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.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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