Coriolis Force Calculator

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 on things 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

Worked Example: Long-Range Artillery

A 45 kg shell traveling at 800 m/s at 40° N latitude:

• F = 2 × 45 × 800 × 7.2921 × 10⁻⁵ × sin(40°)
• F = 3.3748 N

That force is trivial next to the 441 N the shell weighs, which is why nobody notices Coriolis on a rifle range. What matters is that it acts sideways for the whole flight, and sideways acceleration accumulates as t².

Acceleration = F / m = 3.3748 / 45 = 0.0750 m/s²
Deflection over a 30-second flight = ½ × 0.0750 × 30² = 33.8 meters

Thirty-four meters is a miss. Naval and long-range gunnery tables have carried a Coriolis correction since the First World War, and it is the reason a fire-control solution needs to know what latitude the gun is standing at, not just the range to the target.

Fill in the optional flight time below and the calculator works the deflection out for whatever you entered.

Common Real-World Effects

Common Myths

The Coriolis force does not determine which way water spins down a drain. Basin shape, residual currents and how the water was poured in all swamp it. Run the numbers: a 1 kg parcel of water moving at 0.1 m/s at 45° latitude feels about 10⁻⁵ N, roughly a millionth of its own weight. It is measurable in a carefully stilled tank left alone for a day, and invisible in a sink.

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.