Coriolis Force Formula
Calculate the Coriolis force on a moving object in a rotating reference frame.
Explains why weather systems spiral and why long-range projectiles drift.
The Formula
|F_Cor| = 2mΩv sin(φ)
The Coriolis force is a fictitious force experienced by objects moving within a rotating reference frame. On Earth, it is caused by Earth's rotation. It deflects moving objects to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. It is responsible for the rotation of large weather systems (cyclones) and must be accounted for in long-range artillery and ballistics.
Variables
| Symbol | Meaning | Value / Unit |
|---|---|---|
| F_Cor | Coriolis force vector | Newtons (N) |
| m | Mass of the moving object | kg |
| Ω | Angular velocity of Earth's rotation | 7.2921 × 10⁻⁵ rad/s |
| v | Velocity of the object in the rotating frame | m/s |
| φ | Latitude (0° at equator, 90° at poles) | degrees |
| × | Cross product (vector product) | — |
The Coriolis acceleration (force per unit mass) is: a_Cor = 2Ωv sin(φ)
The Coriolis effect is zero at the equator (sin 0° = 0) and maximum at the poles (sin 90° = 1).
Example 1 — Wind Deflection
Calculate the Coriolis acceleration on a 10 m/s wind at latitude 45°N.
Ω = 7.2921 × 10⁻⁵ rad/s
a_Cor = 2 × Ω × v × sin(φ)
a_Cor = 2 × 7.2921 × 10⁻⁵ × 10 × sin(45°)
a_Cor = 2 × 7.2921 × 10⁻⁵ × 10 × 0.7071
a_Cor ≈ 1.03 × 10⁻³ m/s² — tiny for wind, but cumulative over hundreds of kilometers it creates cyclone rotation
Example 2 — Long-Range Artillery
A shell is fired northward at v = 800 m/s at latitude 50°N. How much does it deflect to the right over a 30-second flight?
a_Cor = 2 × 7.2921 × 10⁻⁵ × 800 × sin(50°)
a_Cor = 2 × 7.2921 × 10⁻⁵ × 800 × 0.766 = 0.0894 m/s²
Deflection = ½ × a_Cor × t² = ½ × 0.0894 × 900
Deflection ≈ 40 m to the right — significant enough to require correction in long-range targeting systems
When to Use It
Use the Coriolis formula when:
- Explaining the rotation direction of hurricanes, typhoons, and cyclones
- Correcting long-range ballistic trajectories and missile guidance
- Analyzing ocean current circulation patterns
- Designing large rotating space stations or simulated gravity habitats
- Understanding Foucault pendulum behavior — the classic demonstration of Earth's rotation
Note: The Coriolis effect does not determine which direction water drains in a bathtub or sink — that is a common myth. The Coriolis force is far too weak at those scales. Drain rotation is determined by the initial water movement and basin shape.