Rule of thumb · PhysicsNº 89 / 167

45° for range — in a vacuum

Without air drag, 45° maximizes projectile range; with drag, the real optimum is nearer 30–40°.

Why it works

Drag punishes time spent moving fast through air, favouring flatter launches. Shot-putters release near 37–38°.

When it fails

It also assumes launch and landing at the same height. Throwing from a height, the optimum drops below 45° even without air — a shot putter releasing at 2 m is best near 42°, and with drag on a golf ball the optimum falls to the low 30s and depends on spin.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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What angle gives the longest throw?

Without air drag, 45° maximizes projectile range; with drag, the real optimum is nearer 30–40°. Drag punishes time spent moving fast through air, favouring flatter launches.

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