Projectile Height Calculator Formula
Understand the math behind the projectile height calculator. Each variable explained with a worked example.
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) / gravityVariables
| Variable | Description | Default |
|---|---|---|
velocity | Launch Velocity(m/s) | 30 |
angle | Launch Angle(degrees) | 60 |
gravity | Gravitational Acceleration(m/s²) | 9.81 |
angle_rad | Derived value= angle * pi / 180 | calculated |
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
- 01H = v² * sin²(theta) / (2g)
- 02H = 900 * sin²(60°) / (2 * 9.81)
- 03H = 900 * 0.75 / 19.62
- 04H = 675 / 19.62
- 05H = 34.40 m
Frequently Asked Questions
At what angle is maximum height achieved?
A 90-degree launch (straight up) gives the greatest height, since all velocity goes into the vertical component.
How long does the full flight take?
Total flight time is twice the time to peak: T = 2 * v * sin(theta) / g, assuming launch and landing heights are the same.
Does launch height affect this formula?
This formula assumes launch from ground level. If launched from a height h0, the maximum altitude above the ground is H + h0.
Ready to run the numbers?
Open Projectile Height Calculator