many kilometres the accumulated sideways deflection becomes large enough to require correction.
Explaining ocean gyres
Persistent deflection of wind-driven surface water produces the great rotating gyres of each ocean basin.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the Coriolis force vary with latitude?
The same motion at four latitudes.
| Latitude | Coriolis force (F) | Coriolis acceleration (a) |
|---|---|---|
| 0° | 0 N | 0.0000e+0 m/s² |
| 30° | 1.4584 N | 1.4584e-3 m/s² |
| 45° | 2.0625 N | 2.0625e-3 m/s² |
| 90° | 2.9168 N | 2.9168e-3 m/s² |
Questions
Does the Coriolis effect determine which way a sink drains?
No. The force on a basin of water over a few seconds is thousands of times smaller than the effects of basin shape and how the water was disturbed. The claim is a persistent myth.
Why is there no Coriolis effect at the equator?
Because the acceleration depends on the sine of latitude, which is zero there. Horizontal motion at the equator is parallel to the rotation axis in the relevant sense, so no sideways deflection results.
Why is it called a fictitious force?
Because it appears only because we observe motion from a rotating frame. Seen from space nothing is pushing sideways; the ground has simply rotated beneath the moving object.
Why do cyclones rotate in opposite directions in each hemisphere?
Because the deflection reverses. Air flowing toward a low pressure centre veers right in the north, producing anticlockwise circulation, and left in the south, producing clockwise.
For the rotation rate behind it, see the angular velocity calculator. For the force and acceleration relationship generally, see the force, mass and acceleration calculator.