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Projectile Motion Calculator

Projectile motion splits a launch into a constant horizontal speed and an accelerated vertical motion.

Calculated Result
40.7747 mm

Horizontal range

Horizontal range

40.7747 m

Maximum height

10.1937 m

Time of flight

2.8832 s

Impact speed

20 m/s

Horizontal velocity

14.1421 m/s

Vertical velocity

14.1421 m/s

Time to apex

1.4416 s

40.77 m — Range

Calculation Breakdown

  1. Velocity componentsvₓ = 20·cos 45° = 14.1421 m/s, v_y = 20·sin 45° = 14.1421 m/s
  2. Time of flightt = (v_y + √(v_y² + 2·g·h₀)) / gt=vy+vy2+2gh0gt = \dfrac{v_y + \sqrt{v_y^2 + 2gh_0}}{g}
  3. RangeR = vₓ · t = 40.7747 m

What Is the Projectile Motion Calculator?

A projectile motion calculator describes the curved path of an object launched into the air.

How Does the Projectile Motion Calculator Work?

It separates the motion into constant horizontal velocity and vertical motion under gravity.

Projectile Motion Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

R=vxt,H=h0+vy22gR = v_x t, \quad H = h_0 + \dfrac{v_y^2}{2g}

The horizontal range is the horizontal velocity times the flight time; the apex height adds the vertical rise to any launch height.

How to Use the Projectile Motion Calculator

  1. Enter the launch speed, angle, gravity and any launch height.

Step-by-Step Example Calculation

20 m/s at 45°

Input Values:

initialSpeed:20
angle:45
gravity:9.81
initialHeight:0
Worked Steps: It travels about 40.8 m, peaking at about 10.2 m.

Understanding Your Result

You get the range, maximum height, flight time and impact speed.

Factors That Affect the Result

  • Launch speed, angle, gravity and the starting height.

When Should You Use This Calculator?

  • Use it in physics, sports and ballistics to study trajectories.

Assumptions & Limitations

  • Ignores air resistance, wind and the curvature or rotation of the Earth.

Frequently Asked Questions

Calculation Accuracy & Reference Note

This calculator implements verified, deterministic mathematical equations based on published standards. Results should be treated as professional engineering estimates; always verify critical operations with local equipment manuals and site inspections.

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