BYTETOOLS

Projectile Motion Calculator

Compute time of flight, maximum height, range and impact velocity for a projectile, and see the trajectory plotted on an interactive canvas graph.

2.884 s
Time of flight
10.197 m
Max height
40.789 m
Range
20 m/s
Impact speed

Trajectory

vₓ = v₀cos θ = 14.142 m/s, v_y = v₀sin θ = 14.142 m/s. Flight time solves h₀ + v_y t − ½gt² = 0; range = vₓ × t. Impact at 45° below horizontal. Air resistance is ignored (vacuum model).

What is the Projectile Motion Calculator?

The ByteTools Projectile Motion Calculator takes an initial speed, launch angle and optional launch height and computes everything about the flight: time of flight, maximum height, horizontal range, and the impact speed and angle.

  • Time of flight, max height, range, impact speed and angle
  • Launch height supported (cliff or table launches)
  • Live canvas trajectory plot with axes and ground line
  • Uses standard gravity g = 9.80665 m/s², selectable for Moon and Mars
  • Speed input in m/s, km/h, mph or ft/s
  • 100% private — runs entirely in your browser

How to use the Projectile Motion Calculator

  1. 1

    Enter the initial speed and choose m/s, km/h, mph or ft/s.

  2. 2

    Set the launch angle in degrees and an optional launch height.

  3. 3

    Read time of flight, max height, range and impact velocity.

  4. 4

    Watch the trajectory redraw on the graph as you change inputs.

  5. 5

    Copy the results or try 45° to see the maximum-range case.

About the Projectile Motion Calculator

The ByteTools Projectile Motion Calculator takes an initial speed, launch angle and optional launch height and computes everything about the flight: time of flight, maximum height, horizontal range, and the impact speed and angle. It uses the standard kinematic equations with g = 9.80665 m/s² (standard gravity) and no air resistance.

The trajectory parabola is drawn live on a canvas chart with axes, tick labels and a ground line, so you can see how changing the angle or speed reshapes the flight path. The classic result that 45° maximises range on flat ground — and slightly less when launching from a height — is easy to verify interactively.

Because air drag is ignored, real projectiles (especially fast or light ones) fall shorter than the ideal parabola; results are exact for the vacuum model taught in physics courses. Everything runs 100% locally in your browser with nothing uploaded.

Frequently asked questions

How do you calculate the range of a projectile?

On flat ground with no air resistance, range R = v₀² × sin(2θ) ÷ g. At 20 m/s and 45°, R = 400 × 1 ÷ 9.80665 ≈ 40.8 m. With a launch height the tool solves the full quadratic for flight time first, then multiplies by the horizontal velocity.

What angle gives the maximum range?

45° on level ground, because sin(2θ) peaks at 2θ = 90°. Launching from above the landing level shifts the optimum slightly below 45°, and launching uphill shifts it above. Try it in the calculator — the plotted trajectories make the effect obvious.

How do you find the maximum height?

Maximum height above the launch point is h = (v₀ sin θ)² ÷ (2g) — the point where vertical velocity reaches zero. For 20 m/s at 45°, that is 14.14² ÷ 19.61 ≈ 10.2 m, plus any launch height you started with.

Does this calculator include air resistance?

No. It uses the ideal vacuum model from introductory physics, which is accurate for dense, slow objects over short distances but overestimates range for fast or light projectiles like golf balls and bullets. Real trajectories with drag require numerical simulation.

What is the impact velocity?

It is the speed at landing, combining horizontal velocity (unchanged) and final vertical velocity: v = √(vₓ² + v_y²). Launched and landing at the same height, impact speed equals launch speed; from a raised platform it is higher, per energy conservation v = √(v₀² + 2gh).

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