How is projectile motion calculated?

It separately analyzes horizontal (constant velocity) and vertical (constant acceleration) motion, then combines them for range, height, and flight time.

What launch angle maximizes range?

On level ground with no air resistance, 45 degrees maximizes horizontal range.

Does this account for air resistance?

No — standard formulas assume no air resistance, a reasonable approximation for many scenarios.

Projectile Motion Calculator - CalculatorLabs.net

Projectile Motion Calculator

Projectile motion describes anything launched into the air and left to travel under gravity alone — a thrown ball, a cannonball, or a fired arrow.

Initial Speed (m/s)

Launch Angle (°)

Gravity (m/s²)

Instant Result

Range -

Max Height -

Time of Flight -

What Is a Projectile Motion Calculator?

Projectile motion describes anything launched into the air and left to travel under gravity alone — a thrown ball, a cannonball, or a fired arrow. This calculator finds how far it travels (range), how high it goes, and how long it stays in the air, from the launch speed and angle.

How to Use This Projectile Motion Calculator

Enter the initial launch speed in meters per second.
Enter the launch angle above the horizontal, in degrees.
Leave gravity at 9.81 for Earth, or adjust it for another planet.
Click Calculate to get the range, maximum height, and time of flight.

Formula

Range = (v₀² × sin(2θ)) / g
Max Height = (v₀² × sin²θ) / (2g)
Time of Flight = (2v₀ × sinθ) / g

Worked Example

A ball is launched at 20 m/s at a 45° angle. Range = (20² × sin(90°))/9.81 ≈ 40.77 m. Max Height = (20² × sin²(45°))/(2×9.81) ≈ 10.19 m. Time of Flight = (2×20×sin(45°))/9.81 ≈ 2.88 s.