Projectile Motion Calculator

Range, max height, time of flight from launch speed and angle (level ground, no air drag).

Inputs

Result

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General calculation reads

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How to use this calculator

  • Enter launch speed and angle.
  • Read range + max height + flight time.

About this calculator

Projectile motion (no air resistance) on level ground: horizontal velocity constant; vertical velocity changes with gravity. Max range at θ = 45°. Symmetric launch ↔ landing. Range = v₀² sin(2θ)/g. Real projectiles (baseballs, bullets, golf balls) deviate due to air drag — drag scales with v², so high-speed projectiles fall short of vacuum prediction.

Frequently asked

Why 45° max range?+
Range = v₀² sin(2θ)/g. sin(2θ) maxes at 2θ = 90°, so θ = 45°.
What about air resistance?+
Drag is significant at high speeds (>30 m/s). Real projectiles peak around 30-40°, not 45°.
Different launch and landing height?+
This calc assumes level ground. With Δh: solve quadratic in t. More complex.
Trajectory shape?+
Parabola — symmetric around peak. Apex at half-flight time.
Real-world projectile design?+
Mortars: ~45°. Artillery: 35-45° depending on range. Football kick-off: ~55° to give air time.

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