Projectile Motion Calculator
Find a projectile's range, maximum height and flight time from its launch speed, angle and height.
Range (horizontal distance)
40.7886 m (133.821 ft)
- Maximum height
- 10.1972 m (33.4553 ft)
- Flight time
- 2.88419 s
- Time to the top
- 1.4421 s
- Impact speed
- 20 m/s (72 km/h, 44.7387 mph)
- Impact angle (below level)
- 45°
Lands back at ground level (height 0); ignores air resistance.
Show the work
Sideways part of the speed
vx = v × cos θ
20 × cos 45° = 14.1421 m/s
Upward part of the speed
vy = v × sin θ
20 × sin 45° = 14.1421 m/s
Flight time
t = (vy + √(vy to the power of 2 + 2gh0)) ÷ g
(14.1421 + √(14.1421 to the power of 2 + 2 × 9.80665 × 0)) ÷ 9.80665 = 2.88419 s
Range = sideways speed × time
R = vx × t
14.1421 × 2.88419 = 40.7886 m (133.821 ft)
How it works
vₓ = v cos θ, vᵧ = v sin θ; flight time t = (vᵧ + √(vᵧ² + 2gh₀)) ÷ g; range = vₓ·t; max height = h₀ + vᵧ² ÷ 2g
Questions
- How does the projectile motion calculator work?
- vₓ = v cos θ, vᵧ = v sin θ; flight time t = (vᵧ + √(vᵧ² + 2gh₀)) ÷ g; range = vₓ·t; max height = h₀ + vᵧ² ÷ 2g.
- What do I need to enter?
- Launch speed, Launch speed unit, Launch angle, Launch height, Gravity, Custom gravity. Optional fields can be left blank.
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