Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For K-12 Students · Basketball Shot Arc

Basketball Shot Arc for a basketball free throw

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a basketball free throw live below — adjust the inputs and watch it respond, right in your browser.

Basketball Shot ArcLive

the physics of a jump shot

Controls

Presets

Distance to hoop (m)

Release height (m)

Launch angle (°)

A basketball shot must arrive at the rim from above to have a chance of dropping in. Too flat and the ball meets the front rim; too steep and it needs excess speed. Coaches prize an entry angle around 43–47°, which maximizes the effective size of the hoop the ball sees. Higher release points let shorter players shoot flatter and still score.

▶ Run in Python

Data Inspector

Required speed8.3 m/s

Entry angle41°

Arc qualityideal

Governing equation

v = \frac{g d ^{2}}{2 cos ^{2} θ ( d tan θ - Δ h )}, θ = 5 0^{\circ}, θ_{entry} \approx 4 1^{\circ}

Reading this result: Clean shot: a 41° entry sits in the ideal 40–55° window, so the ball sees the widest effective hoop at 8.3 m/s.

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Basketball Shot Arc for a basketball free throw" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.