Projectile Motion Calculator
Estimate the ideal trajectory of a projectile launched at a chosen speed and angle. The calculator reports flight time, horizontal range and peak height under constant gravity.
How to use this calculator
- Enter launch speed, angle from 0° to 90°, starting height and the local gravitational acceleration.
- Check the labels and units before applying the result to a real task.
- Change one input at a time when comparing scenarios.
Formula and method
vₓ=v cosθ; vᵧ=v sinθ; t=(vᵧ+√(vᵧ²+2gh))/g; x=vₓt
- vₓ=v cosθ; vᵧ=v sinθ; t=(vᵧ+√(vᵧ²+2gh))/g; x=vₓt
- Air resistance, wind, spin, launcher mechanics and uneven landing ground are ignored. Use this for learning and rough estimates, not safety-critical design.
Worked examples
Worked example
Launch at 20 m/s at 45° from ground level with gravity 9.81 m/s².
Ignoring drag, flight time is about 2.88 seconds, horizontal range about 40.8 metres, and peak height about 10.2 metres.
Ignoring drag, flight time is about 2.88 seconds, horizontal range about 40.8 metres, and peak height about 10.2 metres.
Understanding the result
Estimate the ideal trajectory of a projectile launched at a chosen speed and angle. The calculator reports flight time, horizontal range and peak height under constant gravity.
Air resistance, wind, spin, launcher mechanics and uneven landing ground are ignored. Use this for learning and rough estimates, not safety-critical design.
Important notes
Air resistance, wind, spin, launcher mechanics and uneven landing ground are ignored. Use this for learning and rough estimates, not safety-critical design.
Displayed values are rounded for readability; retain appropriate precision when continuing a calculation.
Frequently asked questions
Why does the launch angle affect range?
The angle splits initial velocity into horizontal and vertical components. Those components affect horizontal travel speed and time aloft.
Does the tool include air resistance?
No. It uses the ideal constant-gravity equations and will differ from many real-world trajectories, particularly for light or fast objects.
Can the projectile start above ground level?
Yes. Enter a non-negative initial height; the flight-time calculation includes that height before impact.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.