⚾ Magnus Force Calculator
Calculate the sideways Magnus force produced when a spinning ball moves through air or another fluid, the effect behind curveballs and topspin.
What the Magnus force is
The Magnus effect causes a spinning object moving through a fluid to curve away from its straight-line path. It is why a topspin tennis ball dips, a curveball breaks, and a backspin golf ball stays airborne longer – the spin drags fluid around the object, speeding up flow on one side and slowing it on the other, creating a pressure difference and a sideways force.
The formula
For a spinning sphere, the Magnus force is commonly approximated as F = S × ω × v, where the Magnus coefficient is S = (4/3) × π × r³ × ρ, r is the ball’s radius, ρ is the fluid density, ω is the spin rate in radians per second, and v is the ball’s forward velocity.
This is an idealized approximation for a smooth sphere in an ideal fluid; real balls (with seams, dimples, or surface texture) can deviate meaningfully from this estimate. Provided for general physics and sports-science education.