Projectile Motion Calculator

Estimate flight time, range, and max height from launch speed and angle.

Scratchpad (not saved)

Save to create a persistent, shareable workspace.

What This Calculator Does

Estimate flight time, range, and max height from launch speed and angle.

It combines Launch Velocity, Launch Angle, Gravity to estimate Range, Flight Time, Max Height.

Formula & Method

Core equations:

t_{flight}=\frac{2v_0\sin\theta}{g},\quad Range=\frac{v_0^2\sin2\theta}{g},\quad h_{max}=\frac{v_0^2\sin^2\theta}{2g}

Notation used in the formulas: $R$ = Range; $x_{1}$ = Launch Velocity; $x_{2}$ = Launch Angle; $x_{3}$ = Gravity.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Reference Book

University Physics with Modern Physics

Hugh D. Young and Roger A. Freedman · Pearson

A common undergraduate physics text covering mechanics, electricity, waves, energy, and introductory modern physics.

View Book

Inputs Used

Launch Velocity: Used directly in the calculation.
Launch Angle: Used directly in the calculation.
Gravity: Used directly in the calculation.

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