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Projectile Motion Calculator

Calculate range, maximum height and flight time of a projectile launched at an angle.

About Projectile Motion Calculator

Horizontal and vertical motion are independent: horizontal velocity stays constant while vertical motion is uniformly accelerated. Launching from a height extends flight time and shifts the optimal angle below 45 degrees. The 45-degree optimum only holds for launch and landing at the same height; from any elevation the best angle is lower.

Formula

Projectile Motion

Range = vₓ t, with t from solving h₀ + v_y t − ½ g t² = 0

vₓ
Horizontal velocity component, constant without drag
v_y
Initial vertical velocity component

Worked example

With the default values below, Projectile Motion Calculator returns Horizontal Range of 91.743. Change any input above and every figure here is recalculated in your browser.

Inputs used

Launch speedminimum 0 m/s
30 m/s
Launch angleaccepts 0–90 degrees
45 degrees
Launch heightminimum 0 m
0 m
Gravitational accelerationminimum 0.01 m/s2
9.81 m/s2

Results

Horizontal Range
91.743 m
Maximum Height
22.936 m
Time of Flight
4.325 s
Impact Speed
30.000 m/s
Angle That Maximises Range
45.0 degrees

Step by step

  1. 1Values used
  2. 2Projectile Motion
  3. 3Horizontal Range= 91.743 m
  4. 4Maximum Height= 22.936 m
  5. 5Time of Flight= 4.325 s
  6. 6Impact Speed= 30.000 m/s
  7. 7Angle That Maximises Range= 45.0 degrees

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Projectile Motion calculated?

Range = vₓ t, with t from solving h₀ + v_y t − ½ g t² = 0 Horizontal and vertical motion are independent: horizontal velocity stays constant while vertical motion is uniformly accelerated. Launching from a height extends flight time and shifts the optimal angle below 45 degrees.

Why does Projectile Motion matter?

The 45-degree optimum only holds for launch and landing at the same height; from any elevation the best angle is lower.

What values do I need to enter?

This calculator takes 4 inputs: Launch speed, Launch angle, Launch height, Gravitational acceleration. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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