About

Any object moving freely across Earth's surface experiences lateral deflection caused by the planet's rotation. This apparent force, quantified by the Coriolis parameter f = 2Ωsin(φ), vanishes at the equator and reaches maximum magnitude at the poles. Miscalculating its effect leads to errors in ballistic trajectory prediction, weather system modeling, and ocean current analysis. The acceleration scales linearly with velocity v: faster objects deflect more aggressively, which matters for artillery ranging beyond 30 km and for synoptic-scale meteorology where pressure gradients interact with Coriolis to produce geostrophic wind.

This calculator computes the Coriolis acceleration a_c, the inertial oscillation period T, the radius of curvature R, and the Rossby number Ro for a given latitude, velocity, and characteristic length scale. It assumes a spherical Earth with angular velocity Ω = 7.2921 × 10⁻⁵ rad/s. Results are approximate for mesoscale and synoptic-scale flows. At the equator (φ = 0°), the horizontal Coriolis component is zero and the tool will report this correctly. Pro tip: for flows with Ro > 1, inertial forces dominate and Coriolis effects are negligible in practice.

Formulas

The Coriolis acceleration experienced by an object moving horizontally at velocity v at latitude φ on a rotating sphere:

a_c = 2 ⋅ Ω ⋅ v ⋅ sin(φ)

The Coriolis parameter (also called the planetary vorticity):

f = 2 ⋅ Ω ⋅ sin(φ)

The inertial oscillation period, defining how long a freely moving parcel takes to complete one inertial circle:

T = 2π|f|

The radius of curvature of the deflected trajectory:

R = v|f|

The Rossby number quantifies whether Coriolis or inertial forces dominate at a given scale L:

Ro = vf ⋅ L

Where: Ω = 7.2921 × 10⁻⁵ rad/s (Earth's angular velocity), v = object velocity in m/s, φ = geographic latitude in degrees, L = characteristic length scale in m, f = Coriolis parameter in s⁻¹, a_c = Coriolis acceleration in m/s², T = inertial oscillation period in seconds, R = radius of curvature in m, Ro = dimensionless Rossby number.

Reference Data

Latitude (°)	Coriolis Parameter f (s⁻¹)	Inertial Period (hours)	Deflection at 10 m/s (m/s²)	Context
0	0	∞	0	Equator - no horizontal Coriolis
10	2.53 × 10⁻⁵	69.0	2.53 × 10⁻⁴	Tropical trade wind zone
20	4.99 × 10⁻⁵	34.9	4.99 × 10⁻⁴	Subtropical highs
30	7.29 × 10⁻⁵	23.9	7.29 × 10⁻⁴	Horse latitudes, desert belts
35	8.37 × 10⁻⁵	20.8	8.37 × 10⁻⁴	Mediterranean, mid-latitude cyclones
40	9.37 × 10⁻⁵	18.6	9.37 × 10⁻⁴	Prevailing westerlies onset
45	1.031 × 10⁻⁴	16.9	1.031 × 10⁻³	Standard mid-latitude reference
50	1.117 × 10⁻⁴	15.6	1.117 × 10⁻³	North Sea, Southern Ocean
55	1.195 × 10⁻⁴	14.6	1.195 × 10⁻³	Roaring Forties/Fifties
60	1.263 × 10⁻⁴	13.8	1.263 × 10⁻³	Sub-Arctic / Sub-Antarctic
65	1.322 × 10⁻⁴	13.2	1.322 × 10⁻³	Polar front jet stream
70	1.370 × 10⁻⁴	12.7	1.370 × 10⁻³	Arctic Circle region
75	1.409 × 10⁻⁴	12.4	1.409 × 10⁻³	High Arctic / Antarctic interior
80	1.436 × 10⁻⁴	12.2	1.436 × 10⁻³	Near-polar regions
85	1.453 × 10⁻⁴	12.0	1.453 × 10⁻³	Polar vortex core
90	1.458 × 10⁻⁴	11.97	1.458 × 10⁻³	Geographic pole (maximum)

Frequently Asked Questions

The Coriolis parameter f = 2Ωsin(φ) contains sin(0°) = 0. At the equator, horizontal motion is parallel to Earth's rotation axis projected onto the surface, so no perpendicular deflection component exists. Tropical cyclones cannot form within roughly 5° of the equator because the Coriolis force is too weak to organize rotation.

When Ro << 1, rotation dominates and Coriolis cannot be ignored (e.g., ocean gyres, synoptic weather systems with L ≥ 1000 km). When Ro >> 1, inertial or advective forces dominate and Coriolis is negligible (e.g., a car turning, water draining from a bathtub). The transition zone around Ro ≈ 1 (mesoscale: thunderstorm complexes, sea breezes) requires case-by-case analysis.

No. The Rossby number for a bathroom drain is on the order of 10⁴ to 10⁵. The basin geometry, residual angular momentum from filling, and surface friction overwhelm the Coriolis acceleration by several orders of magnitude. Controlled experiments in very large, still basins (diameter > 2 m) left undisturbed for days can detect the effect, but this is not a household scenario.

For a projectile traveling 800 m/s at 45° latitude with a flight time of 60 s, the lateral deflection is approximately 180 m. Military fire-control systems routinely correct for this. The deflection grows with the square of flight time since the acceleration is continuous, making it critical for artillery beyond 20 km range.

At the pole (φ = 90°), T = 11.97 hours, which is half a sidereal day. At 30° latitude, T doubles to 23.9 hours. As latitude approaches 0°, T tends to infinity. Ocean current measurements in the Baltic Sea clearly show inertial oscillations matching the predicted local period.

The formula is universal for any rotating sphere; only Ω changes. Mars rotates at Ω = 7.088 × 10⁻⁵ rad/s (similar to Earth), so its Coriolis effects are comparable. Jupiter's Ω = 1.758 × 10⁻⁴ rad/s (2.4× Earth's) produces much stronger effects, contributing to its banded atmospheric structure. This tool currently uses Earth's Ω only.