Coriolis Parameter Calculator

The Coriolis parameter is the local strength of the apparent deflecting force that arises because the Earth is a rotating reference frame. Only the component of the planetary rotation vector aligned with the local vertical matters for horizontal motion, which is why f = 2 * omega * sin(phi), with omega = 7.2921e-5 rad/s from the sidereal day of 86164 s and phi the latitude. The consequences follow from the geometry: f vanishes at the equator, reaches about 1.46e-4 per second at the poles, and is roughly 1.46e-4 * sin(phi) in between - near 1.03e-4 at 45 degrees. Its sign flips across the equator, so free motion deflects to the right in the Northern Hemisphere and to the left in the Southern. The inertial period 2*pi/f is 12 hours at the pole, about 17 hours at 45 degrees, and lengthens without bound toward the equator. The related beta parameter, 2 * omega * cos(phi) / R with R about 6371 km, measures how fast f changes with northward distance and is what permits Rossby waves and western boundary current intensification. Whether rotation actually controls a flow is judged by the Rossby number Ro = U / (f * L). Values well under about 0.1 indicate geostrophic balance, where pressure gradient and Coriolis force nearly cancel and flow runs along isobars rather than across them - the regime of synoptic weather systems and ocean gyres, which span hundreds to thousands of kilometers. Values near or above 1 mean inertia dominates and rotation is a minor correction. This is why the frequently repeated claim about draining bathtubs is wrong: at L of about 0.3 m and U of about 0.3 m/s the Rossby number is roughly 40000, so basin geometry and residual swirl overwhelm the planetary term by orders of magnitude. The formula also assumes the traditional approximation, neglecting the horizontal rotation component, which is acceptable for large-scale geophysical flows but not universally.

Gaspard-Gustave de Coriolis, an engineer and professor of mechanics at the Ecole Polytechnique in Paris, published the analysis in 1835 in a memoir on the equations of relative motion in systems of bodies, presented to the Academie des Sciences. His interest was industrial rather than geophysical - he was concerned with rotating machinery such as waterwheels - and he derived what he called a compound centrifugal force, the term appearing in the equations of motion when they are written in a rotating frame. Pierre-Simon Laplace had already encountered related terms in his tidal equations decades earlier, and Sylvestre Lacroix and others had touched on the mathematics, but Coriolis gave the general derivation and the effect took his name. Application to the atmosphere came from William Ferrel, an American schoolteacher and later employee of the Nautical Almanac Office, who in papers from 1856 onward used the deflecting force to explain the observed three-cell structure of atmospheric circulation and the direction of prevailing winds, work that also produced Ferrel's law and the mid-latitude circulation cell that carries his name. Christoph Buys Ballot in the Netherlands stated in 1857 the empirical rule that with your back to the wind in the Northern Hemisphere low pressure lies to your left, which is geostrophic balance in observational form. The parameter f became the central symbol of dynamic meteorology and oceanography in the twentieth century through Vilhelm Bjerknes and the Bergen School, Carl-Gustaf Rossby's 1939 work on planetary waves that introduced the beta effect explicitly, and Henry Stommel's 1948 explanation of westward intensification, which depends entirely on the variation of f with latitude.