MultiSwitch MultiSwitch
SEARCH
SEARCH
Converters Tools Currency Feedback

Projectile Motion Calculator

Calculate range, max height, and flight time

Enter the launch speed, angle, and starting height to see the projectile's flight path.

—
Horizontal range
Max height
Flight time
How this works: standard projectile motion equations with g = 9.81 m/s², ignoring air resistance. Splits the launch velocity into horizontal and vertical components to solve for range, peak height, and time of flight.

How projectile motion works

Once something is launched (a ball, a stone, a stream of water), and if you ignore air resistance, only gravity acts on it. That splits its motion into two independent parts:

  • Horizontal: constant speed, v·cos θ, because nothing pushes it sideways
  • Vertical: starts at v·sin θ and decreases at g = 9.81 m/s² every second, rising, stopping at the peak, then falling

Combining the two gives the familiar parabolic arc. The calculator solves these equations to find how far, how high and how long the projectile flies.

The key equations (launch from ground level)

  • Range R = v² · sin(2θ) ÷ g
  • Maximum height H = v² · sin²θ ÷ (2g)
  • Flight time T = 2v · sin θ ÷ g

With a starting height above the ground, the projectile falls further before landing. The calculator handles that by solving the full vertical equation for when height returns to zero.

Worked example

A ball launched at 20 m/s and 45° from ground level:

  • Range: 400 × sin 90° ÷ 9.81 = 40.8 m
  • Max height: 400 × 0.5 ÷ 19.62 = 10.2 m
  • Flight time: 2 × 14.14 ÷ 9.81 = 2.88 s

FAQ

Is 45° always the best angle for distance?

Only when launch and landing heights are the same and there's no air resistance. Launching from a height, such as a shot put or a cliff, makes a lower angle go further. Real balls also do better below 45° because of drag.

Why do 30° and 60° give the same range?

Range depends on sin(2θ), and sin 60° = sin 120°. Any two angles that add up to 90° land in the same spot on level ground. The steeper one goes higher and stays in the air longer.

How much does air resistance change things?

A lot for light or fast objects. A thrown baseball or golf ball can fall well short of the vacuum prediction. These results are an idealised upper bound, which is ideal for homework and intuition but not for ballistics.

Can I use this on other planets?

These results use Earth's gravity (9.81 m/s²). On the Moon (1.62 m/s²) the same throw would go about six times further.

Related tools

Free Fall Speed, Distance & Time Force & Torque Kinetic & Potential Energy Geometry Scientific Calculator