How the Coriolis Effect Is Calculated
The Coriolis effect is the apparent sideways deflection of an object moving across a rotating reference frame — most commonly Earth's surface. Because Earth completes one rotation every sidereal day (23 hours, 56 minutes, 4 seconds), anything moving over its surface — wind, ocean currents, aircraft, artillery shells, long-range projectiles — is deflected relative to the ground beneath it. This calculator finds the Coriolis acceleration, the Coriolis parameter, and the resulting deflecting force from an object's speed, latitude, and mass, using the standard formula a = 2ωv sin(φ).
Deriving the Coriolis acceleration
In a reference frame rotating with angular velocity ω, an object moving with horizontal speed v experiences an apparent Coriolis acceleration of magnitude a = 2ωv sin(φ), where φ is the latitude. Earth's angular velocity is fixed at ω ≈ 7.2921 × 10⁻⁵ rad/s (2π radians divided by one sidereal day). The term 2ω sin(φ) is called the Coriolis parameter, f = 2ω sin(φ) — a single number, in units of s⁻¹, that meteorologists and oceanographers use to describe how strongly rotation affects motion at a given latitude, independent of speed. Acceleration then simplifies to a = f × v, and by Newton's second law the Coriolis force on an object of mass m is F = m × a = 2mωv sin(φ).
Why direction and latitude matter
The sin(φ) term means the effect is zero at the equator (φ = 0°) and reaches its maximum at the poles (φ = ±90°) — this is one reason tropical cyclones need at least a few degrees of latitude to organize, and why the effect is negligible for short indoor or short-range motion. The sign of the latitude sets the direction of deflection: in the Northern Hemisphere (positive latitude) moving objects are deflected to the right of their direction of travel, and in the Southern Hemisphere (negative latitude) they are deflected to the left. This is why low-pressure storm systems rotate counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.
Practical notes and limits
This calculator uses the standard flat-Earth, horizontal-motion approximation applied to winds, ocean currents, and long-range ballistics — it captures deflection from horizontal velocity and ignores the much smaller Eötvös effect from vertical motion. It also treats φ as constant over the motion, which is accurate for winds and projectiles but breaks down for objects that sweep across large changes in latitude quickly, such as satellites. At everyday scales — a thrown ball, a draining sink, a moving car — the Coriolis force is many orders of magnitude smaller than friction, gravity, or the spin already in the water or object, so it has no measurable effect; it only becomes significant over large distances, long durations, or high speeds, such as multi-day ocean currents, long-range artillery trajectories, and continental-scale atmospheric circulation.