Projectile Motion Calculator

Find how far and how high something goes when launched at an angle, ignoring air resistance.

Fractions and decimals both work.
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Range
Maximum height
Time of flight
Velocity components
Impact speed
Work

Saved Calculations

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Projectile Motion Equations

vx = v cos θ   vy = v sin θ   Max height = h₀ + vy² ÷ 2g
Flight time t = (vy + √(vy² + 2gh₀)) ÷ g   Range = vx × t (= v² sin 2θ ÷ g from the ground)

Worked Example

Tips

From level ground, 45° gives the longest range. Air resistance shortens real ranges, a lot for light or fast objects.