Math & learning

Projectile motion calculator

Explore range, flight time and height for an ideal flight under constant gravity.

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  • Calculated on your device

01 / Your launch conditions

m/s

From 0 to 1,000 metres per second.

degrees

0° is horizontal; 90° is straight up.

m

From 0 to 100,000 metres.

m/s²

Use your problem’s value, such as 9.8. Allowed: 0.001–100.

One model, consistent units. Enter speed in metres per second and height in metres. The object lands on the horizontal ground at y = 0.

This educational model assumes constant gravity and no air resistance. It does not model wind, drag or powered flight. It is not a real-world trajectory prediction.

02 / Your results

40.789 mHorizontal range to ground2.884 s in flight
10.197 mMaximum height above ground10.197 m above the launch point
  • Time to highest point1.442 s
  • Speed at ground20 m/s
  • Impact angle from horizontal-45°
Position during flight (approximate)
Time (s)Distance (m)Height (m)
000
0.4816.7985.665
0.96113.5969.064
1.44220.39410.197
1.92327.1929.064
2.40333.9915.665
2.88440.7890

Height is measured above the ground; a negative impact angle points downward. Results are rounded for display.

How the calculation works

Split launch speed into horizontal v cos θ and vertical v sin θ components. The model uses x(t) = v cos θ × t and y(t) = h₀ + v sin θ × t − ½gt², ending at ground level y = 0. It assumes constant gravity and no air resistance.

Try an example

At 20 m/s and 45°, starting at ground level with g = 9.80665 m/s², the ideal flight lasts about 2.88 seconds, travels 40.79 m and reaches 10.20 m above the ground.

How to use this calculator

  1. Enter launch speed in metres per second and an angle from 0° to 90° measured above the horizontal.
  2. Enter the starting height above the landing ground in metres and a positive gravitational acceleration in m/s². Keep all inputs in these SI units.
  3. Select Calculate trajectory. Review time to ground, horizontal range, maximum height above ground and the sample positions during flight.

Common questions

Does this include air resistance or wind?

No. This model uses constant downward gravity and no drag, wind or lift. It describes ideal introductory-physics motion, so real flights can differ from its numerical estimates.

Is maximum height measured from the launch point?

The maximum height is measured above the landing ground, where y = 0. The result also shows the additional rise above the starting height. Flight time ends when the object reaches that ground level.

Does a 45° launch always travel the farthest?

Only under the equal-launch-and-landing-height, fixed-speed, constant-gravity model without air resistance. A different starting height changes that condition. This tool calculates the chosen angle rather than finding an optimal one.

Further reading: OpenStax: projectile motion