Physics

Projectile Motion Calculator

Enter the launch speed, angle and height to get the horizontal range, peak height, time of flight and impact velocity. The trajectory is drawn to scale with the optimum-angle path for comparison.

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Solid line: your launch. Dashed line: the angle that gives the longest range from this height.

Time (s)DistanceHeightVertical speedSpeed

Runs entirely in your browser. Nothing is uploaded to any server.

What you can work out

Physics problems

Check textbook answers with every intermediate value.

Sports and games

See how angle changes a throw, kick or jump.

Other worlds

Compare the same launch on the Moon or Mars.

How to use the projectile calculator

  1. Set the launchEnter speed, angle and starting height with your units.
  2. Pick the gravityEarth by default, or the Moon, Mars, Venus, Jupiter or a custom value.
  3. Read the flightRange, peak, flight time, impact speed and a trajectory chart.

How projectile motion works

Without air resistance the horizontal and vertical motions are independent. The horizontal speed never changes, while gravity steadily reduces the upward speed, stops it at the peak and then accelerates the projectile downward.

This makes the path a parabola. Complementary angles such as 30 and 60 degrees give the same range when launching from ground level, but the higher angle flies longer and higher.

Horizontal

x = vx * t, constant speed.

Vertical

y = h + vy * t - g * t^2 / 2.

Peak

Reached at t = vy / g, where the vertical speed is zero.

Projectile motion FAQ

What formulas does the calculator use?

Horizontal velocity vx = v cos(angle) and vertical velocity vy = v sin(angle). Time of flight t = (vy + sqrt(vy^2 + 2gh)) / g, range = vx * t and maximum height = h + vy^2 / (2g).

Is 45 degrees always the best angle?

Only when launching and landing at the same height. From a raised launch point the best angle is lower: angle = atan(v / sqrt(v^2 + 2gh)). The calculator shows it for your inputs.

Does it include air resistance?

No. It is the classic drag-free model taught in physics classes. Real balls fall short of these figures, especially at high speed.

Can I launch downwards?

Yes. Use a negative angle (down to -90 degrees) for something thrown downward from a height.

What gravity value is used for Earth?

Standard gravity, 9.80665 m/s^2. Choose Custom to enter any other value.

Try other physics tools

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