Projectile Height Calculator Formula

Understand the math behind the projectile height calculator. Each variable explained with a worked example.

Use the Projectile Height Calculator

Formulas Used

Maximum Height

max_height = pow(velocity, 2) * pow(sin(angle_rad), 2) / (2 * gravity)

Time to Peak

time_to_peak = velocity * sin(angle_rad) / gravity

Variables

VariableDescriptionDefault
velocityLaunch Velocity(m/s)30
angleLaunch Angle(degrees)60
gravityGravitational Acceleration(m/s²)9.81
angle_radDerived value= angle * pi / 180calculated

How It Works

Maximum Projectile Height

The peak altitude of a projectile depends on the vertical component of its launch velocity.

Formula

H = v² * sin²(theta) / (2 * g)

The time to reach the peak is t_peak = v * sin(theta) / g.

Worked Example

A ball is launched at 30 m/s at 60 degrees.

velocity = 30angle = 60gravity = 9.81
  1. 01H = v² * sin²(theta) / (2g)
  2. 02H = 900 * sin²(60°) / (2 * 9.81)
  3. 03H = 900 * 0.75 / 19.62
  4. 04H = 675 / 19.62
  5. 05H = 34.40 m

Ready to run the numbers?

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