What formulas does this use?

For launch and landing at the same height it uses time of flight t = 2·v₀·sin θ / g, maximum height h = (v₀·sin θ)² / (2g), and range R = v₀²·sin(2θ) / g. Velocity components are vₓ = v₀·cos θ and v_y = v₀·sin θ.

Which launch angle gives the greatest range?

On level ground with no air resistance, 45° gives the maximum horizontal range because sin(2θ) is largest at 2θ = 90°. Complementary angles such as 30° and 60° give the same range.

Is air resistance included?

No — this is the idealised no-drag model commonly taught in physics. It also assumes the projectile lands at the same height it was launched from.

What are the velocity components for?

vₓ = v₀·cos θ is the constant horizontal velocity, and v_y = v₀·sin θ is the initial vertical velocity that gravity then slows and reverses. Splitting the launch velocity this way is the key to solving every other quantity.

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

Range depends on sin(2θ), and sin(60°) equals sin(120°). Since 2 × 30° = 60° and 2 × 60° = 120°, both angles share the same sin(2θ) and therefore the same range, though the 60° shot flies higher and lasts longer.

How do I model another planet?

Change the gravity value. Use about 1.62 m/s² for the Moon or 3.72 m/s² for Mars; lower gravity means longer flight times, higher peaks and greater range for the same launch.

Is anything uploaded?

No — everything runs locally in your browser and nothing is sent to a server.

Projectile Motion Calculator

Projectile motion calculator

Enter a launch speed and angle and this tool computes the full idealised trajectory: time of flight, maximum height, horizontal range, and the horizontal and vertical velocity components. It is built for physics coursework and quick checks of the classic no-air-resistance projectile model.

How it works

The launch velocity is split into components, then the standard equations (for launch and landing at the same height) give the rest:

vₓ = v₀·cos θ            v_y = v₀·sin θ
time of flight  t = 2·v₀·sin θ ÷ g
maximum height  h = (v₀·sin θ)² ÷ (2g)
range           R = v₀²·sin(2θ) ÷ g

Gravity g defaults to Earth’s 9.81 m/s² and is editable. Range peaks at a 45° launch angle.

Example

Launch speed 20 m/s at 45°, g = 9.81:

v_y = 20·sin45° = 14.14 m/s; vₓ = 20·cos45° = 14.14 m/s
Time of flight: 2·14.14 ÷ 9.81 ≈ 2.88 s
Max height: 14.14² ÷ (2·9.81) ≈ 10.19 m
Range: 20²·sin90° ÷ 9.81 ≈ 40.77 m

Angle	Range (20 m/s)	Max height
30°	35.31 m	5.10 m
45°	40.77 m	10.19 m
60°	35.31 m	15.29 m

Everything runs locally in your browser — nothing is uploaded.