Coriolis Force Calculator
Calculate Coriolis force on a moving object from mass, velocity, and latitude.
Predicts apparent deflection on a rotating Earth for ballistics.
Coriolis Force
The Coriolis force is an apparent (or fictitious) force experienced by objects moving in a rotating reference frame, such as the surface of the Earth. It does not act on stationary objects — only those moving relative to the rotating frame.
Formula
For horizontal motion on Earth’s surface, the magnitude of the Coriolis force is:
F = 2 × m × v × Ω × sin(φ)
Where:
- m = mass of the object (kg)
- v = horizontal velocity (m/s)
- Ω = angular velocity of Earth = 7.2921 × 10⁻⁵ rad/s
- φ = latitude (in degrees, converted to radians for the sine)
Direction of Deflection
| Hemisphere | Deflection |
|---|---|
| Northern Hemisphere | Right of motion |
| Southern Hemisphere | Left of motion |
| Equator | No horizontal Coriolis force (sin 0 = 0) |
| Poles | Maximum effect (sin 90° = 1) |
Worked Example — Long-Range Artillery
A 45 kg shell traveling at 800 m/s at 40° N latitude:
- F = 2 × 45 × 800 × 7.29 × 10⁻⁵ × sin(40°)
- F ≈ 3.38 N
Over a 30-second flight, this produces several meters of lateral deflection — which is why long-range gunnery, naval artillery, and ballistic missile guidance must compensate for the Coriolis effect.
Common Real-World Effects
| Phenomenon | Coriolis Role |
|---|---|
| Hurricane / typhoon rotation | Sets the direction of cyclone spin |
| Trade winds | Deflects equator-bound air westward |
| Foucault pendulum | Plane of oscillation rotates |
| Long-range artillery | Lateral correction needed |
| Ocean gyres | Drives large-scale circulation |
| Atmospheric jet streams | Maintains zonal flow pattern |
Common Myths
The Coriolis force does not determine which way water spins down a drain — that is dominated by basin shape, residual currents, and asymmetries. The effect is too weak at small scales (a few seconds, a few meters) to matter compared to other forces.
Why “Fictitious”?
In a non-rotating inertial frame, no Coriolis force exists. The “force” is a mathematical bookkeeping term that lets us use Newton’s laws inside a rotating frame, just as the centrifugal force does. For long-range projectiles and atmospheric flow, however, treating it as a real force is the most practical way to model motion.