Magnus Force Calculator — Spinning Ball Lift
The Magnus effect causes a spinning ball in flight to curve — topspin pulls it down, backspin lifts it, sidespin bends it sideways. Enter the radius, spin rate, flight speed and air density to compute the deflecting force.
m
rpm
m/s
kg/m³
m
Lift/deflection force perpendicular to motion
- 1
Angular velocity ω = 2π × rpm ÷ 60
2π × 3,000 ÷ 60 = 314.1593 - 2
Circulation Γ = 2π × r² × ω
2π × 0.037² × 314.1593 = 2.7023Circulation is the strength of the rotating air flow around the cylinder. - 3
Magnus force F = ρ × v × Γ × L
1.225 × 20 × 2.7023 × 1 = 66.2063
How does this calculator work?
Magnus force = ρ v Γ L, where Γ = 2π r² ω is the circulation of a spinning cylinder. A ball spinning at ω rad/s while moving at v m/s through air of density ρ kg/m³ experiences a sideways lift proportional to its rotation and speed — the physics behind a curving football, baseball or cricket delivery.
Formula
How this is calculated
When a ball spins, it drags the surrounding air around with it. On one side, this dragged air moves with the flow; on the other, it fights the flow. Bernoulli's principle means the faster-moving side has lower pressure, creating a net force that pushes the ball sideways — this is the Magnus effect.
The force is computed via the Kutta–Joukowski theorem: F = ρ v Γ L, where ρ is air density, v is the translational speed, L is the effective span, and Γ is the circulation. For a rotating cylinder (or ball approximated as one), Γ = 2π r² ω, where ω is the angular velocity in rad/s.
This model is an idealised potential-flow result. Real balls have complex stitching patterns and turbulent boundary layers — the actual force can differ significantly, especially at very high or very low spin parameters (ωr/v). The result is best used for order-of-magnitude estimates and understanding the effect, not precision aerodynamics.
Frequently asked questions
Rotation drags air around the ball unevenly — one side speeds up and the other slows down relative to the surrounding flow. The pressure difference (Bernoulli) pushes the ball toward the low-pressure side, causing it to curve.
The spin parameter is ωr/v — the ratio of the surface speed (ωr) to the translational speed (v). Values around 0.5–1 give the strongest relative Magnus effect; at very high values real balls can decelerate the effect due to turbulence.
At sea level and 20 °C, air density is about 1.225 kg/m³. At altitude it is lower — for example ~1.06 kg/m³ at 1,000 m and ~0.89 kg/m³ at 2,500 m — which is why balls curve less at high-altitude stadiums.
Also known as
TG we-Calculate Editorial Team. (2026). Magnus Force Calculator — Spinning Ball Lift [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/magnus-force-calculator
TG we-Calculate Editorial Team. "Magnus Force Calculator — Spinning Ball Lift." TG we-Calculate. 2026. https://we-calculate.com/calculator/magnus-force-calculator.
TG we-Calculate Editorial Team, "Magnus Force Calculator — Spinning Ball Lift," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/magnus-force-calculator
@misc{wecalculate_magnus_force_calculator, title = {Magnus Force Calculator — Spinning Ball Lift}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/magnus-force-calculator}}, year = {2026}, note = {TG we-Calculate} }
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