Peak Height Calculator

Calculate the maximum height reached by a projectile at a specific time during its flight

Input Parameters

Calculation Results

Peak Height Result

0.00 m

Calculation Formula

h_peak = v₀ × t × sin(θ) - ½ × g × t²

Where:
h_peak = peak height
v₀ = initial velocity
t = time of flight
θ = launch angle
g = acceleration due to gravity (9.81 m/s²)

Peak Height Calculator Calculator Usage Guide

Learn how to use the Peak Height Calculator and understand the physics behind projectile motion

How to Use This Calculator

  1. Enter the initial velocity of the projectile in meters per second (m/s)
  2. Set the launch angle in degrees (0-90 degrees from horizontal)
  3. Specify the time of flight at which you want to calculate the peak height
  4. Click the "Calculate" button to compute the peak height
  5. The calculator will display the height in meters and show the formula used

Understanding Projectile Motion

This calculator works based on the principles of projectile motion, where an object moves in a parabolic path under the influence of gravity.

The peak height of a projectile occurs at a specific time during its flight, which can be calculated as:

t_peak = v₀ × sin(θ) / g

Where:

  • t_peak = time to reach peak height
  • v₀ = initial velocity
  • θ = launch angle
  • g = acceleration due to gravity (9.81 m/s²)

The formula used in this calculator to determine peak height at a specific time t is:

h_peak = v₀ × t × sin(θ) - ½ × g × t²

Practical Applications

This calculator can be used in various real-world scenarios:

  • Calculating the height of a ball thrown into the air
  • Determining the height of a rocket at a specific time
  • Analyzing the trajectory of various projectiles in sports
  • Engineering applications in ballistics and aerospace

Tip: For the most accurate results, make sure the time of flight you enter is after the projectile has reached its peak height.